Ohata et al.
Progress in Earth and Planetary Science(2022) 9:23
https://doi.org/10.1186/s40645-022-00481-8

Progress in Earth andPlanetary Science

Open Access

RESEARCH ARTICLE

Upper and lower plane bed definitions
revisedKoji Ohata1* , Hajime Naruse1 and Norihiro Izumi2

Abstract
Sedimentary structures in ancient deposits are clues to reconstruct past geohazards. While parallel lamination formedby plane beds is one of the most common sedimentary structures in event deposits such as turbidites, the formative
conditions for plane beds remain unclear. In the literature, two types of plane beds (upper and lower plane beds) exist
and are supposed to develop under different shear stresses, particle sizes, and flow regimes. Here, we present newphase diagrams based on the compilation of existing data regarding formative hydraulic conditions for plane beds
to clarify the formation processes associated with the two types of plane beds. The diagrams indicated that the data
form two separate populations and the gap between them corresponds to the threshold condition of the particle
entrainment into suspension. Lower plane beds form when sediment particles move only as bed load. This phasespace can be discerned from fine sand to gravel and differs from the conventional view in which the formation of
the lower plane bed is limited to grain sizes above 0.7 mm. In addition, our phase diagrams suggest that upper plane
beds appear under conditions of the active suspended load. Our analyses demonstrate that the suspended load
contributes to the formation of plane beds, whereas other mechanisms can also produce fine-grained plane beds inflows with low bed shear stress. Thus, the results of this study suggest that the existing interpretations on fine-grained
parallel lamination such as Bouma’s ­Td division need to be reconsidered. The bedform phase diagrams newly established in this study will be useful for estimating the flow conditions from the geologic records of event beds.
Keywords: Plane bed, Suspended load, Bed load, Bedform
1 Introduction
1.1 General introduction of bedforms

Sand grains on Earth surfaces are carried from mountains
to deep seas by flows, e.g., river, winds, tidal flows, andsediment-laden gravity currents. The transport of thesesediments is not only one of the primary processes of the
Earth’s surface material circulation, including the carbon
cycle (Schlünz and Schneider 2000; Galy et al. 2007), butalso a cause of severe geohazards such as landslides ordebris flows. Such past geohazards can be reconstructedfrom the characteristics of their deposits (e.g., Mitra et al.
2021), suggesting the disaster risk of each region.
*Correspondence: ohata.koji.24z@gmail.com
1
Division of Earth and Planetary Sciences, Graduate School of Science,
Kyoto University, Kitashirakawaoiwake‑cho, Sakyo‑ku, Kyoto‑shi,
Kyoto 606‑8502, Japan
Full list of author information is available at the end of the article

Interaction between flows and solid particles during sediment transport results in various morphologies
including bedforms that display wavy or flat topographies. Bedforms have been found ubiquitously on sediment beds; for instance, in open-channel flows (e.g.,
Collinson 1970; Ma et al. 2017; Galeazzi et al. 2018) andoscillatory flows (e.g., Miller and Komar 1980; Masselink
et al. 2007; Wu and Parsons 2019).
In the past decades, numerous laboratory experiments(e.g., Gilbert 1914; Guy et al. 1966; Southard 1991; Dumas
et al. 2005; Perillo et al. 2014; Bradley and Venditti 2019)and field observations (e.g., Colby and Hembree 1955;
van den Berg 1987; Cisneros et al. 2020) were conductedto obtain empirical relationships between flows and bedforms. Bedform phase diagrams have been used to understand the formation of bedforms in response to flow
behavior (e.g., Chabert and Chauvin 1963; Southard and© The Author(s) 2022. Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which
permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to theoriginal author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images orother third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line
to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory
regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of thislicence, visit http://​creat​iveco​mmons.​org/​licen​ses/​by/4.​0/.

Ohata et al. Progress in Earth and Planetary Science(2022) 9:23

Boguchwal 1990). Recently, Ohata et al. (2017) proposed
bedform phase diagrams in three-dimensional parametric space, and their diagrams successfully characterized
paleo-flow conditions from sedimentary structures.
1.2 Review of plane beds

Plane beds are bedforms that develop in various environments such as alluvial riverbeds (e.g., Hauer et al.
2019) and beach faces (e.g., Vaucher et al. 2018; Vaucher
and Dashtgard 2021). The plane bed phase is characterized by nearly flat topography or low-relief bed waves.
Flume experiments have explained that the migrationof low-relief bed waves over plane beds results in planar
lamination with a few millimeters in thick (Paola et al.
1989, Bridge and Best 1997). Planar lamination in sandstone beds (Fig. 1) is ubiquitously found in fluvial (e.g.,
Umazano et al. 2012; Mazumder and Van Kranendonk
2013), estuaries (e.g., Hori et al. 2001), tidal flat (e.g.,
Chakraborty et al. 2003), shoreface (e.g., Kikuchi 2018),
and submarine fan environments (e.g., Eggenhuisen et al.
2011; Jobe et al. 2012). For example, deposits from turbidity currents (i.e., turbidites) in submarine environments exhibit succession of sedimentary structures called
Bouma sequence, in which parallel lamination is observable in T
­ b and ­Td divisions (Bouma 1962).

Fig. 1 Photographs showing planar lamination in sandy deposits. A
Snapshot of a laboratory experiment conducted at Kyoto University.
Flow is from right to left. Two types of sands (D50 = 0.12 mm and0.53 mm) were used. B Field photograph showing a turbidite
sandstone in the Aoshima Formation of the Miocene Miyazaki Group,Japan

Page 2 of 13

Plane beds were initially referred to as “the smoothphase of bedforms” (Owens 1908; Gilbert 1914). Later,
Simons et al. (1961) used the term “plane” to avoid confusion with the hydraulically smooth phase of flows. Owens(1908) and Strahan et al. (1908) observed that the bed
state changes from ripples to the smooth phase of bedform (i.e., plane bed) and then to antidunes with increasing flow velocity. In addition, the plane bed phase also
appears under the condition when the bed shear stressis lower than that forming ripples or dunes (e.g., Simons
et al. 1961; Southard 1971). Thus, previous studies haverecognized that there are two conditions of plane bed
formation and they are separated by formation conditions of ripples or dunes.
However, the formative process and conditions forphase transition of plane beds remain unclear. It is known
that the plane bed is formed under two different hydraulic conditions, but the reason why the formation conditions are divided into two regions is not well understood.
In previous studies, the two types of plane beds have beenclassified depending on the (1) sediment motion (Simons
et al. 1961; Simons and Richardson 1962), (2) criticality
of Froude number (Venditti 2013; Dey 2014), and (3) sizeof bed material and flow intensity (Allen 1968; Southard1971).
Simons et al. (1961) recognized two conditions ofplane bed in their flume experiments using the medium
sand—plane beds with and without sediment motion. On
the basis of the flume experiments with the two types of
medium sand (D = 0.28 mm and 0.45 mm), Simons et al.
(1961) and Simons and Richardson (1961, 1962) classified
alluvial flows based on bedforms into three regimes—alower flow regime (plane beds without sediment movement, ripples, dunes with ripples superposed, and dunes),a transition zone (washed-out dunes), and an upper flow
regime (plane beds with sediment movement, standing
waves, antidunes, and chutes-and-pools). Simons et al.
(1961) and Simons and Richardson (1962) recognized
this sequence of flow regimes with the increase in flow
intensity. The definition of Simons et al. (1961) has been
employed in the analyses of bedforms (van Rijn 1984b;
Julien and Raslan 1998). For example, the bedform stability diagram proposed by Colombini and Stocchino (2008)
has described plane bed phases as plane beds without
sediment motion and upper plane bed. Bradley and Venditti (2019) cited the phase diagram by Colombini andStocchino (2008) and described the phase of plane beds
without sediment motion as lower plane beds.
Although Simons et al. (1961) noted that flows change
from the lower to upper flow regimes at a Froude number (Fr) less than unity, Venditti (2013) and Dey (2014)
stated that lower and upper flow regimes are consistent
with Froude-subcritical (Fr < 1) and Froude-supercriticalOhata et al. Progress in Earth and Planetary Science(2022) 9:23

flow regimes (Fr > 1), respectively. In other words, following the definition by Venditti (2013) and Dey (2014),
plane bed in the lower regime is generally interpreted toexist at Fr < 1, and plane bed in the upper regime is at or
above Fr = 1.
Allen (1968) and Southard (1971) described bedform phase diagrams based on a compilation of observational data (Fig. 2). In their phase diagrams, there is astable plane bed region where coarse sediment (median
diameter D50 > 0.6–0.7 mm) is transported at low flow
velocities (< 0.5 m/s). Allen (1968) termed this bed state
as a lower-phase plane bed. That is, there are two typesof plane beds with sediment movement, namely lower
plane beds with low flow intensities on coarse sedimentand upper plane beds with high flow intensities on finesediment. Liu (1957) and Bogárdi (1961) also reported
a region of flow conditions in which sediment motion
occurred but ripples or other bedforms did not appear.
In summary, researchers have proposed various definitions and formation conditions of the two types of plane
beds: (1) sediment motion (Simons et al. 1961; Simons
and Richardson 1962), (2) criticality of Froude number(Venditti 2013; Dey 2014), and (3) size of bed material
and flow intensity (Allen 1968; Southard 1971).
In this paper, we compiled a total of 935 sets of existing data from the literature. The dataset indicates that
two separate regimes of plane bed exist and the boundary
between the two plane bed regimes matches the threshold condition for the particle entrainment into suspension (Niño et al. 2003) or sheet flow (traction carpet; Gao2008). We compiled data pertaining to plane beds in unidirectional open-channel flows and plotted them using
dimensionless parameters as axes without any a priori

Fig. 2 Bedform phase diagram for unidirectional currents digitized
after Southard and Boguchwal (1990) for a flow depth of 0.25–0.40 m.
The mean velocity U10, flow depth H10, and grain size D10 denote
10 °C equivalent values

Page 3 of 13

assumption of types of plane beds. Based on this data
analysis, we recognized that the upper plane beds arealways accompanied by suspension or sheet flow.

2 Methods
2.1 Data sources

We compiled from the literature a total of 935 sets ofdata pertaining to plane beds to investigate the plane
bed regimes. The dataset consisted of 890 sets of laboratory data and 45 sets of field data (Tables 1 and 2). A
wide range of hydraulic conditions and sediment calibers
are encompassed in the datasets. The median sediment
diameter ( D50) ranges from 1.1 × ­10–2 to 44.3 mm, theflow depth (h) ranges from 1.2 × ­10–3 to 2.74 m, and theflow velocity (U ) ranges from 0.058 to 2.38 m/s. To compare the transport mode of plane bed formation with thethreshold conditions of sediment motion and the initiation of suspension, we classified the data with sediment
movement into three types based on the suspended sediment concentration (Cs), as follows: (a) The suspended
sediment concentration was measured (hereafter referred
to as data Cs > 0), (b) the suspended sediment concentration was recorded as zero (hereafter referred to as data Cs= 0), and (c) the suspended sediment concentration was
not available (hereafter referred to as data no Cs).
2.2 Dimensionless parameters for morphodynamic
conditionsFirst, we focused on the grain size and the sedimenttransport mechanism (i.e., no sediment movement,
bed load, and suspended load) as controls on plane bed
regimes. Bedform phases were expressed in a space ofdimensionless parameters that reflected the properties offlows and sediment particles (e.g., van den Berg and vanGelder 1993; Ohata et al. 2017). We employed the following dimensionless parameters to represent hydraulic conditions and sediment properties: the particle Reynolds
number (Rep), Shields number (τ∗), and the suspension
index (u∗ /ws).
The particle Reynolds number (Rep) is defined as (Garcia 2000):√
RgD50 D50
(1)
Rep =
ν
where R represents the submerged specific density of thesediment, g denotes the gravitational acceleration, andν denotes the kinematic viscosity of the fluid. The submerged specific density is defined as R = (ρs − ρf )/ρf ,where ρs and ρf represent the sediment and fluid densities, respectively. The kinematic viscosity (ν) was
assumed to be a function of temperature according to
the relationship for water (van den Berg and van Gelder1993):

Ohata et al. Progress in Earth and Planetary Science(2022) 9:23

Page 4 of 13

Table 1 Summary of flume data used for the analysis
Reference# of points

Particlediameter D50[mm]

Flow depth h[m]Flow velocity U[m/s]Particle
Reynolds
number ­Rep

Shields numberτ*

Suspension
index
u*/ws

FroudenumberFr

Barton and Lin(1955)*

11

0.18

0.13–0.24

0.74–1.09

9.74–11.1

0.47–1.13

1.7–2.88

0.52–0.87

Bridge and Best
(1988)

2

0.3

0.1–0.1

0.9–0.98

19.85–21.86

1.29–1.38

1.98–2.02

0.91–0.99

Brooks (1955)*

8

0.09–0.15

0.06–0.09

0.6–0.65

3.7–8.63

0.43–0.77

1.98–5.03

0.71–0.81

Cao (1985)

84

11.5–44.3

0.02–0.26

0.31–1.64

4594–38,250

0.007–0.20

0.07–0.39

0.43–1.75

Chyn (1935)*

2

0.79

0.05–0.06

0.37–0.4

92.99–94.46

0.051–0.057

0.24–0.25

0.51

Costello (1974)*

8

0.6–0.79

0.15–0.16

0.32–0.39

72.28–103.48

0.019–0.055

0.14–0.26

0.26–0.31

E. Pakistan (1966,
68–69)*

4

0.25–0.33

0.15–0.3

0.19–0.86

17.66–28.31

0.019–0.46

0.21–1.27

0.11–0.71

Fukuoka et al.
(1982)

18

0.19–1.6

0.02–0.07

0.35–1.19

10.52–256.97

0.037–0.76

0.18–1.3

0.61–2.12

Gee (1975)

3

0.31

0.08

0.94–1.02

21.73–23.12

0.47–0.55

1.16–1.21

1.06–1.17

0.31–4.94

0.02–0.12

0.49–1.42

21.39–1393.27

0.062–0.90

0.22–1.42

0.79–2.08

Gilbert (1914)*

250

Guy et al. (1966)

48

0.19–0.93

0.09–0.31

0.2–1.64

9.88–121.18

0.022–1.50

0.16–2.32

0.14–1.63

Jopling andForbes (1979)

4

0.05

0.04–0.09

0.06–0.73

1.43–1.47

0.94–4.60

13.1–28.81

0.06–1.11

Jorissen (1938)*

9

0.6–0.91

0.02–0.09

0.26–0.44

57.79–118.26

0.045–0.097

0.22–0.34

0.43–0.59

Julien and Raslan(1998)

18

0.2–0.6

0.04–0.14

0.35–0.79

9.26–51.22

0.13–1.0

0.43–2.87

0.47–0.92

Kalinske and Hsia
(1945)

1

0.01

0.16

0.83

0.15

8

347.790.67

Kennedy (1961)

12

0.23–0.55

0.02–0.11

0.61–1.05

15.68–60.75

0.36–0.62

0.81–1.57

0.73–2.04

Kennedy and
Brooks (1963)

4

0.14

0.07–0.08

0.6–0.67

7.61–7.68

0.54–0.76

2.36–2.81

0.69–0.82

Kuhnle and Wren(2009)

2

0.5

0.17–0.18

0.68

44.89–45.3

0.41–0.64

0.81–1.02

0.51–0.53

Laursen (1958)

1

0.11

0.14

1.02

4.94

0.65

3.64

0.86

Mutter (1971)*

5

0.26

0.01–0.04

0.29–0.79

18.98–20.07

0.21–0.70

0.82–1.51

0.46–1.91

Neill (1967)**

30

5–20

0.03–0.18

0.5–1.13

1348.6–10,896.09 0.023–0.059

0.13–0.21

0.42–1.52

Nomicos (1956)*

12

0.09–0.15

0.07–0.08

0.56–0.81

3.89–8.93

1.96–4.52

0.66–0.95

0.42–0.83

Nordin (1976)

7

0.25–0.25

0.33–0.6

1.26–1.75

15.95–17.64

0.81–1.89

1.76–2.71

0.63–0.81

Pratt (1970)*

12

0.48

0.08–0.46

0.14–0.27

37.89–45.9

0.006–0.02

0.1–0.18

0.08–0.21

Rathbun and Guy(1967)

2

0.3

0.06–0.07

0.23–0.24

20.86

0.026–0.027

0.28–0.29

0.29

Singh (1960)*

30

0.62

0.01–0.07

0.28–0.8

51.98–60.15

0.042–0.56

Stein (1965)*

9

0.4

0.1–0.3

0.94–1.68

33.68–38.15

0.55–2.0

Taki and Parker(2005)

10

0.02–0.12

0.001–0.003

0.15–0.43

0.33–5.28

0.72–2.71

0.24–0.88
1–1.94
3.63–90.52

0.4–1.2
0.71–1.17
1.26–2.94

Tanaka (1970)

10

0.15–0.91

0.04–0.13

0.6–1.86

7.01–110.22

0.55–1.25

0.83–3.85

0.68–2.34

Taylor (1971)31

0.14–3.95

0.06–0.18

0.2–0.88

7.61–1243.08

0.021–0.5

0.14–2.15

0.26–0.84

Ueno (1981)

8

0.23–0.6

0.01–0.03

0.21–0.31

12.48–56.86

0.031–0.08

0.21–0.65

0.52–0.6

U. S. W. Exp. Sta.
(1935)*

75

0.18–4.1

0.01–0.12

0.25–0.68

8.97–1051.56

0.03–0.079

0.15–0.8

0.47–0.76

U. S. W. Exp. Sta.
(1936)***

87

0.46–1.2

0.07–0.08

0.37–0.39

42.18–171.16

0.028–0.075

0.16–0.35

0.42–0.46

Vanoni and
Brooks (1957)*

3

0.14

0.06–0.17

0.63–0.77

6.27–7.17

0.58–0.69

2.61–3.11

0.6–0.81

Williams (1970)

26

1.35

0.02–0.15

0.33–2.34

143.77–228.03

0.033–0.61

0.17–0.75

0.4–3.5

Willis et al. (1972)*

43

0.1

0.12–0.32

0.69–1.57

3.77–4.89

0.40–2.55

3.12–7.9

0.48–1Znamenskaya(1963)*

1

0.18

0.09

0.71

9.7

0.47

1.87

0.77

Ohata et al. Progress in Earth and Planetary Science(2022) 9:23

Page 5 of 13

Table 1 (continued)*Cited from the dataset of Brownlie (2018). **Cited as Neill (1967) in Brownlie (2018). ***Cited as US Waterways Exp. Sta. (1936B) in Brownlie (2018)

Table 2 Summary of field data used for the analysis
References# of points particle
diameter D50[mm]flow depthh [m]flow velocity U Particle[m/s]
Reynolds
number ­Rep

Shields
number τ*

suspension Froude number
index u*/ws Fr

Baird (2010)

1

0.15

1.54

1.04

7.38

2.37

5.09

0.27

Colby andHembree(1955)*

17

0.21–0.32

0.4–0.59

0.96–1.27

8.44–19.8

1.26–2.88

2.15–4.5

0.46–0.54

Culbertson
et al. (1972)

14

0.16–0.24

0.28–1.11

0.46–1.66

5.38–17.82

0.48–2.08

1.3–5.14

0.26–0.52

Mahmood et al.
(1979)*

6

0.08–0.21

1.46–2.32

0.6–0.8

3.57–9.71

0.60–1.45

2.1–7.01

0.13–0.19

Neill (1969)

3

0.34

0.91–2.74

0.67–1.01

20.81–20.81

0.45–1.34

1.16–2.01

0.19–0.22

Simons (1957)

4

0.03–0.36

1.32–1.83

0.59–0.64

0.66–30.93

0.25–2.77

0.74–46.94

0.14–0.17*Cited from the dataset of Brownlie (2018)(3)

no sediment movement and other regimes is defined by
the Shields curve, which is the critical condition for the
initiation of particle motion (e.g., Shields 1936). Basedon Shields’ experimental data, Brownlie (1981) proposeda function describing the threshold condition of particle
motion as:τ∗c = 0.22Re−0.6+ 0.06 exp −17.77Re−0.6(5)ppHere, the shear
 velocity (u∗) for the field data was computed as u∗ = ghS , where S represents the bed slope.
For laboratory data, we removed the sidewall effect andcalculated the bed component of the shear velocity using
the method proposed by Chiew and Parker (1994) (seeOhata et al. (2017) for details). We focused on the analysis of plane bed data in this study; therefore, we assumed
the flow resistance induced by the bedforms is negligible.
The suspension index is expressed as the ratio of theshear velocity (u∗) to the settling velocity of sediment(ws). The settling velocity was estimated using the relationship formulated by Ferguson and Church (2004):

Next, the threshold condition for the initiation of suspension is expressed using the suspension index (u∗ /ws)
(Bagnold 1966; van Rijn 1984a; Niño et al. 2003). The
threshold condition of the particle entrainment into suspension represents the boundary between the bed-loaddominated regime and a regime where the bed materials
are transported with suspension. The threshold condition
for the particle entrainment into suspension, obtained by
Niño et al. (2003), is: 
21.2Re−1.2, 1 < Rep < 27.3
u∗
p
=
(6)
ws c
0.4,
27.3 ≤ Rep
ν = 1.14 − 0.031(T − 15) + 0.00068(T − 15)2 10−6(2)where T represents the water temperature in degree
Celsius. Following van den Berg and van Gelder (1993),
we assumed a value of 20 °C for data where T was notreported. Shields number (τ∗) is defined asu2τ∗ = RgD∗50

ws =

RgD2
 50
3
C1 ν+ 0.75C2 RgD50(4)where constants C1 and C2 were set to 18 and 1, respectively, which were the values for natural sands (Ferguson
and Church 2004).
The sediment transport regimes are classified based on
the transport mechanism—no sediment movement, bedload-dominated, mixed-load, and suspended-load-dominated regimes (Church 2006). The boundary between

We used Eq. (5) (dashed line) and 6 (dotted line) to define
the boundaries of the sediment transport regimes (Figs. 3,4). The region on phase diagrams below the dashed line
denotes the no sediment movement regime, the region
between dashed and dotted lines denotes a bed-load-dominated regime, and the region above the dotted line denotes
a mixed-load or suspended-load-dominated regime where
bed materials are moved in bed load and suspension. To
describe the threshold condition of sediment motion(Eq. 5) on the Rep −u∗ /ws diagram (Fig. 4) and the initiation of suspension (Eq. 6) on the Rep −τ∗ diagram (Fig. 3),

Ohata et al. Progress in Earth and Planetary Science(2022) 9:23

Page 6 of 13

Fig. 3 Plane bed regime in a space of particle Reynolds number Rep versus Shields number τ∗. The dotted line denotes the threshold condition forparticle motion (Eq. 5). The solid line denotes the threshold condition for sediment suspension (Eq. 6). Both lines were extended to Rep = ­10–1 and­105. The plane bed data are divided into two separate regions: the region around the threshold condition of particle motion and the region above
the threshold condition of suspension

Eqs. (5 and 6) are rearranged using Eqs. (1, 3, and 4), whereR = 1.65 (the value for quartz) and ν = 1.0 × ­10–6 (the value
for water with 20 °C).
Second, the plane bed conditions were investigated using
Froude number. Phase diagrams were generated using Rep,u∗ /ws, and Froude number as the axes. Froude number
is the ratio of the inertial force to the gravitational force,
defined as:

Fr = √Ugh(7)

3 Results
3.1 Influence of grain size and sediment transport modeFirst, the plane bed data were plotted in Rep −τ∗ space(Fig. 3) to investigate the relationships among the plane
bed regimes, the particle diameter, and the criteria for
sediment movement. The threshold conditions of particle motion (Eq. 5) and suspension (Eq. 6) are shown in
Fig. 3 as the dashed and dotted lines, respectively. The
median diameter D50 is recast from Rep with R = 1.65
and ν = 1.0 × ­10–6, which is represented on the top axis ofFig. 3.
Shields numbers associated with plane bed conditions range from 0.05 to 10, and the plane bed data
are divided into two separate regions at τ∗ = 0.1–0.2

Ohata et al. Progress in Earth and Planetary Science(2022) 9:23

Page 7 of 13

Fig. 4 Plane bed regime in a space of particle Reynolds number Rep versus suspension index u∗ /ws. The dotted line denotes the thresholdcondition for particle motion (Eq. 5). The solid line denotes the threshold condition for sediment suspension (Eq. 6). Both lines were extended to
Rep = ­10–1 and ­105. The plane bed data are divided into two separate regions: the region around the threshold condition of particle motion and theregion above the threshold condition of suspension(Fig. 3). The plane bed data with low τ∗ plot aroundthe threshold condition of particle motion, and theregion with high τ∗ plots above the threshold condition of suspension. The threshold condition of particle
motion does not divide the plane bed regime; rather,
the threshold condition of suspension runs between thetwo regions of data. The particle Reynolds numbers ofthe data with low τ∗ range 9 < Rep < 4.0 × ­104 (0.2 mm< D50 < 40 mm). In the case of the data with high τ∗,
the particle Reynolds number ranges from 0.1 to 300(0.01 mm < D50 < 2 mm). The data Cs > 0 and fieldobservation data are included in the region of high τ∗.
The data Cs = 0 plot around the threshold condition forparticle motion and τ∗ = 0.4.

Second, the relationships among the plane bed regimes,
the sediment diameter, and the criteria for suspension
were examined by plotting u∗ /ws versus Rep (Fig. 4).
Median diameter D50 is shown on the top axis of Fig. 4.
In Rep–u∗ /ws space, the plane bed data plot in two
regions separated by the threshold condition of suspension (Fig. 4), similar to our results in Rep–τ∗ space(Fig. 3). The threshold condition of particle motion
runs through the middle of the data with a low suspension index. With respect to the particle Reynolds number, the data with a high suspension index plot in theregion 0.1 < Rep < 3.2 × ­103 (0.01 mm < D50 < 2 mm)
and the data with low suspension index plot in theregion 9 < Rep < 4.0 × ­104 (0.2 mm < D50 < 40 mm).

Ohata et al. Progress in Earth and Planetary Science(2022) 9:23

The data Cs > 0 and field data plot above the thresholdcondition of suspension. The data Cs = 0 plot below
and above the suspension criteria.
3.2 Effect of Froude number

We investigated the consistency of the flow regime
concept based on Froude number (Venditti 2013; Dey2014) to plane bed regimes, plotting data in Rep–Fr
space (Fig. 5). The data include Froude numbers ranging from 0.1 to 3.5. The data are not separated withregard to Froude number values. The field data havelower Froude numbers ( Fr < 0.5) and higher Shields
numbers and exceed the threshold condition of suspension (Figs. 3 and 4). For Cs > 0, the data fall in thedomain 0.1 < Fr < 1.3 and the data Cs = 0 distribute in
the domain 0.2 < Fr < 3.5.

Page 8 of 13

4 Discussion
4.1 A new definition for plane beds

Data from the literature including field observations
and flume experiments for plane beds were used to create phase diagrams for plane beds (Figs. 3, 4, 5). Traditionally, the particle diameters or the critical values ofsediment motion or Froude number were used to discriminate lower and upper plane beds. However, ourphase diagrams indicate that this is unlikely (Figs. 3, 4,5). Indeed, the phase regions of the plane beds are notseparated by the traditional indicators such as particle
diameters. In contrast, observational data of the plane
beds plot in two separate regions in the Rep–τ∗ and Rep–u∗ /ws diagrams (Figs. 3, 4), and the boundary between
the two regions corresponds to the threshold condition
for sediment suspension. Therefore, we suggest that theupper and lower plane bed phases separated by the ripple and dune phases (Fig. 2) should be redefined—upper

Fig. 5 Plane bed regime in a space of particle Reynolds number Rep versus Froude number Fr. The data points of plane beds are not discriminatedby Froude number

Ohata et al. Progress in Earth and Planetary Science(2022) 9:23

plane beds are plane beds in which the lower boundaryis the threshold condition for sediment suspension, andlower plane beds are plane beds dominated by bed load.
That is, there is a necessity to modify the classic bedform
phase diagram.
Simons et al. (1961) defined lower plane beds as plane
beds without sediment motion. For the data with a low
Shields number (τ∗ < 0.1–0.2), there are overlaps of data
points pertaining to plane beds with sediment movement and without sediment movement (Fig. 3). Thereis a range of shear stresses in which bed particles could
move because, for example, the sediment bed is composed of natural sands that are somewhat angular andof various sizes. Hence, some data points of plane beds
with sediment motion plotted below the line are definedby the threshold of sediment motion. Also, plane beds
with sediment motion have been observed on a coarsegrained bed (Guy et al. 1966; Southard and Boguchwal
1973; Costello and Southard 1981; Cao 1985). These
results of flume experiments demonstrate that the classical definition of plane beds by Simons et al. (1961) is not
appropriate.
Similarly, Froude number cannot be used to discriminate the two types of plane beds (Fig. 5). Venditti (2013)and Dey (2014) stated that the upper and lower flow
regimes are defined by Froude number. However, bothplane beds with and without suspension can develop
under various Froude numbers (Fig. 4). For example,
plane beds appear with suspended loads in natural rivers
where τ∗ is high and Fr is less than unity due to the great
depth (e.g., Ma et al. 2017). Therefore, we propose thatlower and upper plane beds are not classified by the criticality of Froude number.
It is noteworthy that our analyses indicated that theregime of the lower plane bed extends to the regionof fine-grained sediment (Figs. 3, 4). Southard (1971)
defined lower plane beds as plane beds just above thethreshold of sediment motion under subcritical flow
with relatively coarse grains ( D50 > 0.7 mm). Later, Southard and Boguchwal (1990) proposed bedform phase
diagrams using a compilation of large datasets, although
they omitted the data of relatively fine-grained plane
beds (10 °C-equivalent sediment diameter is smaller than
0.7 mm) under low-velocity flows in their phase diagrams. Southard and Boguchwal (1990) did not include
such data in their diagram because they suspected thatequilibrium had not been attained. However, the duration of experiments performed by Guy et al. (1966) andTaylor (1971), which observed low-velocity plane beds infine sediments, was from several hours to more than 24 h.
The sediment discharge rates for low-velocity plane bedsin the experiments of Guy et al. (1966) and Taylor (1971)
are comparable to those of ripples in their experiments.

Page 9 of 13

Further, the data points of low-flow velocity plane beds
in fine sediment are continuous from those of low-flow
velocity plane beds in coarse sediment (Figs. 3, 4). Therefore, the stable field of the plane bed without suspended
load can be identified from fine sand to gravel.
The origin of the lower plane bed phase in the new definition is puzzling. In previous studies, one of the controlling factors in the lower and upper plane bed regimes
was assumed to be the grain size and flow intensity(Allen 1968; Southard 1971). Leeder (1980) interpreted
that coarse-grained plane beds are formed because flow
separation is prevented by the bed roughness. Recently,
Blois et al. (2014) proposed that bed permeability may be
another explanation for the formation of coarse-grainedplane beds. However, this study established that theregion of coarse-grained plane beds extends continuously
to the fine-grained region, and the conditions for finegrained plane beds were distributed separately in the tworegions: the high- and low-bed shear stresses. Thus, theformation of the lower plane bed cannot be attributed
to bed roughness or permeability owing to the grain size
distribution.
It should be noted here that bed particles are alsotransported in the sheet flow (traction carpet) regime(Sumer et al. 1996), which can be related to the plane
bed. Sheet flows consist of a shear layer of bed load thatmoves under high shear stress (τ∗ > ~ 0.5) where ripples
and dunes are washed out (Sumer et al 1996; Pugh andWilson 1999). Williams (1970) observed that plane bed
developed within sheet flows, and the data from Williams (1970) plotted above the threshold condition ofsuspension, yet no active suspension was observed in
the experiments of Williams (1970) (Figs. 3, 4). Recently,
Hernandez-Moreira et al. (2020) suggested that plane
beds can develop under sheet flows in the intermediate
condition between upstream and downstream migrating
antidunes. However, experiments of sheet flow in open
channels are scarce because laboratory experiments on
sheet flows have been conducted using closed conduits
in order to achieve high shear stresses (Nnadi and Wilson 1992; Sumer et al. 1996) or using oscillatory flowtunnels to simulate storm conditions (Dick and Sleath
1992; O’Donoghue and Wright 2004). Currently, it is difficult to determine whether sheet flow is another possible
mechanism that generates plane beds. Further laboratory
experiments, numerical experiments, and theoreticalconsiderations are required to provide explanations forthe plane bed regimes.
4.2 Theoretical explanation of plane bed formation

The transition from dunes to plane beds has been theoretically explained by the spatial lag between the dune
crest and the location of maximum sediment transport

Ohata et al. Progress in Earth and Planetary Science(2022) 9:23

rate (Kennedy 1963). Dune height decreases when the
maximum sediment transport rate occurs at the downstream of the dune crest. Recently, the spatial lag has
been quantitatively observed under suspended-loaddominated flows (Naqshband et al. 2017), whereas there
was no spatial lag in mixed-load flows (Naqshband et al.
2014). Therefore, the flume experiments by Naqshband
et al. (2014, 2017) indicated that the increase in suspended load flux could lead to the spatial lag between thedune crest and the location of the maximum sedimenttransport rate. Figures 3 and 4 show the data of plane
beds with suspension plotted at a region separated fromthe data of plane beds without suspension. That is, thecompilation of the dataset supports that the spatial lag iscaused by the existence of the suspended load.
Further, the influence of suspended load on the formation condition of bedforms has been demonstrated
in the linear stability analyses by Nakasato and Izumi(2008). Nakasato and Izumi (2008) showed that the maximum Froude number for dune formation decreased byincluding the effect of suspended load; that is, the dune
formation is partly suppressed. Although the results oflinear analyses by Nakasato and Izumi (2008) were verified using the experimental data of dune and antiduneof Guy et al. (1966), the hydraulic conditions of analyses
were limited, and they did not make a comparison withthe data of plane beds. In future theoretical research, it
is required to analyze various conditions (e.g., sediment
diameter and flow depth) and compare the results withthe plane bed data.
4.3 Implication for rock record

Planar parallel lamination is often observed in ancient
sedimentary successions and utilized to interpret thedepositional environments (e.g., Clifton 1976; PlinkBjörklund 2005). For example, planar-laminated sandstones from shallow marine conditions are interpreted
to be formed in nearshore environments where wave collapse generates back-and-forth currents on the sea floor(Clifton 1976; Dumas and Arnott 2005; Vaucher et al.
2018).
In deep marine environments, turbidites may form
planar laminations as the ­Tb and ­Td divisions (Bouma
1962), although both may be absent (e.g., Sumner et al.
2012). The origin of the ­Tb division is attributed toplane bed deposition, whereas that of the ­Td division isenigmatic (Middleton 1993; Talling et al. 2012). Following the definitions of Southard and Boguchwal (1990),
Talling et al. (2012) argued that the origin of T
­ d division in turbidites is not the lower plane beds because
the lower plane beds occur only on the coarse-grained
beds. However, our phase diagrams imply that the origin of planar laminae in sandstone cannot be presumed

Page 10 of 13

depending only on its particle size. Although Southard(1971) and Southard and Boguchwal (1990) suggested
that lower plane beds cannot be formed with sedimentfiner than 0.7 mm in diameter, this study shows that
fine-grained plane beds can develop at low-flow velocity(Figs. 3 and 4). Also, Hesse and Chough (1980) pointed
out the possibility of the existence of fine-grained plane
beds at low shear stress based on the flume experiments
using silt-sized sediment by Rees (1966). Fine-grainedplane beds can be stable at low shear stress because thecritical shear stress to maintain the sediment movement under supersaturated flows where the sedimentis already suspended is different from the critical shear
stress to erode the sediment from the bed (Rees 1966).
Also, ­Td division is composed of silt- and clay-sizedparticles (Bouma 1962), and the cohesion is one of thepossible mechanisms for the formation of plane beds in
open-channel flows (Schindler 2015). Therefore, gaps
in the existing data to explain the origin of ­Td division
should be filled by flume experiments of sedimentladen gravity currents and open-channel flows undercontrolled conditions.

5 Conclusions
In this study, we compiled 935 flume and field datasets
pertaining to plane beds and analyzed the dataset in
the nondimensional parametric space. The results of
our analysis indicate that the formation conditions ofplane beds do not show a clear boundary at the threshold condition of sediment motion, a unique value of particle diameter, or a Froude number of unity, which havebeen traditionally used to define lower and upper plane
beds. Conversely, the formation conditions of plane beds
are distributed in two separate regions, a lower plane
bed dominated by bed load and an upper plane bed inwhich the lower boundary is the threshold condition for
sediment suspension. This study demonstrates that suspended load significantly contributes to the formationof plane beds. Further experiments are needed to understand the mechanisms that can produce fine-grainedplane beds in flows with low-bed shear stress.
Acknowledgements
We are thankful to Gary Hampson, Paul Myrow, Travis Swanson, Harihar
Rajaram, and Ray Kostaschuk, and anonymous reviewers are acknowledged
gratefully for their efforts and insightful comments on earlier versions of themanuscript. We gratefully appreciate J. Bruce H. Shyu, Romain Vaucher, andan anonymous reviewer for valuable suggestions for the improvement in thispaper.
Author contributions
KO proposed the topic and compiled the data. HN and NI contributed tothe interpretation of the results. KO wrote the manuscript and prepared thefigures, and then HN and NI provided feedback on the manuscript and figures.
All authors read and approved the final manuscript.

Ohata et al. Progress in Earth and Planetary Science(2022) 9:23

Page 11 of 13

Funding
This work was partially supported by The Kyoto University Foundation, theJapan Society for the Promotion of Science (JSPS) Grant-in-Aid (KAKENHI)
Grant Number 18J22211 and 20H01985.

Chakraborty C, Ghosh SK, Chakraborty T (2003) Depositional record of tidal-flat
sedimentation in the Permian coal measures of Central India: Barakar
formation, Mohpani coalfield, Satpura Gondwana basin. Gondwana Res
6:817–827. https://​doi.​org/​10.​1016/​S1342-​937X(05)​71027-3
Chiew YM, Parker G (1994) Incipient sediment motion on non-horizontal
slopes. J Hydraul Res 32:649–660. https://​doi.​org/​10.​1080/​00221​68940​
94987​06
Church M (2006) Bed material transport and the morphology of alluvial river
channels. Annu Rev Earth Planet Sci 34:325–354. https://​doi.​org/​10.​1146/​annur​ev.​earth.​33.​092203.​122721
Chyn SD (1935) An experimental study of the sand transporting capacity of
the flowing water on sandy bed and the effect of the compositionof the sand. PhD thesis, Massachusetts Institute of Technology, Cambridge, Massachusetts
Cisneros J, Best J, van Dijk T, de Almeida RP, Amsler M, Boldt J, Freitas B,
Galeazzi C, Huizinga R, Ianniruberto M, Ma H, Nittrouer JA, Oberg K,
Orfeo O, Parsons D, Szupiany R, Wang P, Zhang Y (2020) Dunes in theworld’s big rivers are characterized by low-angle lee-side slopes anda complex shape. Nat Geosci 13:156–162. https://​doi.​org/​10.​1038/​
s41561-​019-​0511-7
Clifton HE (1976) Waveformed sedimentary structures—A conceptual model.
In: Davis RA Jr, Ethington RL (eds) Beach and Nearshore Sedimentation.
Society for Sedimentary Geology (SEPM) Special Publication 24, pp
126–148
Colby BR, Hembree CH (1955) Computations of total sediment discharge, Niobrara River Near Cody, Nebraska. U.S. Geological Survey Water-Supply
Paper 1357
Collinson JD (1970) Bedforms of the Tana River, Norway. Geogr Ann Ser A Phys
Geogr 52:31–56
Colombini M (2004) Revisiting the linear theory of sand dune formation. J
Fluid Mech 502:1–16. https://​doi.​org/​10.​1017/​S0022​11200​30072​01
Colombini M, Stocchino A (2008) Finite-amplitude river dunes. J Fluid Mech
611:283–306. https://​doi.​org/​10.​1017/​S0022​11200​80028​14
Costello WR, Southard JB (1981) Flume experiments on lower-flow-regime bed
forms in coarse sand. J Sediment Res 51:849–864. https://​doi.​org/​10.​
1306/​212F7​DC4-​2B24-​11D7-​86480​00102​C1865D
Costello WR (1974) Development of bed configuration in coarse sands.
PhD thesis, Massachusetts Institute of Technology, Cambridge,
Massachusetts
Culbertson JK, Scott CH, Bennett JP (1972) Summary of alluvial-channel datafrom Rio Grande conveyance channel, New Mexico, 1965–69. U.S.
Geological Survey Professional Paper 562-J
Dey S (2014) Fluvial hydrodynamics: hydrodynamic and sediment transportphenomena. Springer, Germany, p 687
Dick JE, Sleath JFA (1992) Sediment transport in oscillatory sheet flow. J Geophys Res 97:5745–5758. https://​doi.​org/​10.​1029/​92JC0​0054
Dumas S, Arnott RWC (2005) Origin of hummocky and swaley cross-stratification—the controlling influence of unidirectional current strengthand aggradation rate. Geology 34:1073–1076. https://​doi.​org/​10.​1130/​
G2293​0A.1
Dumas S, Arnott RWC, Southard JB (2005) Experiments on oscillatory-flow andcombined-flow bed forms: Implications for interpreting parts of theshallow-marine sedimentary record. J Sediment Res 75:501–513
East Pakistan Water and Power Development Authority (1966, 1968–1969)
Flume studies of roughness and sediment transport of movable bed ofsand. Annual Report of Hydraulic Research Laboratory, Dacca
Eggenhuisen JT, McCaffrey WD, Haughton PDW, Butler RWH (2011) Shallow
erosion beneath turbidity currents and its impact on the architecturaldevelopment of turbidite sheet systems. Sedimentology 58:936–959.
https://​doi.​org/​10.​1111/j.​1365-​3091.​2010.​01190.x
Engelund F (1970) Instability of erodible beds. J Fluid Mech 42:225–244.
https://​doi.​org/​10.​1017/​S0022​11207​00012​10Ferguson RI, Church M (2004) A simple universal equation for grain settling
velocity. J Sediment Res 74:933–937. https://​doi.​org/​10.​1306/​05120​
47409​33
Fukuoka S, Okutsu K, Yamasaka M (1982) Dynamic and kinematic features ofsand waves in upper regime. In: Proceedings of the Japan Society of
Civil Engineers, vol 323, pp 77–89 (in Japanese). https://​doi.​org/​10.​
2208/​jscej​1969.​1982.​323_​77
Galeazzi CP, Almeida RP, Mazoca CEM, Best JL, Freitas BT, Ianniruberto M,
Cisneros J, Tamura LN (2018) The significance of superimposed dunes

Availability of data and materials
The data used for the analysis can be found at [url to be updated at acceptance]. Unpublished data used for the analysis were cited from the dataset of
Brownlie (2018).

Declarations
Competing interests
The authors declare that they have no competing interests.
Author details
1
Division of Earth and Planetary Sciences, Graduate School of Science, Kyoto
University, Kitashirakawaoiwake‑cho, Sakyo‑ku, Kyoto‑shi, Kyoto 606‑8502,
Japan. 2 Division of Field Engineering for the Environment, Faculty of Engineering, Hokkaido University, Kita‑ku, Sapporo‑shi, Hokkaido 060‑8628, Japan.
Received: 20 June 2021 Accepted: 5 April 2022

References
Allen JRL (1968) Current ripples: their relation to patterns of water and sediment motion. North Holland Publishing Company, Amsterdam, p 433
Bagnold RA (1966) An approach to the sediment transport problem fromgeneral physics. U.S. Geological Survey Professional Paper 422-I
Baird DC (2010) Field adjustments of bed form phase diagrams. In: 2nd Joint
federal interagency conference, Las Vegas, pp 1137–1145
Barton JR, Lin PN (1955) A study of the sediment transport in alluvial channels.
Report CEF55JRB2. Colorado State University, Fort Collins
Blois G, Best JL, Sambrook Smith GH, Hardy RJ (2014) Effect of bed permeability and hyporheic flow on turbulent flow over bed forms. Geophys Res
Lett 41:6435–6442. https://​doi.​org/​10.​1002/​2014G​L0609​06
Bogárdi J (1961) Some aspects of the application of the theory of sedimenttransportation to engineering problems. J Geophys Res 66:3337–3346.
https://​doi.​org/​10.​1029/​JZ066​i010p​03337
Bouma AH (1962) Sedimentology of some flysch deposits: a graphic approach
to facies interpretation. Elsevier, Amsterdam, p 168
Bradley RW, Venditti JG (2019) Transport scaling of dune dimensions in shallow
flows. J Geophys Res Earth Surf 124:526–547. https://​doi.​org/​10.​1029/​
2018J​F0048​32
Bridge JS, Best JL (1988) Flow, sediment transport and bedform dynamics over
the transition from dunes to upper-stage plane beds: implications forthe formation of planar laminae. Sedimentology 35:753–763. https://​doi.​org/​10.​1111/j.​1365-​3091.​1988.​tb012​49.x
Bridge J, Best J (1997) Preservation of planar laminae due to migrationof lowrelief bed waves over aggrading upper-stage plane beds: comparisonof experimental data with theory. Sedimentology 44:253–262. https://​doi.​org/​10.​1111/j.​1365-​3091.​1997.​tb015​23.x
Brooks NH (1955) Mechanics of streams with movable beds of fine sand. Proc
Am Soc Civ Eng 81:1–28
Brownlie WR (1981) Prediction of flow depth and sediment discharge in open
channels. Report KH-R43A, W.M. Keck Laboratory of Hydraulics andWater Resources, California Institute of Technology, Pasadena, California.
https://​doi.​org/​10.​7907/​Z9KP8​03R
Brownlie WR (2018) Digitized dataset from "Compilation of alluvial channel
data: laboratory and field" (Version 1.0). CaltechDATA. https://​doi.​org/​
10.​22002/​d1.​943
Cao HH (1985) Résistance hydraulique d’un lit à gravier mobile à penteraide:étude expérimentale. PhD thesis, Ecole Polytechnique Fédérale deLausane, Switzerland
Chabert J, Chauvin JL (1963) Formation des dunes et des rides dans lesmodèles fluviaux. Bulletin du Centre de Recherches et d’Essais deChatouOhata et al. Progress in Earth and Planetary Science(2022) 9:23

in the Amazon River: implications for how large rivers are identified in
the rock record. Sedimentology 65:2388–2403. https://​doi.​org/​10.​1111/​
sed.​12471
Galy V, France-Lanord C, Beyssac O, Faure P, Kudrass H, Palhol F (2007) Efficientorganic carbon burial in the Bengal fan sustained by the Himalayanerosional system. Nature 450:407–410
Gao P (2008) Transition between two bed-load transport regimes: saltationand sheet flow. J Hydraul Eng 134:340–349. https://​doi.​org/​10.​1061/​(ASCE)​0733-​9429(2008)​134:​3(340)
García MH (2000) Discussion of “The legend of A. F. Shields” by J. M. Buffington.
J Hydraul Eng 126:718–720. https://​doi.​org/​10.​1061/​(ASCE)​0733-​
9429(2000)​126:​9(718)
Gee DM (1975) Bed form response to nonsteady flows. J Hydraul Div
101:437–449
Gilbert GK (1914) The transportation of debris by running water. U.S. Geological Survey Professional Paper 86
Guy HP, Simons DB, Richardson EV (1966) Summary of alluvial channel datafrom flume experiments, 1956–61. U.S. Geological Survey Professional
Paper 462-I
Hauer C, Holzapfel P, Tonolla D, Habersack H, Zolezzi G (2019) In situ measurements of fine sediment infiltration (FSI) in gravel-bed rivers with ahydropeaking flow regime. Earth Surf Proc Land 44:433–448. https://​doi.​org/​10.​1002/​esp.​4505
Hernandez-Moreira R, Jafarinik S, Sanders S, Kendall CGSC, Parker G, Viparelli E(2020) Emplacement of massive deposits by sheet flow. Sedimentology
67:1951–1972. https://​doi.​org/​10.​1111/​sed.​12689
Hesse R, Chough SK (1980) The northwest atlantic mid-ocean channel of theLabrador Sea: II. Deposition of parallel laminated levee-muds fromthe viscous sublayer of low density turbidity currents. Sedimentology
27:697–711. https://​doi.​org/​10.​1111/j.​1365-​3091.​1980.​tb016​56.x
Hori K, Saito Y, Zhao Q, Cheng X, Wang P, Sato Y, Li C (2001) Sedimentary faciesof the tide-dominated paleo-Changjiang (Yangtze) estuary during
the last transgression. Mar Geol 177:331–351. https://​doi.​org/​10.​1016/​
S0025-​3227(01)​00165-7
Jobe ZR, Lowe DR, Morris WR (2012) Climbing-ripple successions in turbidite
systems: depositional environments, sedimentation rates and accumulation times. Sedimentology 59:867–898. https://​doi.​org/​10.​1111/j.​
1365-​3091.​2011.​01283.x
Jopling AV, Forbes DL (1979) Flume study of silt transportation and deposition.
Geografiska Annaler Ser A Phys Geogr 61:67–85. https://​doi.​org/​10.​
2307/​520516
Jorissen AL (1938) Étude expérimentale du transport solide des cours d’eau.
Revue Universelle Des Mines 14:269–282
Julien PY, Raslan Y (1998) Upper-regime plane bed. J Hydraul Eng 124:1086–
1096. https://​doi.​org/​10.​1061/​(ASCE)​0733-​9429(1998)​124:​11(1086)
Kalinske AA, Hsia CH (1945) Study of transportation of fine sediments by flowing water. University of Iowa Studies in Engineering, Bulletin No. 29
Kennedy JF (1963) The mechanics of dunes and antidunes in erodible-bed
channels. J Fluid Mech 16:521–544. https://​doi.​org/​10.​1017/​S0022​
11206​30009​75
Kennedy JF, Brooks NH (1963) Laboratory study of an alluvial stream of constant discharge. In: Proceedings of the Federal Inter-Agency Sedimentation Conference, pp 320–330
Kennedy JF (1961) Stationary waves and antidunes in alluvial channels. Report
KH-R-2, W.M. Keck Laboratory of Hydraulics and Water Resources,
California Institute of Technology, Pasadena, California. https://​doi.​org/​
10.​7907/​Z9QR4​V22
Kikuchi K (2018) The occurrence of Paleodictyon in shallow-marine depositsof the Upper Cretaceous Mikasa Formation, Hokkaido Island, northern
Japan: Implications for spatiotemporal variation of the Nereites ichnofacies. Palaeogeogr Palaeoclimatol Palaeoecol 503:81–89. https://​doi.​org/​
10.​1016/j.​palaeo.​2018.​04.​016
Kuhnle RA, Wren DG (2009) Size of suspended sediment over dunes. J Geophys Res Earth Surf. https://​doi.​org/​10.​1029/​2008J​F0012​00.​F02020
Laursen EM (1958) The total sediment load of streams. J Hydraul Div 84(1):1–36
Leeder MR (1980) On the stability of lower stage plane beds and the absenceof current ripples in coarse sands. J Geol Soc 137(4):423–429. https://​doi.​org/​10.​1144/​gsjgs.​137.4.​0423
Liu H-K (1957) Mechanics of sediment-ripple formation. J Hydraul Div 83:1–23
Ma H, Nittrouer JA, Naito K, Fu X, Zhang Y, Moodie AJ, Wang Y, Wu B, Parker G(2017) The exceptional sediment load of fine-grained dispersal systems:

Page 12 of 13

example of the Yellow River, China. Sci Adv. https://​doi.​org/​10.​1126/​
sciadv.​16031​14
Mahmood K, Tarar RN, Hassan SA, Khan H, Masood T (1979) Selected equilibrium-state data from ACOP canals. Report No. EWR-79-2. Civil, Mechanical and Environmental Engineering Department, George Washington
University, Washington, DC
Masselink G, Austin MJ, O’Hare TJ, Russell PE (2007) Geometry and dynamics ofwave ripples in the nearshore zone of a coarse sandy beach. J Geophys
Res Oceans 112:C10022
Mazumder R, Kranendonk MJV (2013) Palaeoproterozoic terrestrial sedimentation in the Beasley River Quartzite, lower Wyloo Group, Western
Australia. Precambr Res 231:98–105. https://​doi.​org/​10.​1016/j.​preca​
mres.​2013.​03.​018
Middleton GV (1993) Sediment deposition from turbidity currents. Annu Rev
Earth Planet Sci 21:89–114. https://​doi.​org/​10.​1146/​annur​ev.​ea.​21.​050193.​000513
Miller MC, Komar PD (1980) A field investigation of the relationship between
oscillation ripple spacing and the near-bottom water orbital motions. J
Sed Res 50:183–191
Mitra R, Naruse H, Fujino S (2021) Reconstruction of flow conditions from 2004
Indian Ocean tsunami deposits at the Phra Thong island using a deepneural network inverse model. Nat Hazard 21:1667–1683
Mutter DG (1971) A flume study of alluvial bed configurations. Master’s thesis,
Faculty of Graduate Studies, University of Alberta, Edomonton, Alberta,
CanadaNakasato Y, Izumi N (2008) Linear stability analysis of small-scale fluvial bed
waves with active suspended sediment load. J Appl Mech 11:727–734.
https://​doi.​org/​10.​2208/​journ​alam.​11.​727 ((in Japanese with English
abstract))
Naqshband S, Ribberink JS, Hurther D, Hulscher SJMH (2014) Bed load andsuspended load contributions to migrating sand dunes in equilibrium.
J Geophys Res Earth Surf 119:1043–1063. https://​doi.​org/​10.​1002/​2013J​
F0030​43.​2013J​F0030​43
Naqshband S, Hoitink AJF, McElroy B, Hurther D, Hulscher SJMH (2017) A sharp
view on river dune transition to upper stage plane bed. Geophys Res
Lett 44:11437–11444. https://​doi.​org/​10.​1002/​2017G​L0759​06
Neill CR (1969) Bed forms in the lower Red Deer River, Alberta. J Hydrol
7:58–85. https://​doi.​org/​10.​1016/​0022-​1694(68)​90195-9
Niño Y, Lopez F, Garcia M (2003) Threshold for particle entrainment into
suspension. Sedimentology 50:247–263. https://​doi.​org/​10.​1046/j.​1365-​
3091.​2003.​00551.x
Nnadi FN, Wilson KC (1992) Motion of contact-load particles at high shear
stress. J Hydraul Eng 118:1670–1684. https://​doi.​org/​10.​1061/​(ASCE)​
0733-​9429(1992)​118:​12(1670)
Nomicos GN (1956) Effects of sediment load on the velocity field and friction
factor of turbulent flow in an open channel. PhD thesis, California
Institute of Technology, Pasadena, California
Nordin CF (1976) Flume studies with fine and coarse sands. U.S. Geological
Survey, Open File Report No. 76-762
O’Donoghue T, Wright S (2004) Concentrations in oscillatory sheet flow for
well sorted and graded sands. Coast Eng 50:117–138. https://​doi.​org/​
10.​1016/j.​coast​aleng.​2003.​09.​004
Ohata K, Naruse H, Yokokawa M, Viparelli E (2017) New bedform phase diagrams and discriminant functions for formative conditions of bedforms
in open-channel flows. J Geophys Res Earth Surf 122:2139–2158.
https://​doi.​org/​10.​1002/​2017J​F0042​90
Owens JS (1908) Experiments on the transporting power of sea currents.
Geogr J 31:415–420
Paola C, Wiele S, Reinhart M (1989) Upper-regime parallel lamination as theresult of turbulent sediment transport and low-amplitude bed forms.
Sedimentology 36:47–59
Perillo MM, Best J, Garcia MH (2014) A new phase diagram for combined-flow
bedforms. J Sediment Res 84:301–313
Plink-Björklund P (2005) Stacked fluvial and tide-dominated estuarine deposits
in high-frequency (fourth-order) sequences of the Eocene Central
Basin. Spitsbergen Sedimentol 52(2):391–428. https://​doi.​org/​10.​1111/j.​
1365-​3091.​2005.​00703.x
Pratt CJ (1970) Summary of experimental data for flume tests over 0.49 mm
sand. Department of Civil Engineering, University of Southampton,
Southampton

Ohata et al. Progress in Earth and Planetary Science(2022) 9:23

Pugh FJ, Wilson KC (1999) Velocity and concentration distributions in sheet
flow above plane beds. J Hydraul Eng 125:117–125. https://​doi.​org/​10.​1061/​(ASCE)​0733-​9429(1999)​125:​2(117)
Rathbun RE, Guy HP (1967) Measurement of hydraulic and sediment transportvariables in a small recirculating flume. Water Resour Res 3:107–122.
https://​doi.​org/​10.​1029/​WR003​i001p​00107
Rees AI (1966) Some flume experiments with a fine silt. Sedimentology
6:209–240. https://​doi.​org/​10.​1111/j.​1365-​3091.​1966.​tb015​78.x
Schindler RJ, Parsons DR, Ye L, Hope JA, Baas JH, Peakall J, Manning AJ, Aspden
RJ, Malarkey J, Simmons S, Paterson DM, Lichtman ID, Davies AG,
Thorne PD, Bass SJ (2015) Sticky stuff: redefining bedform prediction inmodern and ancient environments. Geology 43:399–402. https://​doi.​
org/​10.​1130/​G36262.1
Schlünz B, Schneider RR (2000) Transport of terrestrial organic carbon to theoceans by rivers: re-estimating flux-and burial rates. Int J Earth Sci
88:599–606
Shields A (1936) Application of similarity principles and turbulence research to
bed-load movement (English translation of an original German manuscript). Soil Conservation Service Cooperative Laboratory, California
Institute of Technology Pasadena, California (trans: Ott, WP and van
Uchelen J. C.)
Simons, DB, Richardson, EV (1961) Forms of bed roughness in alluvial channels.
J Hydraul Div 87
Simons DB, Richardson EV (1962) The effect of bed roughness on depth-discharge relations in alluvial channels. U.S. Geological Survey Professional
Paper 1498-E
Simons DB, Richardson EV, Albertson ML (1961) Flume studies using medium
sand (0.45 mm). U.S. Geological Survey Water-Supply Paper 1498-A
Simons DB (1957) Theory and design of stable channels in alluvial material.
PhD thesis, Colorado State University, Fort Collins, Colorado
Singh B (1960) Transport of bed-load in channels with special reference togradient and form. PhD thesis, University of London, London
Southard JB (1971) Representation of bed configurations in depth-velocitysize diagrams. J Sediment Res 41:903–915. https://​doi.​org/​10.​1306/​
74D72​3B0-​2B21-​11D7-​86480​00102​C1865D
Southard JB (1991) Experimental determination of bed-form stability. Ann Rev
Earth Planet Sci 19:423–455. https://​doi.​org/​10.​1306/​74D72​914-​2B21-​
11D7-​86480​00102​C1865D
Southard JB, Boguchwal LA (1973) Flume experiments on the transition fromripples to lower flat bed with increasing sand size. J Sediment Res
43:1114–1121. https://​doi.​org/​10.​1306/​74D72​914-​2B21-​11D7-​86480​
00102​C1865D
Southard JB, Boguchwal LA (1990) Bed configurations in steady unidirectional water flows. Part 2. Synthesis of flume data. J Sediment Petrol
60:658–679
Stein RA (1965) Laboratory studies of total load and apparent bed load. J Geophys Res 70:1831–1842. https://​doi.​org/​10.​1029/​JZ070​i008p​01831
Strahan A, Lamplugh M, Cornish V, Mill D, Evans D, Tizard C, Creak C, Chisholm
GG, Owens JS (1908) Experiments on the transporting power of sea
currents: discussion. Geogr J 31:420–425
Sumer BM, Kozakiewicz A, Fredsøe J, Deigaard R (1996) Velocity and concentration profiles in sheet-flow layer of movable bed. J Hydraul Eng
122:549–558. https://​doi.​org/​10.​1061/​(ASCE)​0733-​9429(1996)​122:​
10(549)Sumner EJ, Talling PJ, Amy LA, Wynn RB, Stevenson CJ, Frenz M (2012) Facies
architecture of individual basin-plain turbidites: comparison withexisting models and implications for flow processes. Sedimentology
59:1850–1887. https://​doi.​org/​10.​1111/j.​1365-​3091.​2012.​01329.x
Taki K, Parker G (2005) Transportational cyclic steps created by flow over anerodible bed. Part 1. Experiments. J Hydraul Res 43:488–501. https://​doi.​
org/​10.​1080/​00221​68050​95001​47
Talling PJ, Masson DG, Sumner EJ, Malgesini G (2012) Subaqueous sedimentdensity flows: depositional processes and deposit types. Sedimentology 59:1937–2003. https://​doi.​org/​10.​1111/j.​1365-​3091.​2012.​01353.x
Tanaka Y (1970) An experimental study on anti-dunes. Disast Prevent Res InstAnn 13B:271–284
Taylor BD (1971) Temperature effects in alluvial streams. Report KH-R-27, W.M.
Keck Laboratory of Hydraulics and Water Resources, California Instituteof Technology, Pasadena, CA. https://​doi.​org/​10.​7907/​Z9377​6PN

Page 13 of 13

United States Army Corps of Engineers, U.S. Waterways Experiment Station,
Vicksburg, Mississippi (1935) Studies of river bed materials and their
movement with special reference to the lower Mississippi River, p 161
Ueno T (1981) On the regions of occurrence of ripples and dunes. Proc Jpn
Conf Hydraul 25:93–98. https://​doi.​org/​10.​2208/​prohe​1975.​25.​93 ((inJapanese))
Umazano AM, Bellosi ES, Visconti G, Melchor RN (2012) Detecting allocyclic
signals in volcaniclastic fluvial successions: facies, architecture andstacking pattern from the Cretaceous of central Patagonia, Argentina. J
S Am Earth Sci 40:94–115. https://​doi.​org/​10.​1016/j.​jsames.​2012.​09.​005
van den Berg JH (1987) Bedform migration and bed-load transport in somerivers and tidal environments. Sedimentology 34:681–698. https://​doi.​
org/​10.​1111/j.​1365-​3091.​1987.​tb007​94.x
van den Berg JH, van Gelder A (1993) A new bedform stability diagram, withemphasis on the transition of ripples to plane bed in flows over finesand and silt. In: Marzo M, Puigdefabregas C (eds) Alluvial sedimentation. Blackwell Scientific Publications, vol 17. International Associationof Sedimentologists, pp 11–21
van Rijn LC (1984a) Sediment transport, part II: suspended load transport.
J Hydraul Eng 110:1613–1641. https://​doi.​org/​10.​1061/​(ASCE)​0733-​
9429(1984)​110:​11(1613)
van Rijn LC (1984b) Sediment transport, part III: bed forms and alluvial roughness. J Hydraul Eng 110:1733–1754. https://​doi.​org/​10.​1061/​(ASCE)​
0733-​9429(1984)​110:​12(1733)
Vanoni VA, Brooks NH (1957) Laboratory studies of the roughness andsuspended load of alluvial streams. Report E-68, W.M. Keck Laboratoryof Hydraulics and Water Resources, California Institute of Technology,
Pasadena, California
Vaucher R, Dashtgard SE (2021) Nearshore bedforms, reference module inearth systems and environmental sciences. Elsevier, Amsterdam
Vaucher R, Pittet B, Passot S, Grandjean P, Humbert T, Allemand P (2018) Bedforms in a tidally modulated ridge and runnel shoreface (Berck-Plage;
North France): implications for the geological record. Bulletin De La
Société Géologique De France. https://​doi.​org/​10.​1051/​bsgf/​20180​04
Venditti JG (2013) Bedforms in sand-bedded rivers. In: Shroder J, Wohl E (eds)
Treatise on geomorphology, vol 9. Academic Press, San Diego, pp
137–162
Williams GP (1970) Flume width and water depth effects in sediment transport
experiments. U.S. Geological Survey Professional Paper 562-H
Willis JC, Coleman NL, Ellis WM (1972) Laboratory study of transport of finesand. J Hydraul Div 98:489–501
Wu X, Parsons DR (2019) Field investigation of bedform morphodynamics
under combined flow. Geomorphology 339:19–30
Znamenskaya NS (1963) Experimental study of the dune movement of sediment. In: Soviet hydrology: selected papers. American GeophysicalUnion, Washington, DC, pp 253–275

Publisher’s NoteSpringer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.