JANUARY 2016

YU ET AL.

159

Fortnightly Variation in the Bottom Thermal Front and Associated Circulation
in a Semienclosed Sea
XIAOJIE YU, XINYU GUO, AND HIDETAKA TAKEOKA
Center for Marine Environmental Study, Ehime University, Matsuyama, Ehime, Japan(Manuscript received 10 April 2015, in final form 21 July 2015)
ABSTRACT
Summer hydrographic data from 1971 to 2000 demonstrate the presence of bottom cold water (BCW) and abottom thermal front around the BCW in a semienclosed sea in the Seto Inland Sea of Japan. The horizontal
gradient of water temperature across the bottom front was larger in neap tide than in spring tide, which is the
opposite the pattern observed in the fortnightly variations in other areas (e.g., the Irish Sea). A numerical model for
the Inland Sea reproduced the presence of BCW and a bottom front as well as the same fortnightly variation in thehorizontal gradient of water temperature across the bottom front as in observational data. Being the same BCW as
those in other areas, the presence of BCW in the Inland Sea is also caused by spatial variation in tidal mixing. The
intensification of the bottom front in neap tide in the Inland Sea results from a combination of tidal mixing andhorizontal advection of warm water to the BCW. The presence of a bottom residual current in the direction acrossthe bottom front results in the horizontal advection of warm water to the BCW, and its fortnightly variation is
responsible for the fortnightly variation of the bottom front in the Inland Sea. The presence of the BCW induces asurface cyclonic circulation in the direction approximately along the bottom front; the intensification and weakening of the bottom front with the spring–neap tidal cycle, combined with the fortnightly variation in the bottom
boundary layer thickness, produce a slightly stronger surface cyclonic circulation in neap tide than in spring tide.

1. Introduction
Following the study by Simpson and Hunter (1974)
that revealed the presence of a tidal front in the Irish
Sea and its formation mechanism, there have been
many studies on surface thermal fronts, that is, tidal
fronts in shelf seas and bays in summer (e.g., Simpson
et al. 1978; Ou 1984; Loder and Greenberg 1986; Lie
1989; Wang et al. 1990; Simpson and Sharples 1994).
Spatial variations in tidal currents induce the establishment of mixed regions and stratified areas. Strong
tidal currents in mixed regions overcome the buoyancy input by surface heat fluxes and maintain homogeneity in the water column; weak tidal currents inareas of stratification, however, cannot homogenize
the water column in the vertical direction. The transition zone between these two regions is the tidal
front, across which the surface temperature gradientis large.

Corresponding author address: Xinyu Guo, Center for Marine
Environmental Studies, Ehime University, 2-5 Bunkyo-Cho,
Matsuyama 790-8577, Japan.
E-mail: guoxinyu@sci.ehime-u.ac.jp
DOI: 10.1175/JPO-D-15-0071.1
Ó 2016 American Meteorological Society

The thermal front is present not only in the surface
layer but also in the bottom layer. Water is usuallycolder in the bottom layer of a stratified area compared
to in mixed areas and is called bottom cold water(BCW). Consequently, the bottom thermal front, although not as demarcated as the surface one, forms
between the mixed area and the stratified area. The
presence of BCW and the bottom front are confirmed byfield observations in the Irish Sea (Hill et al. 1997;
Horsburgh et al. 2000; Xing and Davies 2001b; Brown
et al. 2003), North Sea (Brown et al. 1999), and Yellow
Sea (Yuan and Li 1993; Su and Huang 1995).
Some studies have reported residual currents aroundthe bottom thermal front and BCW. Based on observations, Hill et al. (1994) reported the presence of acyclonic gyre in the western Irish Sea in summer andconcluded that the gyre is closely associated with thebottom thermal front and the BCW. Using the observed
density field and the thermal-wind equation, Horsburgh
et al. (2000) predicted a cyclonic, near-surface jet along
the bottom thermal front in the Irish Sea in summer.
Using the same method, Hill et al. (2008) demonstrated
that a density field associated with a bottom thermal
front can be used to diagnose a surface current that is

160

JOURNAL OF PHYSICAL OCEANOGRAPHY

VOLUME 46

FIG. 1. Monthly sampling stations (red dots) in the Seto Inland Sea. The black line with numbers
from 1 to 7 denotes stations bisecting the BCW from which data are presented in Fig. 5.

consistent with the movement of drifters. Bottom friction
is likely an essential condition for the formation of surface cyclonic circulation (Hill 1996). Three-dimensionalmodels developed based on realistic bathymetry data
and forcing inputs were also used to reproduce the BCW
and to develop interpretation of its dynamics (Xing andDavies 2001b; Horsburgh and Hill 2003; Holt and Proctor
2003; Xing and Davies 2005; Davies and Xing 2006).
Since the tidal current cycles between spring tide andneap tide, its induced vertical mixing must also have thesame cycle. A general hypothesis on this variation is thatthe mixed area becomes enlarged during spring tide
when the position of the tidal front shifts to the stratified
area; the mixed area becomes small in neap tide, and thetidal front retreats to the mixed area (Simpson andBowers 1981; Mountain and Taylor 1996). Yanagi andTamaru (1990) and Sun and Isobe (2006) reported
fortnightly variation not only in the position of the tidal
front but also in the horizontal gradient of the sea surface temperature across the tidal front that is intensifiedin spring tide and weakened in neap tide. Based on fieldmeasurements, Lwiza et al. (1991) found that the residual current along a tidal front in the North Sea isstrong in spring tide and weak in neap tide.
Based on the same principle, the bottom thermal front
and associated circulation are also affected by fortnightly variation in the tidal current. Using a numericalmodel, Horsburgh and Hill (2003) found that the horizontal gradient of bottom temperature across the bottom thermal front and the kinetic energy of the residual
current above the bottom thermal front become stronger after spring tide but weaker after neap tide in the
Irish Sea. Using a different numerical model, Luyten
et al. (2003) also demonstrated fortnightly variation in
the vertical structure of water temperature and thermal
circulation in the North Sea: the surface mixed layer

becomes shallow (deep) and the baroclinic circulation isintensified (weakened) during spring (neap) tide.
The nature of the surface tidal front and the bottom
thermal front is such that they form not only in shelf seas
but also in bays and inland seas where the change in tidal
current is as large as in the shelf seas. The Seto Inland
Sea (Fig. 1) is a semienclosed sea located in westernJapan. It opens to the Pacific Ocean through the Bungo

FIG. 2. Observational data in July during 1971 to 2000 in Iyonada grouped as spring tide (circles), neap tide (triangles), andothers (squares). Abscissa is the observational month (July) andday. Numbers inside the panel denote the observational year.
Water temperature (8C) is that at 50-m depth for station 3. The
black line shows seasonal variation given by monthly climatology
in June, July, and August, defined at the middle of each month. The
circles with red lines (72, 82, 87, 92, 93, 95, 96, and 98) denote thedata averaged for spring tide, and the averaged result is shown by
a red circle on 15 Jul. The triangles with blue lines (75, 77, 78, 79,
and 88) indicate the data averaged for neap tide, and the averaged
result is shown with a blue triangle on 15 Jul.

JANUARY 2016

161

YU ET AL.

FIG. 3. Bathymetry (m) and model domain of the Seto Inland Sea. The open boundaries are
the south sides of the Bungo Channel (south boundary) and Kii Channel (dashed line). The red
dots along the coastline denote the mouths of rivers. Section AB in the model is denoted asa red line. The yellow triangle in the Hayasui Strait indicates the measurement point for tideelevation and tidal current (Fig. 7).

Channel and Kii Channel, through which the tidal wave
enters the Seto Inland Sea (Yanagi and Higuchi 1981).
Inside the Seto Inland Sea, there are several wide basins
called ‘‘nada’’ in Japanese, including Iyo-nada, Suonada, Hiuchi-nada, and Harima-nada, which are interconnected by narrow straits. The tidal currents arestrong (.1 m s21) in the straits due to the small crosssectional area but weak (;0.1 m s21) in the nadas due totheir large cross-sectional area (Takeoka 2002).
Different tidal mixing capability between the straits
and the nadas results in different vertical density structure in summer between the two areas. Water in thestraits is well mixed and the water temperature increases
from spring to summer simultaneously within the entire
water column. On the other hand, water in the nadas iswarmed quickly in the surface layer and slowly in thebottom layer; consequently strong stratification develops in summer (Takeoka 1985). The tidal fronts,
which have apparent fortnightly variation, are formed in
the surface layer between the well-mixed straits and thestratified nadas (Yanagi and Tamaru 1990).
Another aspect of different tidal mixing in straits andnadas is that the coldest water is found in the bottom
layer of the nadas in summer because stratification there
inhibits downward heat transfer (Takeoka 1985). Although not as sharp as the surface tidal front, a bottom
thermal front can be identified around the coldest waterin summer (Takeoka et al. 1993). The presence of the
BCWs has been suggested to be a key factor of the formation of subsurface chlorophyll-a maximum above andaround the BCWs because of the supply of nutrients fromthe BCW to the area with high chlorophyll-a concentration(Yamamoto et al. 2000). The subtidal current above the
BCW shows surface cyclonic circulation such as that in the

Hiuchi-nada (Guo et al. 2004), Iyo-nada, Suo-nada, andHarima-nada (Chang et al. 2009). However, its fortnightly
variation remains largely unknown.
To date, fortnightly variation in the bottom thermal
front and associated circulation have been examined by
two numerical simulations (Horsburgh and Hill 2003;
Luyten et al. 2003), but examination of fortnightly variation based on observational data remains lacking. Furthermore, there is likely different fortnightly variation in
the bottom thermal front between the inland sea and theshelf sea (e.g., the Irish Sea). As our first objective in thisstudy, we want to confirm the fortnightly variation in thebottom thermal front using observational data. We collected in situ hydrographic data in the Seto Inland Sea
from 1971 to 2000 from the Fishery Research Agency,
Japan, and examined fortnightly variation of the watertemperature gradient across the bottom of the front insummer. Our analysis of the hydrographic data presents astrong bottom thermal front in neap tide rather than inspring tide, which is the opposite of the fortnightly variations identified by the numerical models for the Irish Sea(Horsburgh and Hill 2003).
The second objective in this study is to understand
why the unexpected fortnightly variation in the bottom
thermal front occurs in the Seto Inland Sea and how it

TABLE 1. Model cases and forcing factors.
Case 0Case 1Case 2

Case 3

Case 4

Tide
Heating
River discharge
Winds

Tide

Tide
Heating

Tide
Heating
River discharge

Tide
Heating
Winds

162

JOURNAL OF PHYSICAL OCEANOGRAPHY

VOLUME 46

FIG. 4. Difference in water temperature (8C) between the surface layer (0 m) and bottom layer (the deepest
sampling depth at each station) in the climatology data from April to September, obtained as averages of datacollected in the same months between 1971 to 2000.

affects the fortnightly variation in the circulation above
the bottom thermal front. To reach this goal, we developed a three-dimensional numerical model that can
reproduce the presence of the BCW in the Seto Inland
Sea and the fortnightly variation in the bottom thermal
front found in the observational data.

2. Observational data and model description
Regular hydrographic observations at monthly intervals have been carried out over the past 40 yr byprefectural fishery research centers at 344 stations in the
Seto Inland Sea (Fig. 1), and we were able to obtain datafrom 1971 to 2000, including water temperature andsalinity at depths of 0, 10, 20, 30, 50, 75, and 100 m.
The data were processed as follows: To determine
monthly climatology and to reveal seasonal variation, weaveraged data collected in the same month over 30 yr(1971–2000). As shown later, the bottom thermal front
was well developed in summer (June–August). July was
selected as the best month for examining fortnightly
variations based on June being the rainy season andAugust being the typhoon season in the Seto Inland Sea.
Among several areas of BCW in the Seto Inland Sea, weconcentrated on those in the Iyo-nada having a water
depth of approximately 70 m, close to that in the Irish Sea.
For data analysis based on tides (fortnightly variation), we calculated the moon age from the observational day of every data and chose 5 days centered on
the day of spring (neap) tide as the period for analyzing
data from the same spring (neap) tide. For the BCW in
the Iyo-nada, we chose seven stations (1–7 in Fig. 1)
where the observations were finished in the same day.
During a period from 1971 to 2000, there were eightobservations whose moon age were spring tide andwhose Julian calendar were in the first half of July andfive observations whose moon age were neap tide
and whose Julian calendar were in second half of July(Fig. 2). We defined the former eight observations as
the group for spring tide and the latter five observations
as the group for neap tide. To avoid influences of seasonal variation on fortnightly variation, we calculated
the anomaly of each set of data to its corresponding
seasonal signal and averaged all the anomalies in each

JANUARY 2016

YU ET AL.

163

FIG. 5. Depths (m) of data (black dots), contours (red lines), and magnitude of the horizontal gradient (color) along the samplingstations bisecting the BCW (stations 1 through 7 in Fig. 1). (a),(b) Water temperature (8C); (c),(d) salinity; and (e),(f) density (kg m23).
The units for gradient are 8C km21 for water temperature, km21 for salinity, and kg m23 km21 for density. The upper three panels show thespring tide period, and the lower three panels show the neap tide period. The thick black lines in (e) and (f) denote the position of thebottom boundary layer where the density is 0.5 kg m23 less than that at the deepest data point.

group to represent fortnightly variation. The seasonal
signal corresponding to each set of data was calculated
by substituting the observational date to a seasonalvariation curve given by the monthly climatology that is
the average of all the data in the same month from 1971
to 2000 and is defined at the middle of each month(black thick line in Fig. 2). To obtain a visual effectclose to a field observation, we finally added the seasonal signal on 15 July to the averaged anomaly for thespring tide and neap tide groups, respectively.
The model was applied to the area of the Seto Inland
Sea shown along with the bathymetry in Fig. 3. The
numerical model of Chang et al. (2009) was used in thisstudy without modification. The model is based on the
Princeton Ocean Model, which is a three-dimensional,
primitive equation, sigma-coordinate model (Blumberg
and Mellor 1987; Mellor 2003). It uses a second momentum turbulent closure scheme to calculate the vertical mixing coefficients (Mellor and Yamada 1982) andthe Smagorinsky formulation to parameterize the horizontal mixing coefficients (Smagorinsky 1963).
The model has a spatial resolution of ;1 km (1/ 1208 in
the meridional direction and 1/ 808 in the zonal direction)and 21 sigma layers in the vertical direction. The forcing includes wind stresses, heat flux, evaporation andprecipitation, and river discharges, all of which are
specified in the model using monthly climatology data
(Chang et al. 2009) for the purpose of reproducing

seasonal variations. Along the open boundary, monthly
mean water temperature and salinity values and themonthly normal component of subtidal velocity andsurface elevation are specified from a diagnostic modelwith a larger domain. Tidal currents represented by thesum of four tidal constituents, M2, S2, K1, and O1,
having harmonic constants from a tide model for alarger domain (Guo et al. 2013), were linearly superimposed on the corresponding normal component of
the subtidal velocity at the open boundary.
The model calculation was started in January with a
total integration period of 3 yr. The model results were
saved at 1-h intervals. A tide filter (Hanawa and
Mitsudera 1985) was used to remove the tidal components; the current without the tidal component iscalled a residual current in this study. A stationary
seasonal variation was confirmed by comparing themodel results in the second and third years of model
integration. The analysis was based on model results inthe third year. The settings of the model were divided
into five cases with different considerations of forcing
factors (Table 1): case 0, all forcing factors were considered, including the tide, surface heat flux, river discharge and wind; case 1, only tide was considered; case2, tide and surface heat flux were considered; case 3,
tide, surface heat flux, and river discharge were considered; and case 4, tide, surface heat flux, and wind
were considered.

164

JOURNAL OF PHYSICAL OCEANOGRAPHY

VOLUME 46

FIG. 6. Difference of monthly averaged water temperature (8C) between the surface layer (0 m) and bottom layer(the deepest grid point) from April to September (case 0).

3. Resultsa. Observational data
We used the difference in water temperature between
the surface layer (0 m) and the bottom layer (the deepest

sampling depth at each station) to demonstrate the development of seasonal stratification in the Seto Inland
Sea from April to September (Fig. 4). Temperature
differences began to appear in April, increased from
May to June, reached a maximum in July and August,

FIG. 7. (a) Tide elevation (m) and (b) tidal current velocity (m s21) in the Hayasui Strait(yellow triangle in Fig. 3) in case 1. In (a), S indicates spring tide and N indicates neap tide. The
red dots in (a) indicate the day corresponding to spring and neap tides, on which the model
results are presented in the following figures.

JANUARY 2016

YU ET AL.

165

FIG. 8. Model result (red line) and magnitude of its horizontal gradient (color) along section AB. (a),(b) Water temperature (8C);(c),(d) salinity; and (e),(f) density (kg m23) for case 0. The units for gradient are 8C km21 for water temperature, km21 for salinity, andkg m23 km21 for density. Color in (e) and (f) denotes the velocity (m s21) of normal residual current to section AB. Positive values indicate
current flowing northwestward, while negative values indicate current flowing southeastward. Arrows in (e) and (f) indicate the residual
current (m s21) along section AB. The position of section AB is shown in Fig. 3. The upper three panels show data from a day in spring tide
(red S in Fig. 7), and the lower three panels show data from a day in neap tide (red N in Fig. 7). The thick red lines in (e) and (f) denote theposition of the bottom boundary layer where the density is 0.5 kg m23 less than that of the bottom grid point. The black boxes in (a) and(b) show the area where the maximum bottom temperature gradient is, as shown in Fig. 10a.

and disappeared in September. Along with seasonalvariation, there was also apparent spatial variation:
larger in the nadas and smaller in the straits. The areas
with the largest differences in water temperature in thenadas in July corresponded to areas of BCW.
Along the stations bisecting the BCW in the Iyo-nada(labeled 1–7 on the black line in Fig. 1), the lowest watertemperature was found at a depth of 50 m at station 4,
but the highest temperature at the sea surface was observed at the same station (Figs. 5a,b). The water temperature at station 1 was generally homogeneous.
Consequently, the greatest vertical difference in watertemperature was at station 4 and the smallest is at station
1. This spatial structure is maintained at both spring tideand neap tide (Figs. 5a,b). Salinity was generally low inthe surface layer but was higher in the bottom layer(Figs. 5c,d). The influence of salinity on the spatial
structure of the density field was slight, and the spatial
variations in the density field were essentially determined by water temperature (Figs. 5e,f).
The fortnightly variation in temperature, salinity, anddensity shown in Fig. 5 illustrates that the greatest variation is found mainly in the horizontal gradients in thebottom water for temperature and density, which were
smaller in spring tide (Figs. 5a,e) than in neap tide
(Figs. 5b,f). The maximum horizontal gradient of bottom water temperature was ;0.078C km21 in spring tide
(Fig. 5a) and ;0.098C km21 in neap tide (Fig. 5b), increasing by ;0.028C km21 from spring tide to neap tide.
The bottom thermal front defined as the place with the
maximum horizontal gradient of water temperature was
located between stations 2 and 3, and its position

166

JOURNAL OF PHYSICAL OCEANOGRAPHY

VOLUME 46

FIG. 9. (a) Horizontal distribution of water temperature (8C; red line) and the magnitude of the gradient (8C km21; color) at a depth of
45 m in spring tide; (b) as in (a), but for neap tide; residual currents (m s21) at depths of (c) 10 m and (e) 45 m for spring tide; residual
currents (m s21) at depths of (d)10 m and (f) 45 m for neap tide. All results are from case 0. The arrows in (c)–(f) show the direction of thecurrent, while the color indicates the magnitude of current.

changed little with the spring–neap tidal cycle. The
fortnightly variation in the horizontal gradient of bottom water temperature here is the opposite of the pattern observed in the Irish Sea where the horizontal
gradient of bottom water temperature is larger in springtide than in neap tide (Horsburgh and Hill 2003).

b. Model results
The horizontal distribution of water temperature
differences between the surface layer (0 m) and bottom
layer (the deepest depth on each model grid) in themodel results shows that stratification in the nadas starts
in April, increases in May and June, becomes strongest
in July and August, and gradually decreases in September (Fig. 6). This progression is consistent with theobservational data (Fig. 4).
The enclosed structure of water temperature difference
between the surface layer and bottom layer, corresponding to the presence of BCW, is also found in themodel results. By comparing the location of BCWs
(Figs. 4, 6) with the distribution of the Simpson–Hunterparameter log10(H/U3) (Fig. 4 in Takeoka 2002; H iswater depth; U is amplitude of tidal currents) or that estimated by using our model results (data not shown), it isapparent that the BCWs approximately overlap withareas with a large value of log10(H/U3) where the tidal
mixing is weak. This fact suggests that the spatial variation of tidal mixing is an essential condition for the formation and location of BCW and bottom thermal front.

1) FORTNIGHTLY VARIATION OF HORIZONTALGRADIENT OF BOTTOM WATER TEMPERATURE
IN IYO-NADA

From the time series of tide elevation (Fig. 7a) andtidal current velocity (Fig. 7b) at the Hayasui Strait(indicated by a yellow triangle in Fig. 3) in July based on
the results of a model driven by tide forcing alone (case1), we can see that there are three spring tides (1, 15, and
29 July) and two neap tides (8 and 22 July). The tideelevation ranged from about 21.5 to 1 m in spring tideand from 20.5 to 0.5 m in neap tide. The tidal current
was about 1.5 m s21 in spring tide and 0.4 m s21 in neap
tide. For a purpose of examining fortnightly variations in
the bottom thermal front and associated residual currents, we mainly analyzed the results on 8 July (neaptide) and 15 July (spring tide).
The model results were similar to observational data,
showing a general spatial distribution of water

JANUARY 2016

YU ET AL.

167

FIG. 10. (a) Time series of the maximum value of the water temperature gradient (8C km21)
within the area of the black box in Fig. 8a for each of the four cases. (b) Time series of BBL
thickness (m; red thick line in Fig. 8e) at the location with maximum water temperature gradient shown in (a) for four cases.

temperature across the BCW in the Iyo-nada that does
not change with the modulation of spring and neap tides(Figs. 8a,b). The fortnightly variation appears mostly inthe horizontal gradient of bottom water temperaturethat is larger in neap tide than in spring tide by about
0.258C km21 (Figs. 8a,b). The pattern of salinity in themodel results (Figs. 8c,d) was similar to that in the observational data, being low in the surface layer and highin the bottom layer. The bottom layer density generally
follows the water temperature, and its gradient is also
larger in neap tide than in spring tide, inferred from thespaces among contour lines (Figs. 8e,f).
The magnitude of the horizontal temperature gradient at a depth of 45 m indicates that an increased horizontal gradient of water temperature in neap tideoccurred in a large area between the Iyo-nada and the
Hayasui Strait (Figs. 9a,b). The water temperatures
ranged from 17.08 to 18.58C in a narrowband in neap tide
(Fig. 9b) and from 17.58 to 19.08C in a slightly wider bandin spring tide (Fig. 9a).
The time series of the maximum horizontal gradientof bottom water temperature around the bottom
thermal front (area enclosed in the black box in
Figs. 8a and 8b) showed a sequential modulation in
July with a cycle between spring tide and neap tide
(black line in Fig. 10a), which was smaller in springtide and larger in neap tide. The magnitude had a value
of ;0.358C km21 in spring tide and ;0.658C km21 inneap tide. These values are slightly larger than theobserved results, but the intensification of the bottom

thermal front in neap tide is consistent with theobservations.

2) FORTNIGHTLY VARIATION OF CIRCULATION IN
IYO-NADA
From the vertical distribution of the residual current
normal to section AB (color tone in Figs. 8e,f), we canidentify three major structures. One is a generally positive
surface current near the strait (x coordinate 5 0–15 km).
The others are from surface layer to subsurface layer:a negative current structure from 15 to 35 km and a positive current structure from 35 to 55 km. The two opposite
currents are ;0.15 m s21 in neap tide and ;0.10 m s21 inspring tide.
The two opposite currents are a part of the cyclonic
circulation above the BCW in Iyo-nada (Figs. 9c,d). This
circulation is slightly stronger in neap tide than in springtide. For example, the northeastward current on theeastern side of the cyclonic circulation was about 0.12
to 0.16 m s21 in neap tide but 0.08 to 0.12 m s 21 inspring tide.
The residual current parallel to section AB (arrows in
Figs. 8e,f) flows from the BCW to the strait in the surface
layer but from the strait to the BCW in the bottom layer.
The surface current parallel to section AB is likely a partof the southwestward current on western side of thecyclonic circulation above the BCW (Figs. 9c,d). After
passing the area of BCW, this surface current separates
from the cyclonic circulation above the BCW and flows
toward the strait. The bottom current parallel to section

168

JOURNAL OF PHYSICAL OCEANOGRAPHY

VOLUME 46

FIG. 11. Horizontal distribution of water temperature (8C; red line) and magnitude of gradient (8C km21; color overlay) at a depth of 45 m
for cases 2, 3, and 4. (top) Spring tide and (bottom) neap tide.

AB is strong in the area close to the strait and weak in
the area of BCW (Figs. 9e,f). Between the strait and theBCW, the bottom current is weak and does not have afixed direction in neap tide but has a strong and fixed
direction in spring tide (Figs. 9e,f). As shown in section
4a, this fortnightly variation of bottom residual current
between the strait and the BCW plays an important rolein the fortnightly variation of bottom thermal front.

The horizontal gradient of the bottom water temperature has similar temporal variation in cases 0 and 3(Fig. 10a), indicating that wind plays a negligible role infortnightly variation. The same implications are present
for similar temporal variations of horizontal gradient ofbottom water temperature in cases 2 and 4 (Fig. 10a).

4. Discussion
a. Causes of stronger horizontal gradient of bottom
water temperature in neap tide than in spring tide
The formation of the BCW is essentially caused by surface heating and spatial variation in tidal mixing; the fortnightly variation in the BCW is therefore generally
considered to be a result of the change in local mixing ability.
However, other processes such as the change in ambient
currents with tidal modulation can also modify the relation
between the BCW and the tidal cycle. To find the dynamicalcauses for the intensification of the bottom horizontal gradient of water temperature in neap tide in our study area,
which was confirmed by both observational data and model
results, we designed three numerical experiments (Table 1)with the following forcing factors: tide and surface heat flux
(case 2); tide, surface heat flux, and river discharge (case 3);
and tide, surface heat flux, and wind (case 4).

FIG. 12. Time series of water temperature (8C; after being detided by a tide filter) at grid point M (red line) and grid point N(blue line) shown on Fig. 9a at a depth of 45 m for case 0; S and N in
red represent spring tide and neap tide, respectively.

JANUARY 2016

YU ET AL.

169

FIG. 13. (a) Daily increase in water temperature, (b) sum of advection and vertical diffusion terms, (c) advection
term, (d) vertical diffusion term [contour interval (CI) 5 0.05] in July at grid point M for case 0; S and N in red
represent spring and neap tides, respectively (All values 8C).

Case 2 shows a little stronger horizontal gradient ofbottom water temperature in neap tide than in springtide, but the magnitude of the gradient and its fortnightly variation range are much smaller than those incase 0 (Fig. 10a). Case 3 shows a similar magnitude of
gradient of bottom water temperature and a similar
fortnightly variation range as case 0. Therefore, riverdischarge is an important forcing factor for the magnitude of the bottom water temperature gradient and its
fortnightly variation in our study area.
The fortnightly variations of the bottom boundary layer(BBL) in four cases (Fig. 10b) are the same: thick in springtide and thin in neap tide, corresponding well to the changeof tidal mixing. On the other hand, the BBL changes
largely among four cases: thicker in cases 2 and 4 than incases 0 and 3 and thicker in case 3 than in case 0. The
addition of river discharge intensifies stratification andtherefore suppresses the development of BBL in cases
0 and 3. The difference between case 0 and case 3 is thewind stresses, the inclusion of which probably intensifies
surface mixing in case 0, promotes downward transport ofsurface water with low salinity and high temperature water, and results in a thinner BBL in case 0 than in case 3.

The horizontal distribution of water temperature andits gradient at a depth of 45 m in cases 2, 3, and 4 (Fig. 11)
confirms the interpretation from Fig. 10a. Cases 2, 3, and4 also show a larger gradient of water temperature inneap tide than in spring tide, which is the same as case0 (Fig. 9). In cases 2 and 4, the magnitude of the temperature gradient and its fortnightly variation range aresmaller than those in case 0 (Fig. 9), while in case 3 themagnitude of the temperature gradient and its fortnightly variation range becomes larger, which is close to
those in case 0 (Fig. 9).
To demonstrate the critical process in the fortnightly
variation described earlier, we compared the results at
two grid points (M and N in Fig. 9a) in case 0. Point M is
located inside the BCW, while point N is at the outeredge of the BCW. The temperature at point M increased
at almost the same rate during the spring–neap–spring
tidal cycle (Fig. 12). However, the temperature at point
N increased much faster from spring tide to neap tide,
stopped, or even decreased around neap tide and thenincreased to the next spring tide. Such differences in therate of increase between points M and N induce a larger
difference between these two points in neap tide than in170

JOURNAL OF PHYSICAL OCEANOGRAPHY(a) deltTVOLUME 46(b) sum of advective and vertical diffusion0
Depth(m)

10
20
30
40
50
S

N
(c) Advection

SSN(d) Vertical diffusion

S

N
8

S
15

S
1

N
8

S
15

0
Depth(m)

10
20
30
40
50
S
1

−0.5 −0.4 −0.3 −0.2 −0.1

0

0.1 0.2 0.3 0.4 0.5

FIG. 14. As in Fig. 13, but for grid point N.

spring tide and finally generate the larger gradient inneap tide than in spring tide.
To identify an explanation for the different rate ofbottom water temperature increase inside and outside
the BCW, we calculated the contribution of the terms in
the equation for water temperature.
The change in water temperature T over change intime t is given by›T
5 AdvT 1 VdfT 1 HdfT 1 RadT ,›t(1)where AdvT is the advection term, VdfT is the vertical diffusion term, HdfT is the horizontal diffusion term, RadT isthe radiation term, and the overbar above each term is thetide filter. The daily change in water temperature can beobtained by integrating Eq. (1) over 24 h as shown in Eq. (2):
ð 24
ð 24
AdvT dt 1
VdfT dt
DT daily 5
0

1

ð 24
0

0

HdfT dt 1ð 24
RadT dt .

(2)0

Since the horizontal diffusion term is much smaller than
the advection and vertical diffusion terms, and theradiation term does not vary with tidal cycle, we focus on
the relationship between the advection and vertical diffusion terms with respect to the daily change in temperature.
The daily change of water temperature at point M(Fig. 13a) is mainly controlled by the advection and vertical diffusion terms because the sum of advection andvertical diffusion terms (Fig. 13b) may explain almost allof the variations in Fig. 13a. The advection in the midlayer
is generally positive (Fig. 13c), indicating that advection
brings warmer water, therefore increasing the watertemperature at point M. The vertical diffusion term in the
midlayer is generally negative (Fig. 13d), indicating thatthe heat transferred to the midlayer by advection is distributed downward through vertical diffusion. Both advection and vertical diffusion show greater values in thespring tide than in neap tide, but the sum of the two does
not show apparent fortnightly variation (Fig. 13b). Consequently, the water temperature at point M increases atthe same rate during the spring–neap–spring tidal cycle.
The variation of water temperature at point N(Fig. 14a) is also controlled by the advection and vertical
diffusion term (Fig. 14b). The advection (Fig. 14c) andvertical diffusion (Fig. 14d) terms at point N show similar patterns as those at point M, but there are also some

JANUARY 2016

YU ET AL.

171

FIG. 15. Horizontal distribution of residual current (m s21; arrow), water temperature (8C; red line; CI 5 0.25), and the component ofresidual current (m s21) flowing along the direction of the water temperature gradient [color; defined by Eq. (3)] at a depth of 45 m on 1, 4,
8, 10, and 15 Jul, covering a cycle from spring tide to the next spring tide for case 0.

notable differences. The advection term is much larger
in the spring tide but becomes negative shortly after
neap tide in the midlayer. This process induces the sumof advection and vertical diffusion to be much larger inspring tide but negative after neap tide. The change insign of the advection term is likely caused by the change
in the current field because the horizontal gradient ofwater temperature does not change its sign during thespring–neap–spring tidal cycle. As a result, the watertemperature at point N increases faster from spring tideto neap tide but stops or even decreases after neap tide.
Therefore, we attribute the different fortnightly variation of water temperature at points M and N to the advection term at point N.
To see what really occurs in the advection process, we
calculated the residual current component UV in the
direction along the gradient of water temperature using
the following equation:
›T
›T
1y
u
V  =T›x›y
5 sﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ
UV 5
 2  2ﬃ .
j=Tj
›T
›T
1
›x
›y

(3)

Here, u and y are the eastward and northward components, respectively, of the residual current. If UV is
positive, the residual current in the direction across theisotherms brings colder water to areas with high temperature and vice versa. From the horizontal distribution of UV (color overlay in Fig. 15) and residual
currents (black arrows in Fig. 15) at a depth of 45 m, we
can clearly see that there is a strong negative value areafrom the strait to the nada during the spring tide (1 July;Fig. 15a), which brings warmer water from the strait tooutside of the BCW and increases the temperature
there. This negative current is maintained on 4 July(Fig. 15b) but weakens or even becomes positive near
the outside of the BCW during neap tide (8 July;Fig. 15c), indicating that it transfers colder water to theoutside of the BCW from the inside. The UV stays
positive after neap tide (10 July; Fig. 15d) but becomes
negative again in spring tide (15 July; Fig. 15e). Consequently, the water temperature at N increases much
faster from spring tide to neap tide and stops or evendecreases after neap tide.
The residual current in case 1 (data not shown), that is,
tide-induced residual current, flows from the strait to thenada and is stronger in spring tide than in neap tide.

172

JOURNAL OF PHYSICAL OCEANOGRAPHY

VOLUME 46

FIG. 16. Density (kg m23, black contours), residual current component normal to section AB (m s21; color), and residual current
component parallel to section AB (m s21, arrows) for cases 2, 3, 4, and the difference between cases 2 and 3 (case 3 2 case 2). Positive
values for residual current component normal to section AB indicate inward current while negative values indicate outward current.
Section AB is shown in Fig. 3. (top) Spring tide (red S in Fig. 7) and (bottom) neap tide (red N in Fig. 7). The thick red lines denote theposition of the bottom boundary layer where the density is 0.5 kg m23 less than that of bottom grid point. The density in cases 2 and 4 iscalculated by setting salinity to 34.

Since it is strong only in the vicinity of the strait andcannot bring warm water from the strait to central areaof the nada, this tide-induced residual current can only
partly explain the strong and negative UV from the strait
to the nada during the spring tide in case 0 (Fig. 15a).
The addition of river discharge in case 3 nearly reproduced the strong and negative UV from the strait to thenada during the spring tide in case 0 (Fig. 15a), indicating that the bottom estuarine current also plays arole in carrying warm water from the strait to the central
area of the nada. The addition of surface heating in case
2 and that of winds in case 4 has little effect on explaining the movement of warm water from the strait to
the nada in spring tide. Therefore, advection heating by
tide-induced residual current and the bottom estuarine
current from the strait to the BCW are both importantcausative factors for the temperature increase outside of
the BCW in spring tide.
A comparison of the residual current along section
AB in cases 2–4 presents more information on the effects of the bottom residual current on the bottom
thermal front (Fig. 16). The bottom residual current
flows from the strait to the BCW in cases 2–4. This

current in case 3 is stronger in spring tide (Fig. 16c) thanin neap tide (Fig. 16d). Such fortnightly variation is apparent in case 0 (Figs. 8e,f) but not apparent in cases 2
and 4. The difference between case 3 and case 2 shows astronger bottom current in the area between the strait
and the BCW (Figs. 16g,h), which must be a part of estuarine circulation over the entire basin because thedifference in the boundary condition between two cases
is the inclusion of river discharge in case 3 but exclusion of
it in case 2. The fortnightly variation of the difference inresidual currents between case 3 and case 2, which isstronger in neap tide than in spring tide, is also consistent
with the well-known response of an estuarine circulation
to the variation of tidal mixing with spring–neap tidal
cycle, that is, the strong tidal mixing in spring tideinduces a weak estuarine circulation and vice versa.
Although being the same tidally influenced sea, thebottom thermal front in the Irish Sea is strong in springtide but weak in neap tide (Horsburgh and Hill 2003).
This fortnightly variation is opposite to that in our study
area. Holt and Proctor (2003) mentioned a current fromthe North Channel to the Irish Sea and its important rolein bringing warm water to the BCW in the Irish Sea.

JANUARY 2016

YU ET AL.

173

FIG. 17. Horizontal distribution of residual current at a depth of 10 m for cases 2–4. (top) Spring tide and (bottom) neap tide. The arrowshows the direction of current and the color overlay shows the magnitude of the current (m s21).

Since the current from the North Channel to the Irish
Sea is influenced by shelf edge flow and wind (Xing andDavies 2001a), we suppose that its fortnightly variationis small and does not affect the fortnightly variation in
the gradient of the bottom thermal front in the Irish Sea.
Therefore, the gradient of the bottom thermal front in
the Irish Sea is controlled mainly by the fortnightly
variation of tidal mixing around the bottom thermal
front, that is, the mixing area expands toward thestratification area in spring tide and retreats in neap tide;consequently, the gradient of the bottom thermal front
in the Irish Sea is stronger in spring tide than in neap tide
(Horsburgh and Hill 2003).
In our study area, not only tidal mixing but also bottom residual current in the direction of the cross front
affect the gradient of the bottom thermal front. As
demonstrated by our sensitivity experiments, the intensification of bottom residual currents between thestrait and the BCW in case 3 induces a strong fortnightly
variation in the gradient of the bottom thermal front. In
some sense, the bottom residual currents between thestrait and the BCW in our study area act as a ‘‘bridge’’ tobring the warm water from the strait to the outside of the
BCW. The arrival of warm water at the outside of the
BCW then intensifies the bottom thermal front. A
comparison of case 2 and case 3 also supports this scenario. The bottom residual current in the cross-front
direction between the strait and the BCW is stronger incase 3 than in case 2; the gradient of the bottom thermal

front is also stronger in case 3 than in case 2. Therefore, astronger bottom residual current in the cross-front direction between the strait and the BCW induces astronger bottom thermal front, as also demonstrated by
the fortnightly variation of those in case 3. Therefore,
the different behavior of ambient currents in the crossfront direction between our study area and the Irish Sea
is the essential cause for the opposite fortnightly variation of bottom thermal front in two regions.

b. How does the bottom density gradient influence thesurface cyclonic circulation during the spring–neaptidal cycle?
As described above, we set three cases (cases 2–4) toelucidate the variation of cyclonic circulation influenced
by heating (case 2), river discharge (case 3), and wind(case 4). In case 2, even though the bottom temperature
gradient is larger in neap tide than in spring tide, thehorizontal distribution at the depth of 10 m (Figs. 17a,b)
and the vertical distribution at the AB section (color;
Figs. 16a,b) of the cyclonic circulation both showed circulation is larger in spring tide than in neap tide, which is
the opposite of the pattern in case 0 (Figs. 8e,f; Figs. 9c, d).
The addition of wind in case 4 (color; Figs. 16e,f, 17e,f)
did not change the fortnightly variation in the surface
cyclonic circulation in case 2. However, the addition ofriver discharge in case 3 (color; Figs. 16c,d, 17c,d) produces consistent fortnightly variation in the surface cyclonic circulation as observed for case 0.

174

JOURNAL OF PHYSICAL OCEANOGRAPHY

VOLUME 46

FIG. 18. Vertical distribution of the (a) time variable term, (b) advection term, (c) Coriolis force, (d) pressure gradient, and (e) verticalviscosity term in the momentum equation in the direction along section AB on 15 July (spring tide) for case 0 (CI 5 2) (All values m2 s22).

To understand dynamical causes for the different
fortnightly variations in the surface cyclonic circulationin cases 0, 2, 3, and 4, we calculated the terms of the
momentum equation [Eq. (4)] in the direction along the
AB section in case 0 and applied the tide killer filter toevery term to obtain tide-averaged results (Fig. 18):
›DU
1 adv 1 cor 1 pre 1 ver_vis 1 Fx 5 0.
›t

(4)Here, D is water depth, U is the velocity component
along the AB section, adv is the advection term, cor is
the Coriolis forcing term, pre is the pressure gradientterm, ver_vis is the vertical eddy viscosity term, and Fx isthe horizontal eddy viscosity term. The overbar above
each term is the tide filter.
Along section AB, the major momentum balance near
the strait (0–15 km) is between the advection term
(Fig. 18b) and the pressure gradient term (Fig. 18d),
from which we can infer that a tide-induced residual
current dominates in this area. In the area from 15 to

55 km, the major momentum balance is between the
Coriolis force (Fig. 18c) and the pressure gradient force(Fig. 18d), from which we can infer that the cyclonic
circulation above the BCW is a geostrophic current.
Based on the thermal-wind equation (Gill 1982) andassuming zero velocity at the sea bottom, we calculate
the geostrophic current normal to section AB using themodeled density field (Fig. 19). The result showed acyclonic circulation pattern from surface to subsurface,which is stronger in neap tide than in spring tide in case
0 and case 3 but is weaker in neap tide than in spring tidein case 2 and case 4 (Fig. 19). Since all of these featuresare similar to the residual currents calculated by thenumerical model (Figs. 8e,f, 16), the geostrophic balance
likely works well to explain the dynamics of the cyclonic
circulation above the BCW.
Here, we consider the fortnightly variation of
the cyclonic circulation above the BCW from theperspective ofÐ geostrophic balance. The velocityzV(z) 5 2g/(rf ) 2h (›r)/(›x) dz, based on the thermalwind equation, is not only related to the horizontal
density gradient ›r/›x, but also depends on theJANUARY 2016

YU ET AL.

175

FIG. 19. Vertical distribution of calculated geostrophic current (m s21) from thermal-wind equation by using modeled density at section
AB in Iyo-nada for case 0 and cases 2, 3, and 4 in (top) spring tide and (bottom) neap tide.

thickness of the BBL, where the horizontal density
gradient is present. From Figs. 8e and 8f and Fig. 16, we
can see that the BBL is thicker in spring tide than inneap tide in all cases. The observed BBL (Figs. 5e,f) is
thicker in spring tide than in neap tide and is much
more pronounced for station 3. This verifies that themodeled BBL is thicker in spring tide than in neap tide.
The effect of BBL thickness on the cyclonic circulation above the BCW is different in all of the cases. In
cases 0 and 3, the BBL is generally thin (Fig. 10b), andthe bottom density gradient and its fortnightly variation
are generally large (Fig. 10a). Therefore, the cyclonic
circulation above the BCW follows the fortnightly variation in the bottom density gradient, being strong inneap tide but weak in spring tide. In cases 2 and 4,
however, the BBL is generally thick (Fig. 10b), and thebottom density gradient and its fortnightly variation are
generally small (Fig. 10a). Therefore, the cyclonic circulation above the BCW follows the fortnightly variations in the BBL thickness, being strong in spring tide
but weak in neap tide.

5. Conclusions
The results based on observational data and modelingboth show that the bottom temperature gradient inspring tide is smaller than that in neap tide in Iyo-nada of
the Seto Inland Sea in July, which is different from thepattern observed in the Irish Sea where the bottom front
gradient is larger in spring tide than in neap tide. The
main mechanism causing such a different pattern in Iyonada and the Irish Sea is likely to be the horizontal advection of heat by the residual currents in Iyo-nada.
The temperature in the center of the BCW in Iyonada increased at almost the same rate during thespring–neap–spring tidal cycle, while that outside of the
BCW increased sharply from spring tide to neap tide,
decreased shortly after neap tide, and then increased
again for the next spring tide. The sharp increase intemperature during spring tide was induced by the crossfront bottom residual current, bringing warmer waterfrom the strait. This cross-front current is actually a
combination of tide-induced residual current and thebottom estuarine current from the strait to the nada,
which finally induced the larger temperature difference,that is, the larger temperature gradient in neap tide thanin spring tide. Therefore, the difference between the
Iyo-nada and the Irish Sea is that the bottom front gradient should be explained by the differing horizontal
water advection and vertical mixing. In the Iyo-nada,both vertical mixing and horizontal advection are important in determining the bottom temperature gradient

176

JOURNAL OF PHYSICAL OCEANOGRAPHY

during spring–neap tidal cycles. In the Irish Sea, verticalmixing is the major factor in determining the bottom
temperature gradient during the spring–neap tidal cycle.
The BBL in Iyo-nada in summer is thicker in springtide than in neap tide in both observational data andmodeling results because the larger tidal current
generates a larger vertical diffusion coefficient and thus
forms a thicker BBL in spring tide.
The cyclonic circulation above the BCW is mainly ingeostrophic balance. When considering the effect of tide,surface heating, and wind, the bottom density gradientchanges little during the spring–neap tidal cycle, and theeffect of BBL thickness on the cyclonic circulation islarger than that of the bottom density gradient; thus, thecyclonic circulation is stronger in spring tide than in neap
tide. However, after adding the influence of river discharge, the bottom density gradient changes greatly
during the spring–neap tidal cycle; meanwhile, the BBL
becomes thin because of the intensification of stratification by river runoff. Consequently, the effect of the bottom density gradient on circulation becomes large,
inducing greater circulation in neap tide than in springtide. In the Irish Sea, both the bottom temperature gradient and the BBL thickness are larger in spring tide thanin neap tide (Horsburgh and Hill 2003); therefore, cyclonic circulation is larger in spring tide than in neap tide.
Acknowledgments. This study was supported byfunding from JSPS KAKENHI (26287116). X. Yu
thanks the China Scholarship Council (CSC) and Agriculture, Forestry and Fisheries Research Council for
supporting her stay in Japan. The authors thank the tworeviewers for their insightful comments that helped to
improve the original manuscript.
REFERENCES
Blumberg, A. F., and G. L. Mellor, 1987: A description of a three
dimensional coastal ocean circulation model. Three-Dimensional
Coastal Ocean Models, Coastal Estuarine Sci. Monogr., Vol. 4,
Amer. Geophys. Union, 1–16, doi:10.1029/CO004p0001.
Brown, J., A. E. Hill, L. Fernand, and K. J. Horsburgh, 1999: Observations of a seasonal jet-like circulation at the central North
Sea cold pool margin. Estuarine Coastal Shelf Sci., 48, 343–355,
doi:10.1006/ecss.1999.0426.
——, L. Carrillo, L. Fernand, K. J. Horsburgh, A. E. Hill, E. F.
Young, and K. J. Medler, 2003: Observations of the physicalstructure and seasonal jet-like circulation of the Celtic Sea and
St. George’s Channel of the Irish Sea. Cont. Shelf Res., 23,
533–561, doi:10.1016/S0278-4343(03)00008-6.
Chang, P.-H., X. Guo, and H. Takeoka, 2009: A numerical study ofthe seasonal circulation in the Seto Inand Sea, Japan.
J. Oceanogr., 65, 721–736, doi:10.1007/s10872-009-0062-4.
Davies, A. M., and J. Xing, 2006: Effect of topography and mixing
parameterization upon the circulation in cold water domes.
J. Geophys. Res., 111, C03018, doi:10.1029/2005JC003066.

VOLUME 46

Gill, A. E., 1982: Atmosphere–Ocean Dynamics. Academic Press,
662 pp.
Guo, X., A. Futamura, and H. Takeoka, 2004: Residual currents
in a semi-enclosed bay of the Seto Inland Sea, Japan.
J. Geophys. Res., 109, C12008, doi:10.1029/2003JC002203.
——, K. Harai, A. Kaneda, and H. Takeoka, 2013: Simulation of
tidal currents and nonlinear tidal interactions in the Seto Inland Sea, Japan. Rep. Res. Inst. Appl. Mech. Kyushu Univ.,
145, 43–52.
Hanawa, K., and H. Mitsudera, 1985: On daily average of oceanographic data (in Japanese). Coastal Oceanogr. Bull., 23, 79–87.
Hill, A. E., 1996: Spin down and the dynamics of dense pool gyresin shallow seas. J. Mar. Res., 54, 471–486, doi:10.1357/
0022240963213538.
——, R. Durazo, and D. A. Smeed, 1994: Observations of a cyclonic gyre in the western Irish Sea. Cont. Shelf Res., 14, 479–
490, doi:10.1016/0278-4343(94)90099-X.
——, J. Brown, and L. Fernand, 1997: The summer gyre in thewestern Irish Sea: Shelf sea paradigms and management implications. Estuarine Coastal Shelf Sci., 44, 83–95, doi:10.1016/
S0272-7714(97)80010-8.
——, ——, ——, J. Holt, K. J. Horsburgh, R. Proctor, R. Raine,and W. R. Turrell, 2008: Thermohaline circulation of shallow
tidal seas. Geophys. Res. Lett., 35, L11605, doi:10.1029/
2008GL033459.
Holt, J. T., and R. Proctor, 2003: The role of advection in determining the temperature structure of the Irish Sea. J. Phys.
Oceanogr., 33, 2288–2306, doi:10.1175/1520-0485(2003)033,2288:
TROAID.2.0.CO;2.
Horsburgh, K. J., and A. E. Hill, 2003: A three-dimensional model ofthe density-driven circulation in the Irish Sea. J. Phys. Oceanogr., 33, 343–365, doi:10.1175/1520-0485(2003)033,0343:
ATDMOD.2.0.CO;2.
——, ——, J. Brown, L. Fernand, R. W. Garvine, and M. M. P.
Angelico, 2000: Seasonal evolution of the cold pool gyre in thewestern Irish Sea. Prog. Oceanogr., 46, 1–58, doi:10.1016/
S0079-6611(99)00054-3.
Lie, H.-J., 1989: Tidal fronts in the southeastern Hwanghae(Yellow Sea). Cont. Shelf Res., 9, 527–546, doi:10.1016/
0278-4343(89)90019-8.
Loder, J. W., and D. A. Greenberg, 1986: Predicted positions of
tidal fronts in the Gulf of Maine region. Cont. Shelf Res., 6,
397–414, doi:10.1016/0278-4343(86)90080-4.
Luyten, P. J., J. E. Jones, and R. Proctor, 2003: A numerical studyof the long- and short-term temperature variability and thermal circulation in the North Sea. J. Phys. Oceanogr., 33, 37–56,
doi:10.1175/1520-0485(2003)033,0037:ANSOTL.2.0.CO;2.
Lwiza, K. M. M., D. G. Bowers, and J. H. Simpson, 1991: Residual
and tidal flow at a tidal mixing front in the North Sea. Cont.
Shelf Res., 11, 1379–1395, doi:10.1016/0278-4343(91)90041-4.
Mellor, G. L., 2003: Users guide for a three-dimensional, primitive
equation, numerical ocean model (2003 version). Atmosphericand Oceanic Sciences Program, Princeton University Rep., 53 pp.
——, and T. Yamada, 1982: Development of a turbulence closure
model for geophysical fluid problems. Rev. Geophys., 20, 851–
875, doi:10.1029/RG020i004p00851.
Mountain, D. G., and M. H. Taylor, 1996: Fluorescence structure in
the region of the tidal mixing front on the southern flank ofGeorges Bank. Deep-Sea Res. II, 43, 1831–1853, doi:10.1016/
S0967-0645(96)00054-9.
Ou, H. W., 1984: Geostrophic adjustment: A mechanism forfrontogenesis. J. Phys. Oceanogr., 14, 994–1000, doi:10.1175/
1520-0485(1984)014,0994:GAAMFF.2.0.CO;2.

JANUARY 2016

YU ET AL.

Simpson, J. H., and J. R. Hunter, 1974: Fronts in the Irish Sea.
Nature, 250, 404–406, doi:10.1038/250404a0.
——, and D. Bowers, 1981: Models of stratification and frontal
movement in shelf seas. Deep-Sea Res., 28A, 727–738,
doi:10.1016/0198-0149(81)90132-1.
——, and J. Sharples, 1994: Does the Earth’s rotation influence thelocation of the shelf sea fronts? J. Geophys. Res., 99, 3315–
3319, doi:10.1029/93JC03281.
——, C. M. Allen, and N. C. G. Morris, 1978: Fronts in the continental shelf. J. Geophys. Res., 83, 4607–4614, doi:10.1029/
JC083iC09p04607.
Smagorinsky, J. S., 1963: General circulation experiments withthe primitive equations. I. The basic experiment. Mon. Wea.
Rev., 91, 99–164, doi:10.1175/1520-0493(1963)091,0099:
GCEWTP.2.3.CO;2.
Su, J. L., and D. J. Huang, 1995: On the current field associatedwith the Yellow Sea cold water mass. Oceanol. Limnol. Sin.,
26, 1–7.
Sun, Y.-J., and A. Isobe, 2006: Numerical study of tidal front withvarying sharpness in spring and neap tidal cycle. J. Oceanogr.,
62, 801–810, doi:10.1007/s10872-006-0099-6.
Takeoka, H., 1985: Density stratification in the Seto Inland Sea.
Umi Sora, 60, 145–152.
——, 2002: Progress in Seto Inland Sea research. J. Oceanogr., 58,
93–107, doi:10.1023/A:1015828818202.
——, O. Matsuda, and T. Yamamoto, 1993: Processes causing thechlorophyll a maximum in the tidal front in Iyo-nada, Japan.
J. Oceanogr., 49, 57–70, doi:10.1007/BF02234009.

177

Wang, D. P., D. Chen, and T. J. Sherwin, 1990: Coupling between
mixing and advection in a shallow sea front. Cont. Shelf Res.,10, 123–136, doi:10.1016/0278-4343(90)90026-I.
Xing, J., and A. M. Davies, 2001a: The influence of shelf edge flows andwind upon the circulation on the Malin shelf and in the Irish Sea.
Cont. Shelf Res., 21, 21–45, doi:10.1016/S0278-4343(00)00073-X.
——, and ——, 2001b: A three-dimensional baroclinic model of the
Irish Sea: Formation of the thermal fronts and associatedcirculation. J. Phys. Oceanogr., 31, 94–114, doi:10.1175/
1520-0485(2001)031,0094:ATDBMO.2.0.CO;2.
——, and ——, 2005: A model study of spin-down and circulation
in a cold water dome. Ocean Dyn., 55, 199–212, doi:10.1007/
s10236-005-0007-4.
Yamamoto, T., T. Hashimoto, H. Takeoka, T. Sugiyama, andO. Matsuda, 2000: Middle layer intrusion as an importantfactor supporting phytoplankton productivity at a tidal front in
Iyo nada, the Seto Inland Sea, Japan. J. Oceanogr., 56, 131–
139, doi:10.1023/A:1011126911262.
Yanagi, T., and H. Higuchi, 1981: Tide and tidal current in the Seto
Inland Sea (in Japanese). Proc. 28th Conf. on Coastal Engineering, Tokyo, Japan, Japan Society of Civil Engineers, 555–558.
——, and H. Tamaru, 1990: Temporal and spatial variations in a
tidal front. Cont. Shelf Res., 10, 615–627, doi:10.1016/
0278-4343(90)90041-J.
Yuan, Y.-L., and Li, H.-Q., 1993: On the circulation structure andformation mechanism of the cold water mass of the Yellow
Sea (I)—Zero-order solution and circulation structure. Sci.
China Chem., 36, 1518–1528.