Progress in Oceanography 212 (2023) 102986

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Progress in Oceanography
journal homepage: www.elsevier.com/locate/pocean

Burst events of near-inertial waves in the Beaufort Sea
Shuya Wang a, Qun Li b, *, Anzhou Cao c, a, Xinyu Guo aaCenter for Marine Environmental Studies, Ehime University, Matsuyama, JapanMNR Key Laboratory for Polar Science, Polar Research Institute of China, Shanghai, Chinac
Ocean College, Zhejiang University, Zhoushan, Chinab

A R T I C L E I N F O

A B S T R A C T

Keywords:
Near-inertial wave
Arctic Ocean
Turbulent mixing

Based on moored observations from the Beaufort Gyre Exploration Project, seven burst events of near-inertial
waves (NIWs) during September 2017-September 2018 are investigated in this study. These NIW events are
divided into two groups. Four NIW events in group I are dominated by downgoing components associated withnear-inertial currents in the magnitude of about 0.1 m/s. The plane-wave fitting results indicate that these NIWs
have much smaller vertical wavelengths and energy fluxes than those in the mid-latitude oceans. By performing
simulations with the slab model and analyzing sea ice conditions, we find that one NIW event is directly excitedby the wind in the ice-free summer of 2018. Whereas, the other three NIW events are likely induced by the ice
motion. For NIWs in group II, the downgoing and upgoing components are comparable in strength. The
downgoing NIWs could be directly forced by the wind; whereas the upgoing ones may be related to the eddy
events.The occurrence of the NIW events caused strong shears and hence smaller Richardson number, further
resulting in the elevation of the energy dissipation rate. Results of this study can improve our understanding on
the NIW dynamics and their influence on the mixing in the Arctic Ocean.

1. Introduction
Near-inertial waves (NIWs),which have frequencies close to the local
inertial frequency, are ubiquitous in the ocean. In the global ocean, inputof the wind into the near-inertial motions is 0.3–1.5 TW according toprevious studies (Alford, 2001, 2003, 2020; Furuichi et al., 2008; Jiang
et al.,2005; Simmons and Alford, 2012; Watanabe and Hibiya, 2002),
which is generally comparable to the energy conversion from barotropic
tides to internal tides (Simmons et al., 2004; Niwa and Hibiya, 2011).
The breaking of NIWs causes intense turbulent mixing in the ocean,
especially in the upper layers (Alford et al., 2016; Mackinnon et al.,2017; Whalen et al., 2020). Hence, NIWs are an important step in theocean energy cascade and play a key role in the global ocean energy
budget. As a result, understanding the generation, propagation, anddissipation of NIWs is of great importance.
Wind contributes the most to the generation of NIWs. In the low- andmid-latitude oceans, tropical cyclones and storms are capable of exciting
strong NIWs because of their large wind stresses (Alford et al., 2016).
The NIWs generated by tropical cyclones are associated with strong
near-inertial currents in the magnitude of 0.1–1 m/s, and they could lastfor one to several weeks after the passage of the tropical cyclones (e.g.,

Sanford et al., 2011; Alford et al., 2012; Cao et al., 2018; Johnston et al.,2021; Löb et al., 2021). During the downward propagation of NIWs, they
may interact with large-scale circulations or mesoscale eddies, leading
to the occurrence of refraction or reflection and hence the redistributionof energy (Zhai et al., 2005; Byun et al., 2010; Kawaguchi et al., 2016;2020; Jeon et al., 2019; Yu et al., 2022). In addition, other processes,
such as the adjustment of frontal flows or eddies (Alford et al., 2013;
Nagai et al., 2015) and flow-topography interaction (Nikurashin andFerrari, 2010) can also give rise to NIWs in the ocean.
Compared with the mid-latitude oceans, the Arctic Ocean is largely
covered by sea ice, causing the dampening of the input of wind energy
into the ocean. However, over the past few decades, the Arctic Ocean has
undergone rapid changes, with the warming of sea water and decline ofsea ice (Serreze et al., 2007; Polyakov et al., 2017; Lind et al., 2018). As aresult, there appears an increasing trend of near-inertial energy in theupper Arctic Ocean (Dosser and Rainville, 2016; Polyakov et al., 2020).
Several studies have demonstrated the intensification of NIWs would
lead to the enhancement of shear and energy dissipation, which further
elevates the vertical heat flux (Polyakov et al., 2020; Dosser et al., 2021).
This in turn modulates the sea ice budget in the Arctic Ocean. However,other observational results indicate that the increase of near-inertial* Corresponding author.
E-mail address: liqun@pric.org.cn (Q. Li).
https://doi.org/10.1016/j.pocean.2023.102986
Received 19 September 2022; Received in revised form 26 December 2022; Accepted 3 February 2023
Available online 6 February 2023
0079-6611/© 2023 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/bync-nd/4.0/).

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Progress in Oceanography 212 (2023) 102986

energy does not definitely cause the elevation of energy dissipation,
which could be due to the synchronous increase in vertical wavelengthof NIWs and the suppression by strong stratification at intermediate
depth (Rippeth et al., 2015; Lincoln et al., 2016; Fine and Cole, 2022). In
other words, the role of NIWs in such “wind-ocean-ice” feedback cycle
remains unclear and needs further clarification. Hence, NIWs in the
Arctic Ocean are getting increasing attention by researchers.
Observational studies have been conducted to examine the NIWs in
the Arctic Ocean. Their results indicate that the energy of NIWs in the
Arctic Ocean is typically low, which is 1–2 orders of magnitude lower
than that in the mid-latitude oceans (Halle and Pinkel, 2003; Merrifield
and Pinkel, 1996; Pinkel, 2005). This can be largely attributed to thedampening effect of the sea ice. When the sea surface is covered by ice,the direct momentum transfer from the wind to NIWs is inhibited(Dosser et al., 2014; Dosser and Rainville, 2016; Cole et al., 2018). Evenstrong storms do not induce significant near-inertial responses in theocean, resulting in low near-inertial energy and shears (Rainville andWoodgate, 2009; Martini et al., 2014). In contrast, during the ice-freestage, the input of wind energy is unaffected, thereby enhancing of
NIWs in the upper ocean (Rainville and Woodgate, 2009; Lincoln et al.,2016; Kawaguchi et al., 2019). Apart from sea ice, weak Beta effect andshallow mixed layer in the Arctic Ocean also lead to the reduction ofnear-inertial energy in the mixed layer (Guthrie & Morison, 2021).
Moreover, it should be noted that the semidiurnal tidal frequencies fall
into the near-inertial band in the Arctic Ocean. Recently numerical re­sults suggest that NIWs in this region can also be generated by diurnal
tidal forcing over topographies due to the advection effect (Urbancic
et al., 2022; Wang et al., 2022).
The occurrence of NIW events is associated with intensified turbulent
mixing, and corresponding energy dissipation rates are usually muchhigher than those driven by double diffusion convection (Shibley et al.,2017; Polyakov et al., 2019). In the central Arctic Ocean, Fer (2014)
observed an energy dissipation rate over 10-8 W/kg in the upper 100 m
after a storm and suggested that the NIWs driven by storms are one
possible reason. In addition, results of Kawaguchi et al. (2016) indicatethat NIWs in the Chukchi Sea caused elevated energy dissipation below
the thermocline as they propagated downward through an anticycloniceddy. The NIW-induced turbulent mixing in the upper Arctic Ocean
could increase the vertical heat flux (Rainville et al., 2011; Fine et al.,2021), and thereby transports more heat from the warm Atlantic Water
into the surface layer (Meyer et al., 2017).On the whole, significant
progress has been made by all the aforementioned studies. However,Fig. 1. (a) Bathymetry of the Beaufort Sea (shading, unit: m). Isobaths are denoted by gray contours. Location of mooring A is indicated by red plus. Raw obser­
vations of (b) zonal and (c) meridional velocities (shadings, unit: m/s) as well as (d) buoyancy frequency (shading, unit: s− 2).
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owing to great difficulties and high costs, long-term observations withhigh temporal resolution are rare, making it difficult to understand the
NIWs and their mechanisms lying behind in the Arctic Ocean.
The Beaufort Gyre Exploration Project (BGEP; https://www.whoi.
edu/beaufortgyre; Proshutinsky et al., 2009) has deployed four moor­ings in the Beaufort Sea since 2003. During September 2017-September
2018, the high-frequency McLane Moored Profiler (MMP) was equipped
at one mooring (Mooring A, Fig. 1a), which provides a good opportunity
for us to investigate the NIWs in this region. In the study, NIW events in
the Beaufort Sea observed by Mooring A are presented. Seven burst
events of NIWs were recorded during the observational period. The
characteristics and generation mechanisms of NIWs and their impacts on
the mixing are analyzed. The remainder of this paper is organized asfollows. The datasets and analyzing methods used in this study are
introduced in Section 2. Observational results and corresponding in­
terpretations are presented in Section 3. Finally, the paper is summa­
rized in Section 4.

is the depth.
NIWs are decomposed into upgoing and downgoing components. We
first calculate the wavenumber-frequency spectrum using the twodimensional Fourier transform of complex velocity (u + iv) or shear(uz + ivz). Then, upgoing and downgoing components of the NIWs are
obtained by the inverse Fourier transform of the spectral density in thefour quarters of the wavenumber-frequency spectrum. This method has
been widely used in previous studies (e.g., Alford et al., 2012, 2017; Caoet al., 2019; Halle and Pinkel, 2003; Kawaguchi et al., 2019). Notably,
for NIWs, the propagation directions of the phase and energy areopposite in the vertical direction. To avoid confusion, here “upgoing”
and “downgoing” describe the propagation directions of the NIW
energy.
To explore the NIW characteristics (e.g., frequency and wavelength),plane-wave fitting is performed (Alford and Gregg, 2001; Alford et al.,2012; Cao et al., 2018). To minimize the effects of stratification, we use
Wentzel–Kramers–Brillouin (WKB) scaled variables in the WKB
stretched depth coordinate (Alford et al., 2012; Sun and Pinkel, 2012).
The WKB stretched depth is calculated with the time-averaged stratifi­

2. Methodology

cation during the whole observational period N(z), that is,/∫zN(z) N0 dz
zWKB =

2.1. Data
In this study, observations at the BGEP Mooring A during September
2017-September 2018 are used (https://www2.whoi.edu/site/beau
fortgyre/), which was deployed at (75◦ 1.10′ N, 150◦ 8.43′ W) in the
Beaufort Sea (Fig. 1a).The MMPwas equipped to measure the currents(u, v), temperature (T), and salinity (S). Profiles within 43–223 m weretaken every-three hours. The vertical resolution of the data is 2 m.
Fig. 1b-d show the raw observations of horizontal velocities and buoy­
ancy frequency calculated from T and S.
An upward-looking sonar (ULS) provided the information about ice
drift speed and ice draft. Here, we use the processed data provided by
the BGEP (https://www2.whoi.edu/site/beaufortgyre/data/moorin
g-data/mooring-data-description/). The processed ice drift speed has atemporal interval of one hour, while the daily ice draft statistics aredelivered in the output data from the BGEP.
In addition to the moored observations, other datasets are also usedas supplementary. The 10-m wind speed is obtained from the National
Centers for Environmental Prediction Climate Forecast System Version 2(NCEP CFSv2, https://www.hycom.org/dataserver/ncep-cfsv2). The
data are provided hourly on a 0.2◦ ×0.2◦ grid. The sea ice concentration
is obtained from the Global Ocean Sea Ice Concentration Time Series
REPROCESSED (https://marine.copernicus.eu/), with a spatial (tem­poral) resolution of 25 km (1 day). It is computed by using passive mi­crowave data from satellites.

43

where N0 is the depth-averaged value of N(z) (Alford and Gregg, 2001;
Cole et al., 2018). We begin the integration at 43 m which is the upper
depth range for the MMP observation. The WKB scaled velocities arecalculated by,√̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅
(4)(uWKB , vWKB ) = (u, v) N0 /N(z)Then, we fit the WKB scaled variables with the plane-wave solution
by using the least-squares method, i.e.,Ψ = Re{ Ψ0 exp[i(ωt − mzWKB − ϕ) ]}(5)

where Ψ0, ω and ϕ are the amplitude, frequency, and phase of the NIW,
respectively.
2.3. Slab model
The Pollard-Millard slab model (Pollard and Millard, 1970) is
adopted to predict the wind-driven inertial motions in the mixed layer.
The governing equation for this model isdZT+ (r + if0 )Z =
dt
H

(6)

where Z = u +iv is the currents in the mixed-layer, f0 is the local Coriolis
frequency, r is the damping coefficient, T = (τx +iτy )/H is the windstress, and H is the mixed-layer depth.
The wind stress is calculated with the wind speed from CFSv2 and awind speed-dependent Cd as in Oey et al. (2006). We solve Equation (6)by using the spectral solution method proposed by Alford (2003). The
solution contains both the Ekman component ZE and inertial currents Zf.
)(
The former can be calculated byZE = T/ r + if0 H, and then Zf is ob­
tained by Zf = Z − ZE. The inertial energy flux into the ocean is computed
as the product of the wind stress and inertial currents. Following Martini
et al. (2014), the slab model is adopted for both ice-free and ice-covered
conditions; however, it can only model the inertial motions in an ice-freeocean.

2.2. Data processing
NIWs are extracted by a fourth-order Butterworth filter, with a cutoff
frequency of [1.75 2.15] cpd. Semidiurnal tides are contained in thisband and cannot be completely separated from the NIWs. However,previous studies have suggested weak semidiurnal tidal currents in the
Beaufort Sea basin (Padman and Erofeeva, 2004; Dosser et al., 2014;
Martini et al., 2014; Dosser and Rainville, 2016; Fine et al., 2021),
implying they make minor contributions to the filtered velocities.
Thereafter, near-inertial kinetic energy and 2-m shear squared are
calculated as follows:
)
1( 2
KEf =
(1)
u + v2f
2 f
and( )2 ( )2
∂uf
∂vf
Sf2 =
+
∂z
∂z

(3)

3. Results
3.1. Overall view of NIWs

(2)

We present an overall view of the observed NIWs in this section. Firstof all, the seasonal dependence of NIWs can be easily found in Fig. 2a,

where uf (vf) is the filtered zonal (meridional) near-inertial current, and z
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Progress in Oceanography 212 (2023) 102986

Fig. 2. (a) Depth-averaged near-inertial kinetic energy during the observational period. Blue and red lines indicate the raw and smoothed results, respectively. (b)Depth-time map of near-inertial kinetic energy (shading, unit: m2/s2). (c and d) Same as (a and b) but for near-inertial shear. Seven NIW events are denoted bygreen rectangles.

large KEf mainly observed in the region shallower than 100 m. But forthe other events, the KEf is enhanced in the deeper region (>150 m,
event 4) or basically uniform in the vertical direction (events 1, 2, and
6). In terms of the duration time, several NIW events lasted forapproximately-one month (e.g., events 2, 3, 4, and 7). In contrast, thesince the KEf is rather weak in the winter. Second, the KEf exhibits
remarkable intermittence. Seven burst events of NIWs are identified by
the pronounced peaks of KEf, which occurred in spring, summer, andautumn.These observed NIWs exhibit different patterns. As shown in
Fig. 2b, several NIWs are surface intensified (events 3, 5, and 7), with

Fig. 3. (a) Depth-averaged downgoing and upgoing near-inertial kinetic energy during the observational period. (b) Same as (a) but for near-inertial shears. Seven
NIW events are denoted by green rectangles. Note that “upgoing” and “downgoing” describe the propagation direction of energy.
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duration time of NIW event 6 was only 11 days, which is the shortest.
As for the near-inertial shear squared, its depth-averaged result(Fig. 2c) generally shares a similar pattern to the KEf. The strongest nearinertial shear is observed in March 2018 (event 3). However, the nearinertial shear is not highly correlated with the KEf all the time. In
other words, the NIWs with high KEf do not cause strong shear, such as
the events 1 and 2; while the peak of near-inertial shear squared also
appears in May 2018 when the burst events of NIWs are absent. In
addition, the near-inertial shear is basically surface intensified foralmost all the events (Fig. 2d), which is different from the KEf as
analyzed above.
Then we examine the upgoing and downgoing components of thenear-inertial kinetic energy and shears. As shown in Fig. 3a, the upgoingand downgoing components make different contributions to the energy
for different NIW events. Based on their contributions to near-inertial
energy, the seven NIW events are divided into two groups. For group I
which includes events 3, 4, 5, and 7, the downgoing components are
dominant, and the corresponding KEf is at least twice as high as that of
the upgoing ones (Fig. 3a). Additionally, during the four events, thedowngoing components generally induce stronger shears than theupgoing ones (Fig. 3b). Nevertheless, for the other three NIW events (1,2, and 6), the KEf of the upgoing components is comparable to or evenslightly larger than that of the downgoing ones. These NIW events areclassified as group II. Similar to KEf, near-inertial shear squared for theupgoing and downgoing components is basically at the same level(events 1 and 2), except for that in event 6 (Fig. 3b). In the following
section, the two groups of NIW events are explored individually.

3 and 5, the pronounced NIW packets were radiated downward from thenear-surface region (Fig. 4a and 4c). After about two weeks, the radia­
tion penetrated to approximately 100 m, and no further downgoingradiation persisted in the deeper layers. Although the NIWs in event 7
also originated from the near-surface zone, they seem to the restricted inshallow water (<80 m). Below that, the near-inertial currents are weak(Fig. 4d). Moreover, the NIWs in event 4 show a different pattern(Fig. 4b), since the wave packet is found in the deeper layers (140–220m). Because the temporal variation of stratification is not significant
during these NIW events (Fig. 1d), such difference in the verticalstructure may be due to other factors such as the non-local forcing andice characteristics (Cao et al., 2018; Cole et al., 2018). In addition,compared with the NIWs in the mid-latitude oceans which can propa­
gate downward deeper than 800 m (Alford et al., 2012), the downward
migration of NIW packets in the Beaufort Sea only exists in the region
shallower than ~ 200 m. Similar feature of NIWs was also found in the
Chukchi Sea by Rainville and Woodgate (2009). With respect to thestrength of NIWs, except for those in event 4, near-inertial currents
during the other three events reach 0.1 m/s. The magnitude is compa­
rable to that previously observed in the Arctic Ocean (e.g., Rainville andWoodgate, 2009; Kawaguchi et al., 2016; 2019), but lower than thatobserved in the mid-latitude oceans (~0.3 m/s; e.g., Alford et al., 2012;2017; Chen et al., 2013; Cao et al., 2018).
To further examine the characteristics of these NIWs (e.g., frequency,
wavenumber, and group velocity), plane-wave fitting is adopted. Here,
we use the time-averaged stratification calculated from the temperatureand salinity observed by the MMP (Fig. 5a). The maximal buoyancy
frequency is located at z = 65 m. The WKB stretched depth is shown in
Fig. 5b. To minimize the errors in the calculation of the downward
vertical group speed and energy flux, we use the downward components
rather than the total near-inertial currents in the plane-wave fitting.
Also, because NIW packets appear in different depths during these
events, different depth ranges are considered in our calculation(Table 1). Moreover, event 7 is not fitted because the NIWs are surface-

3.2. NIW events in group I
Group I contains four NIW events which are dominated by down­going components. Fig. 4 displays vf during the four events. On thewhole, upward-tilting phase of velocity is clearly seen, indicating thedowngoing propagation of NIW energy into the deeper ocean. For events

Fig. 4. Depth-time map for meridional near-inertial currents (shadings, unit: m/s) during NIW events (a) 3, (b) 4, (c) 5, and (d) 7.
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Fig. 5. (a) Time-averaged stratification during the observational period. Vertical-averaged value is indicated by vertical dashed line. (b) WKB stretched depth. The
red dashed line denotes the unstretched depth for reference. (c-e) WKB scaled meridional near-inertial velocities (shadings, unit: m/s) in WKB stretched depth
coordinate for NIW events 3, 4, and 5, respectively. Dashed lines in (c-e) indicate phase lines calculated by plane-wave fitting.

Fig. 6. (a) Time series of wind speed from NCEP CFSv2, (b) inertial energy flux and (c) cumulative energy transfer calculated by the slab model. Seven NIW eventsare denoted by green rectangles.

trapped. As shown in Fig. 5c-e, the near-inertial velocities are in straightphase lines after WKB stretching. The phase lines for the plane-wave
fitting results show good consistency with the observations. The fitted
results listed in Table 1 indicate that the frequencies of NIWs are closerather than exactly equal to the local inertial frequency. Red shift (ω <f0) occurred in event 3; while small blue shift (ω > f0) occurred in events

4 and 5. In terms of the vertical scale, the NIWs in the three events all
have a wavelength smaller than 100 m, which is basically comparable tothat previously observed by Ice-Tethered Profilers with Velocity (ITP-V)
in the Beaufort Sea (Cole et al., 2018) as further evidenced by thewavenumber spectra of near-inertial shear (see supporting information).
NIWs in event 4 have the largest wavelength among the three events,
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Table 1
Plane wave fitting results for NIW events 3, 4 and 5. cgz* is the group speed calculated by Equation (7), while c+gz is estimated from the downward migration of KEf. Notethat all the results are calculated with WKB scaled velocity and stretched depth.
NameTime range

Depth range (m)ω/f0m (rad/m)L (m)cgz* (m/day)c+gz (m/day)Fv (W/m2)

Event 3

2018031520180322
2018042020180427
2018061820180626

90–150

0.98

0.14

44

–

4.0

5 × 10-5

160–222

1.02

0.11

59

4.1

2.7

5 × 10-5

80–126

1.01

0.15

42

1.0

1.2

1 × 10-5

Event 4
Event 5

- Not calculated.

which is nearly 1.5 times than that in event 5. This could be the reason
why the near-inertial shears in event 4 are weaker than those in theother two NIW events (Figs. 2 and 3). In other words, the variation ofvertical scales of NIWs compensates the changing of KEf and hence in­fluences the near-inertial shear, which lowers the correlation between
the near-inertial energy and shear (Fine and Cole, 2022). In addition, it
should be noted that the vertical wavelength of the observed NIWs aremuch smaller than those observed in mid-latitude oceans as reported inprevious studies [e.g., 130–300 m in the Northern Pacific (Alford, 2010;
Alford et al., 2012); 260–370 m in the Northern South China Sea (Caoet al., 2018); 650 m in the Northern Atlantic (Yu et al., 2022)]. Thisimplies that the NIWs in the Beaufort Sea would be more easily dissi­
pated and hence are not radiated downward into the deep ocean.
With the obtained frequency and wavenumber of the NIWs, their
vertical group speed is calculated by (Pinkel, 2005; Alford et al., 2012)cgz =ω2 − f02mωvariations in wind stress cause the divergence and convergence of hor­izontal currents. Thereafter, the currents pump the mixed layer to create
NIWs downgoing into the ocean interior (D’Asaro, 1985; Martini et al.,2014; Alford et al., 2016). To explore whether the four NIW events ingroup I are caused by wind, simulations based on the slab model are
conducted. Because of the lack of observations in the upper 40 m, we use
a constant mixed layer depth H = 20 m following Kawaguchi et al.
(2019). During the whole observational period, the wind speed isgenerally lower than 10 m/s (Fig. 6a). Also, no remarkable increase inwind speed is found during the four events. Except for those in event 7(Fig. 6b), the inertial energy fluxes during events 3, 4, and 5 are nearlyzero. Correspondingly, the cumulated energy transfer does not exhibit
an increasing trend or a staircase (Fig. 6c). This result indicates that theobserved downgoing near-inertial energy is not strongly correlated withthe wind work except in the case of event 7. Thus, wind may not be
responsible for the generation of NIWs in events 3, 4, and 5.
It should be noted that in the Arctic Ocean, the presence of sea ice
considerably dampens the input of wind energy into the near-inertial
motions in the ocean. Hence, examination on the ice condition during
the observational period is necessary. At the mooring location, the sea
ice concentration is nearly 100 % from late October 2017 to the end ofJune 2018. This further confirms that the NIWs in events 3, 4, and 5
cannot be directly driven by the wind. In contrast, an ice-free ocean
appears in summer (event 7), suggesting that NIWs in event 7 are
generated by the wind, combining with the aforementioned analysis. In
addition to the wind, ice motion is another factor that could generate
NIWs (McPhee and Kantha, 1989; Dosser and Rainville, 2016): The ice
keels in the oceans play a similar role to the bottom topographies.
During the sub-inertial motion of ice, horizontal gradients in its drift
speed or bottom roughness induce a vertical velocity perturbation at theresonant inertial frequency beneath the ice keel, which further disturbs
the bottom of the mixed layer depth so as to generate downgoing NIW
packets. Here, the ice drifting speed is obtained from the ULS data, andpart of the data is discarded because of large abnormal values. During
events 3, 4, and 5, although the ice speed is not the fastest (Fig. 7b), thedaily-averaged ice draft reaches its highest value (Fig. 7c). Additionally,
the standard deviation of the ice draft is also elevated at the same time,
which is possibly related to the short-time variation of the ice draft as ice
keels or ridges pass by (Brenner et al., 2021). The above two conditions
would be beneficial for generating downgoing NIWs. Therefore, theobserved NIWs during these events are speculated to be induced by ice
motion. Moreover, Dosser and Rainville (2016) also found that subinertial ice speed correlates with the amplitude of NIWs in the Beau­
fort Sea to an extent, particularly in autumn and winter. This implies
that ice motion may play a considerable role in driving NIWs in icecovered oceans. However, it should be noted that other factors such as
the non-local forcing may also contribute to the downgoing near-inertial
energy, but they could be difficult to identify using observations at only
one fixed location.
Combining with the aforementioned analysis, we conclude that thegeneration of downgoing NIW packets in group I can be attributed to thewind and ice motion. The NIWs in event 7 during the summer of 2018
are directly driven by the wind. But for the other three events (3, 4, and
5) under the ice-covered condition, ice motion is considered to be the(7)Note that this equation cannot be applied for sub-inertial waves.
Additionally, cgz is also estimated by tracking the downgoing radiationof the WKB scaled near-inertial kinetic energy as a comparison (seesupporting information) [Yu et al., 2022]. The vertical group speeds
obtained by the above two methods are generally equal (Table 1). The
downward propagation of near-inertial energy is the fastest during event
3 but the slowest during event 5. Additionally, the estimated verticalgroup speeds are much lower than those in the mid-latitude oceans,
which exceed 10 m/day [13 m/day in the Northern Pacific (Alford et al.,2012); 60 m/day in the Northern Atlantic (Yu et al., 2022)]. This could
be another reason why the observed NIWs in group I cannot propagate
into the deep water. Furthermore, we estimate the vertical near-inertial
energy flux by,
Fv = cgz KEfWKB(8)As mentioned by Alford et al. (2012), Ef≈KEf (Ef is the near-inertial
energy) is an excellent assumption for near-inertial waves, which also
works in the Arctic Ocean as evidenced by Cole et al. (2018). The esti­
mated energy fluxes (Table 1) are basically comparable to those in Halleand Pinkel (2003) who calculated Fv in the Beaufort Sea using thespectral method. However, they are one order of magnitude lower thanthose observed in the central Arctic Ocean (Fer, 2014). Moreover, they
are rather weak compared to those in the mid-latitude oceans (~10-3 W/
m, Alford et al., 2012). This implies that the NIWs in the Beaufort Sea
may not have influences on the mixing in the deep ocean below thepycnocline.
Based on the above results, the main characteristics of the NIWs ingroup I can be concluded. These NIWs are associated with downward
energy radiation. During the four events, the NIWs lasted for approxi­
mately 2–4 weeks. By performing plane-wave fitting, we find that they
have smaller vertical wavelength (<100 m) and induce weaker verticalenergy fluxes (~10-5 W/m2) compared with those in the mid-latitude
oceans.
Then generation mechanism of NIWs in group I is investigated.
Downgoing NIW packets are usually caused by the wind. Local
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Fig. 7. Time series of (a) ice concentration, (b) ice speed, (c) daily mean and STD of ice draft during the observation period. Wind speed is reduced to 1/50 andplotted in (b) as a comparison. Seven NIW events are denoted by green rectangles.

possible cause for the observed downgoing near-inertial energy.

3.3. NIW events in group II
Then attention is paid to the NIW events in group II. Differing fromthose in group I, the phase of near-inertial velocities is nearly verticalFig. 8. (a) Meridional near-inertial currents as well as their (b) downgoing and (c) upgoing components (shadings, unit: m/s) during events 1, 2, and 6.
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Progress in Oceanography 212 (2023) 102986

instead of tilting, indicating a vertical standing wave pattern (Fig. 8a).
Correspondingly, the velocities for the upgoing and downgoing com­ponents are basically comparable (Fig. 8b and 8c), in accordance withthe results in Section 3.1. Recalling Fig. 6, wind work is enhanced forevents 1 and 6, during which the ice concentration is low. This indicatesthat the downgoing components of NIWs could be directly forced by thewind. Subsequently, we mainly focus on the generation mechanism of
the upgoing NIWs.
The upward radiation of near-inertial energy can be attributed toseveral reasons. In the Arctic Ocean, numerical results indicate thatupward semidiurnal (near-inertial) internal waves can be generated by
diurnal tidal forcing over topographies because of the advection effect(Urbancic et al., 2022; Wang et al., 2022). However, in the central
Beaufort Sea where the mooring A is located, the sea bottom is quite flat.
Furthermore, tidal currents in the study region are rather week (Padman
and Erofeeva, 2004). Based on the above reasons, this mechanism could
not be responsible for the generation of the observed upgoing NIWs.
Previous studies have demonstrated the presence of eddies in the
Beaufort Sea (Carpenter and Timmermans, 2012; Zhao and Timmer­
mans, 2015), which may modulate the propagation of NIWs. As shownin Fig. 9a, four eddies are detected during the observational period. A
strong subsurface eddy is found between events 1 and 2; while anotherone is observed exactly during event 6. Furthermore, by comparing the
KE in the low-frequency and near-inertial bands, we find that theenhancement of upgoing KEf is partly associated with large KEL, indi­
cating that their generation may be related to the eddy event (Fig. 9b).
Whereas, eddy detected in June 2018 is not related to upgoing KEf.
According to Kunze (1985), NIWs would be reflected in a positive
relative vorticity field due to the increase of effective Coriolis frequency,i.e.,1feff = f0 + ζ
2where ζ = ∂∂xv −(9)∂u∂y is the relative vorticity. Considering that we only

have data from one mooring, the poor man’s vorticity (PMV) is calcu­
lated following Halle and Pinkel (2003),
PMV = 2

∂v⊥
∂c

(10)

in which where v⊥ is the component of the low-frequency velocity
perpendicular to the drift direction, and c is the along-drift coordinate.
In the calculation, a frozen mesoscale field is assumed, and the data
spaced in time at a fixed location are converted to space according toZhao and Timmermans (2015). According to Fig. 9c, the strong sub­surface eddy in mid-October 2017 is associated with a large Rossby
number (Ro = PMV/f0). However, for most of the time during NIW
events 1 and 2, Ro remains at a low level. This indicates that eddyinduced relative vorticity could not be the cause of upgoing nearinertial energy during the two events. In other words, the correspond­
ing mechanism is still unknown and needs further exploration.
In contrast, during event 6, bands for negative and positive vortic­
ities alternate in the center of the eddy (July 2017), implying that part of
the near-inertial energy would be reflected. However, it should be notedthat there exist another possible mechanism resulting in the generationof upgoing NIWs. Low-frequency motions such as the eddies and fronts
could give rise to NIWs whenever the geostrophic balance is not satisfied(Liang and Thurnherr, 2012; Alford et al., 2013; 2016; Nagai et al.,2015). This mechanism works if the background flows have large Rossby

Fig. 9. (a) Depth map for low-frequency background currents (shadings, unit: m/s). Eddy events are denoted by red inverse triangles. (b) Time series of KE for lowfrequency motions (blue) and NIWs (red) as well as the downgoing (green) and upgoing components (yellow). The KE of NIWs is enlarged by a factor of 40 forcomparison. (c) Depth-time map for the Rossby number (PMV/f0, shading). Black contours in (a) and (c) indicate isopycnals. NIW events 1, 2, and 6 are denoted bygreen rectangles.
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Progress in Oceanography 212 (2023) 102986

where the constants ε0 and N0 are set to 7 × 10-10 W/kg and 5.2 × 10s , respectively; S8 is the 8-m near-inertial shears. The shear in the GM
spectrum is given by

numbers. In the Arctic Ocean, the horizontal scales of eddies are
considerably smaller than those in the mid-latitude oceans (Carpenter
and Timmermans, 2012; Zhao et al., 2014; Zhao and Timmermans,
2015; Wang et al., 2020). Therefore, Ro approaching unity is foundduring the eddy event in July 2018 as shown in Fig. 9c. The subsurface
eddy tends to become unstable and hence excites NIWs during theadjustment process. Nevertheless, clarifying the contributions of thismechanism could be difficult with observations at only one fixed loca­
tion. Future studies involving numerical simulations may be helpful incorresponding clarification.

3 − 1

3
2
SGM
= πj* EGM bN02 kcrit (N/N0 )22(12)

where j*=3 is the vertical mode number, b = 1300 m is the scale
depth of thermocline, the critical wavenumber is set to kcrit = 0.6 rad/s,
and the non-dimensional energy level EGM = 6.3 × 10-5. Note that all theabove constants are the same as those in Kawaguchi et al. (2016), whoused this parameterization to estimate the NIW-induced energy dissi­
pation in the Chukchi Sea. The result shown in Fig. 10b is generallycomparable to that estimated by the fine-scale parameterization at thesame location (Fine and Cole, 2022), indicating the reasonability of ourcalculated results. Large energy dissipation rates are observed in events
3, 4, and 5, with a magnitude over 10-8 W/kg. These values of ε arenearly-two orders of magnitude larger than those in the upper layers of
the central Arctic Ocean (Dosser et al., 2021), suggesting that theoccurrence of NIW events could drive strong mixing in the upper ocean.
Additionally, some elevated dissipation rates are found beyond the pe­riods with burst events of NIWs. This could be due to the smaller verticalscale of these weak NIWs as analyzed in Section 3.2. In contrast, ε re­mains at a low level during the NIW events of group II, with corre­
sponding magnitudes lower than 10-10 W/kg.
Turbulent mixing drives vertical heat fluxes and thereby has thepotential to modulate the sea ice budget in the Arctic Ocean (Rippeth
et al., 2015; Meyer et al., 2017; Fine and Cole, 2022). Here, we calculate
the vertical heat flux induced by the NIWs using the following equation,

3.4. Implications on mixing
NIWs are considered as one of the energy source of turbulent mixing
in the Arctic Ocean, especially in the upper ocean (Rippeth and Fine,
2022). Considering that the observed NIWs in the Beaufort Sea havemuch smaller wavelengths than those in the mid-latitude oceans, they
are believed to cause intense mixing. The Richardson number of the
NIWs is estimated byRiNIW = N2 /S2f . During the observational period,

the stratification below 50 m does not show evident seasonal variations(Fig. 1d). As a result, RiNIW is primarily determined by the near-inertial
shears (Fig. 10a). Generally, the criterion for shear instability is the in­verse RiNIW > 4 (Thorpe, 2005). Here, large values of the inverse RiNIW
reaching 4 are found in events 3, 4, and 5, during which the downgoing
NIWs are dominant. However, for NIWs in group II, the inverse RiNIW issmall, indicating a low possibility of shear instability.
Furthermore, the turbulent kinetic energy dissipation rate caused by
NIWs is estimated via semi-empirical parameterization (Gregg, 1989;
Kawaguchi et al., 2016). In this parameterization, the observed nearinertial shears and stratification are used, that is,( / )( / 4 )(11)ε = ε0 N 2 N02 S84 SGM

FhNIW = − ρ0 Cp KzNIW

∂T
∂z

(13)

where ρ0 = 1025 kg/m3 is the seawater density, Cp≈3991.9 J/kg/K is
the specific heat of sea water and KzNIW = 0.2εNIW /N2 is the diapycnal

Fig. 10. Depth-time map for (a) the inverse gradient Richardson number Ri-1 (shading), (b) energy dissipation rate (log form, shading, unit: W/kg) and vertical heat
flux (shading, unit: W/m2) induced by NIWs. (d) Time-averaged temperature profiles. In (c) and (d), the horizontal dashed lines indicate the depth with zero verticalgradient of temperature. Seven NIW events are denoted by green rectangles in (a-c).
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Progress in Oceanography 212 (2023) 102986

diffusivity caused by NIWs. Due to the limited vertical range of the highfrequency MMP observations, only the warm Pacific Water is observed,
whose intrusion causes a local maximum of temperature at a depth ofapproximately 80 m (Fig. 10d) (Toole et al., 2010). The warm Atlantic
Water cannot be found as it stays always below a depth of 200 m(Lincoln et al., 2016). Because the vertical temperature gradients aboveand below the warmest layer are opposite, bidirectional heat fluxes arepresented in the calculated results, which are enhanced during someburst events of NIWs (Fig. 10c). In other words, NIW-induced mixing
transports the heat upward and downward so as to cool the layers ofwarm Pacific Water, especially in event 3. In addition, the estimated
FhNIW is preliminarily comparable to those in the Beaufort Sea and Ca­
nadian Basin reported by previous studies (Dosser et al., 2021; Son et al.,2022). The above result suggests an important role of NIWs in modu­
lating the heat content in the upper Arctic Ocean.

Declaration of Competing Interest
The authors declare that they have no known competing financial
interests or personal relationships that could have appeared to influence
the work reported in this paper.
Data availability
Data will be made available on request.
Acknowledgements
Observational data were collected and made available by the Beau­
fort Gyre Exploration Program based at the Woods Hole Oceanographic
Institution (https://www2.whoi.edu/site/beaufortgyre/) in collabora­tion with researchers from Fisheries and Oceans Canada at the Instituteof Ocean Sciences. Insightful comments from the two reviewers are
gratefully acknowledged.
This study was supported by the National Key Research and Devel­
opment Plan of China (No.2019YFE0105700), the National Natural
Science Foundation of China (No.42176244), the China ScholarshipCouncil (No. 202006325025) and the CAS Key Deployment Project ofCentre for Ocean Mega-Research of Science (No. COMS2020Q07).

4. Summary
NIWs are widespread in the Arctic Ocean, which have a great in­fluence on the turbulent mixing in this region, especially in the upper
layers. In this study, NIWs in the Beaufort Sea are explored by analyzing
the high-frequency MMP observations from the BEGP. During theobservational period (September 2017-September 2018), Seven burst
events of NIWs are captured. They are divided into two groups based on
their energy propagation properties.
NIWs in group I (events 3, 4, 5, and 7) are dominated by downgoingenergy propagation, associated with near-inertial currents in a magni­
tude of 0.1 m/s. By performing plane-wave fitting, we find that the
wavelengths of these NIWs are approximately 40–70 m, which are muchsmaller than those in the mid-latitude oceans. The downward nearinertial energy flux is in a magnitude of 10-5 W/m2. This agrees withprevious observations in the Beaufort Sea (Halle and Pinkel, 2003), but
is at least one order of magnitude lower than those in the central Arctic
Ocean (Fer, 2014) and mid-latitude oceans (Alford et al., 2013; Yu et al.,2022). The generation mechanisms for the four NIW events are different.
Event 7 occurred in summer under an ice-free condition, which is
excited by the wind by conducting simulation with the slab model. The
other three events (3, 4, and 5) are found in the ice-covered stage. Large
ice draft associated with high daily variability is observed during these
events, indicating that these NIWs are likely generated due to the ice
motion.
As for the NIW events (1, 2, and 6) in group II, the upgoing anddowngoing components become comparable. The results of the slab
model suggest that the downgoing components could be generated by
the wind in an ice-free stage. However, how the upgoing ones are
generated remains unclear. During events 1 and 2, the low relative
vorticity is observed for most of the time, suggesting that the upgoing
NIWs are unlikely to be correlated with eddies. In contrast, the presenceof positive relative vorticity during event 6 implies that part of thedowngoing near-inertial energy may be reflected. Moreover, given that
the NIW events occurred during the passage of an eddy, they may also be
generated due to the adjustment of the eddy because of their large
Rossby number (~1). However, the contributions of the two mecha­
nisms remain unknown and require further exploration in future studies.
The occurrence of NIW events has strong implications on turbulent
mixing. High inverse Richardson numbers associated with the nearinertial shears are found to approach 4 during strong NIW events,
implying the possibility of the occurrence of shear instability. Further­more, the energy dissipation rate of NIWs is estimated by a semiempirical parameterization, whose magnitude reaches as high as 10-8
W/kg. The enhancement of turbulent mixing by NIWs would influence
the vertical heat and nutrient flux in the upper Arctic Ocean, hence
further modulating the sea ice budget in this region (Dosser and Rain­ville, 2016; Schulz et al., 2022). We hope that the findings of this study
can provide valuable insights on NIW dynamics in the Arctic Ocean.

Appendix A. Supplementary material
Supplementary data to this article can be found online at https://doi.
org/10.1016/j.pocean.2023.102986.
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