Enhanced mixing induced by internal solitary waves in the South China Sea

Continental Shelf Research 49 (2012) 34–43

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Enhanced mixing induced by internal solitary waves in the South China Sea Jiexin Xu a,b, Jieshuo Xie a,b, Zhiwu Chen a, Shuqun Cai a,n, Xiaomin Long a a b

State Key Laboratory of Tropical Oceanography, South China Sea Institute of Oceanology, CAS, Guangzhou 510301, China University of the Chinese Academy of Sciences, Beijing 100049, China

a r t i c l e i n f o

a b s t r a c t

Article history: Received 23 March 2012 Received in revised form 15 September 2012 Accepted 17 September 2012 Available online 23 September 2012

In this paper, based on the limited observational data of the internal solitary waves (ISWs) near the Dongsha Islands in the northern South China Sea (SCS), the temporal and spatial enhanced mixing during the passage of ISWs is discussed. It is found that, when ISWs pass, the mixing rate increases largely. The variation of the time-averaged vertical current shear agrees well with the KdV equation theory, indicating a minimum shear near the background main thermocline. In the upper layer, when the ISWs arrive, the maximum turbulent dissipation rate and the diapycnal mixing rate can increase by three orders of magnitude; after the passage of ISWs, the mixing reduces sharply to a normal magnitude as that before the arrival of the ISWs. In the upper layer, two types of the instantaneous enhanced mixing versus depth are categorized, one type has several enhanced mixing peaks at different depths when the ISW is about to arrive or to leave, and the other type has only one enhanced mixing peak. In general, the maximum instantaneous enhanced mixing occurs at depths about 10–50 m above the disturbed thermocline. The mixing rate increases largely when the gradient Richardson number is less than 1/4, indicating that the shear instability might be a vital mechanism to the local mixing; and it is interesting to find that, the enhanced mixing occurs when the Froude number approximately equals critical value of unity. & 2012 Elsevier Ltd. All rights reserved.

Keywords: Internal Solitary waves Mixing rate KdV equation South China Sea

1. Introduction Turbulent mixing in the marginal seas plays an important role on the global oceanic circulation and heat transport. The diapycnal mixing in open oceans ranges from 5  10  6 m2 s  1 to 3  10  5 m2 s  1. Because of the interaction between the strong tidal current and the small-scale bottom topography, the turbulent dissipation and the diapycnal mixing in marginal seas are 100– 1000 times larger than those in the interior of open oceans (Munk and Wunsch, 1998; Garrett and Laurent, 2002). As one of the largest marginal seas in the Pacific Ocean, the South China Sea (SCS) features sharply changing bottom topography and strong tidal currents. However, less attention has been paid to the mixing in the SCS. Based on a mooring current data on the shelf of the northern SCS, Zhang et al. (2005) estimated the averaged turbulent dissipation rate and mixing rate, which are 10  9–10  5 W kg  1 and 10  6–10  3 m2 s  1, respectively. Lu et al. (2009) analyzed the turbulent mixing in this region, and suggested that the shelf break of the northern SCS is a strong mixing zone. Tian et al. (2009) studied the mixing rates east and west of the Luzon Strait, documenting that the mixing on the western side

n

Corresponding author. Tel.: þ86 20 89023186; fax: þ 86 20 84451672. E-mail address: [email protected] (S. Cai).

0278-4343/$ - see front matter & 2012 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.csr.2012.09.010

(SCS) is about 2 orders larger than that on the eastern side (the Pacific). A lot of factors, including local topography, strong tidal currents, stratification and internal waves etc., may contribute to the large turbulent variability. Internal solitary waves (ISWs) are ubiquitous in the northern SCS. They are observed by either remote sensing (Zhao et al., 2004) or in-situ measurement (Ramp et al., 2004). Satellite images show that the ISWs are generated in the Luzon Strait and propagate westward across the deep sea basin to the continental shelf break of the SCS (Zhao et al., 2004). Generally, these waves are generated by tidal currents flowing over the rapid variation bottom topography in the stratified ocean. In the previous studies, it was suggested that the ISW carried enormous energies during its propagation, e.g., from numerical simulations, Bogucki et al. (1997) pointed out that up to 73% of the internal wave energy was in the ISW, and from insitu observations, Ramp et al. (2004) claimed that the ISW was the most energetic motion passing the observed site. As the waves interact with the topography, energy carried by the ISWs is converted to smaller scale motions/overturns and finally dissipates by turbulence. ISWs may be a vital source to local mixing, e.g., they were observed to mix the water column at the depth of maximum density gradient (Bogucki and Garrett, 1993); MacKinnon and Gregg, (2003) also found that the strong mixing observed in the thermocline was largely caused by the passage of ISWs; Carter et al. (2005) pointed out that the large-amplitude

J. Xu et al. / Continental Shelf Research 49 (2012) 34–43

nonlinear ISWs on the Monterey Bay shelf made a great contribution to the mixing, and the elevation ISWs accounted for 20% of the observed turbulent kinetic energy dissipation. An important mechanism of the ISW dissipation is the formation of shear instabilities (Farmer and Smith, 1978). With echo sounders, Sandstrom and Oakey (1995) associated the high turbulent mixing with a highly sheared subsurface interface. Moum et al. (2003) indicated that, during the shoreward propagation of ISWs, a large vertical shear instability was visible from the trough to the tail of the ISW. However, few studies focus on the mixing characteristics during the passage of the ISWs, and the vertical variation of the mixing is rarely addressed. The purpose of this paper is to study where the enhanced mixing happens and how it varies versus depth and time during the passage of ISWs, respectively. After describing the moored observational data and methods in Section 2, the results are presented in Section 3. Conclusions follow in Section 4.

2. Data and method

induced by vertical shear flow (Aguiar-Gonza´lez et al., 2011; Wiles et al., 2006). Consequently, assuming that the turbulence is isotropic, and that the turbulent dissipation is balanced by the shear production due to gradients of velocity in vertical, also that there is no net change in the quantity of turbulent kinetic energy, the turbulent dissipation rate e could be obtained by Elsner and Elsner (1996), sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi  2  2 @u @v ð1Þ S¼ þ @z @z

e¼

15 2 uS 2

ð2Þ

where u is the kinematic viscosity coefficient that equals to 10  6 m2 s  1, u and v are the eastward and northward components of the current velocity. Here, due to the coarse observational resolution, the 4 m vertical current shear S is used. Once the turbulent dissipation is calculated, the diapycnal mixing rate Kr can be estimated according to the Osborn parameterization model (Osborn, 1980), K r ¼ ge=N2

The data were collected from April to June, 1998 during the SCS Monsoon Experiment (SCSMEX) by R/V Shiyan No. 3, which was anchored at a site south of the Dongsha Islands (201220 N, 116150.630 E) with a total water depth of 472 m (Fig. 1). The current data were collected by a 300 kHz Acoustic Doppler Current Profiler (ADCP). The vertical resolution of ADCP was 4 m, and the current was recorded at an interval of 30 s on June 14, whilst it was recorded at an interval of 1 min in the other days. The current data collected by ADCP were only available from 10 to 142 m. The top 10 m blank is due to the removal of top ADCP bins that are contaminated by the surface reflection of the echoes of the side slopes, which is a common procedure for ADCP data processing (Liu and Weisberg, 2005), whilst the data blank below 142 m is due to the limitation of the instrument. Both the salinity and temperature data were sampled with a CTD (Conductivity, Temperature, Depth) which was cast to near the sea bottom. The vertical sampling interval for the salinity and temperature data was 1 m, and the data were recorded at an interval of 3 h. A strong depression ISW, with a maximum velocity of 2.097 m s  1 at a depth of 58 m, was observed on June 14, 1998 (Cai et al., 2002). Its passage period is about 18.3 min with a first mode phase speed of 1.36 m s  1. In recent years, a combination of CTD and ADCP data with different resolutions has been expanded to study mixing processes

35

ð3Þ

where g is the mixing coefficient and is taken as 0.11 based on the previous in-situ measurement in the SCS (Lu et al., 2009), ffi qffiffiffiffiffiffiffiffiffiffiffi N ¼  rg @@zr is the buoyancy frequency. Since there are no synchronous in-situ observational temperature and salinity data during the passage of ISWs, we calculated the buoyancy frequency based on the temperature and salinity recorded by the CTD at the time which is the closest to the passage of ISWs. The gradient Richardson number Rig is defined by, Rig ¼

N2

ð4Þ

S2

It is considered that, a parallel, steady sheared stratified flow becomes unstable and more turbulent with a stronger mixing when Rig becomes lower than a critical number of 1/4 in the field observation (Kundu and Beardsley, 1991). To investigate the characteristics of the time-averaged vertical current shear during the passage of ISWs, the KdV-equation model is also employed. Starting with the Boussinesq approximation to the classical hydrodynamic equations for an incompressible fluid, the solution in a two-dimensional Cartesian x, z coordinate system for the vertical velocity of the ISW, w, can be represented by an expansion in eigenmodes, w¼

n X

gi W i ðzÞoi ðx,tÞ

ð5Þ

i¼1

where oi is the horizontal component of w, the constant gi is the weight of ith mode wave and Wi is the modal dimensionless eigenfunction with its maximum value normalized to unity. The eigenfunction Wi satisfies the boundary value generalization equations as follows, 1 d dW N2 ðr Þþ 2 W ¼ 0 r dz dz c

ð6Þ

Wð0Þ ¼ 0,WðhÞ ¼ 0

ð7Þ

where ci (i¼ 1,2,3,y) is ith mode phase speed and h is the depth of water column. Wi can be found by the Thompson–Haskell method (Haskell, 1953). For a plane progressive wave propagating in the x-direction, the Korteweg–de Vries equation follows from this system,

Zt þcZx þ aZZx þ bZxxx ¼ 0 Fig. 1. Bottom topography of the northern SCS, where % is the observational site in our study, while ’ and K are the mooring sites in Zhang et al. (2005) and Tian et al. (2009), respectively.

ð8Þ

where Z  is the displacement of the isopycnal surface, R R0 2 3c 0 dW 3 c a ¼ 2Q dz is the nonlinear parameter, b ¼ 2Q h dz h W dz is

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J. Xu et al. / Continental Shelf Research 49 (2012) 34–43

R 0  2 the dispersion parameter and Q ¼ h dW dz the normalizing dz factor, and ith mode ISW displacement should be given by,

Zi ðx,z,tÞ ¼ Z0 gi W i ðzÞsech2 ðji Þ V i ¼ ci þ

ai Z0 3

,

D2i ¼

ð9Þ

sffiffiffiffiffiffiffiffiffiffi 12bi

ð10Þ

ai Z0

here, Vi is the nonlinear speed, Z0 the amplitude of the ISW, ji ¼(x  Vit)/Di the phase lag. From the continuity equation for an incompressible flow, the horizontal velocity and its vertical current shear can be acquired, ui ¼ Z0 V i gi

dW i 2 sech ðji Þ dz

ð11Þ

2

dui d Wi 2 ¼ Z0 V i sech ðji Þ dz dz2

ð12Þ

Thus, we can calculate the velocity and its vertical current shear by solving the KdV equation (Cai. et al., 2003), and the results are compared with the observational ones. Under the approximation of a two-layer model (Pierini, 1989), U 1 ¼ c1 Z0 =h1

ð13Þ

U 2 ¼ c1 Z0 =h2

ð14Þ

where U1 and U2 are the maximum observational velocities in the upper and lower layers, h1 and h2 are the undisturbed depths of the upper and lower layers, respectively. Here, the background main thermocline is supposed at h1 where the buoyancy frequency is the maximum. Thus, base on the Eq. (13), the amplitude of the ISW for the KdV solution, Z0, can be calculated since U1 is known. Due to the passage of depression ISWs, the upper layer deepens and its disturbed thickness is defined as, H ¼ h1 þ Z0

ð15Þ

and the thermocline at H is defined as the disturbed thermocline.

3. Results and discussion 3.1. Mixing without ISW events in the northern SCS Based on the equations (1–3), the turbulent dissipation rate and the mixing rate without ISW events are estimated and compared with previous studies (Table 1). When there is no ISW, the observed turbulent dissipation and diapycnal mixing rates are 10  10–10  7 W kg  1 and 10  8–10  5 m2 s  1, respectively. Although the vertical sampling resolution in our observations is coarse, our results basically match those previous studies obtained in the northern SCS (Zhang et al., 2005; Lu et al., 2009; Tian et al., 2009), but our resulted upper limit of the diapycnal mixing rate without ISW events is about 2 orders smaller. This might be because that, their maximum mixing rates are obtained either on the continental shelf or near the Luzon Strait where the ISWs are very active and the current field is very complicated due

to the Kuroshio intrusion, thus the upper limit of mixing rate of their studies is far much larger. 3.2. Enhanced mixing during the passage of ISWs Xu et al. (2011) documented the Froude number (Fr¼9u/c9, where u is the current speed at a depth and c is the first mode phase speed.) greater than unity near the main thermocline as a criterion to discriminate the ISW events on May 17, May 19, May 24, June 11 and June 14 during the SCSMEX. Here, the duration when the Froude number near the background main thermocline is greater than 1 is defined as the passage period of ISWs. Thus, the passage periods of these five ISW events are 6 min, 9 min, 9 min, 9 min and 7.5 min, respectively. By averaging the current velocity during the passage period of ISWs, the time-averaged vertical current shear could be calculated, and then it is compared with the solution of KdV equation model. Fig. 2 illustrates a good match between the solution of the KdV equation and our observational result in all five ISW events, demonstrating that: (1) our analyses based on the coarse vertical resolution of observation are capable of describing the mixing characteristics of ISWs, and (2) the observed ISWs during the SCSMEX are mainly the KdV-type ISWs. The match between both results may be due to the following reasons, first, the observed profiles are calculated using the time-averaged vertical current shear, which may reduce the nonlinearity of the observed ISWs; second, as we will discuss later, breaking event does not occur in our observed ISWs cases. It shows that the vertical current shear generally has a value of about 10  3–10  2 s  2 and is the smallest near the background main thermocline. The vertical current shear calculated from both observations and solutions of KdV equation suggests that, the mixing rate (or the vertical current shear) has a minimum value near the background main thermocline, i.e., when the ISWs pass, the time-averaged mixing near the background main thermocline is not enhanced significantly. Our available effective observational current data are only from 10 m to 128 m, thus we calculate the various parameters at different depths in the upper layer by Eqs. (2) and (3). Since we have no synchronous current, temperature and salinity data during the passage of ISWs, thus we have to choose the temperature and salinity data obtained near the passage of ISWs to calculate the buoyancy frequency. For example, in the case of the ISW on June 14, 1998, since the current data are recorded at about 10:43–11:23, while the temperature and salinity data are recorded at 10:55, thus we suppose that the profile of buoyancy frequency changes slightly within 40 min before and after the passage of ISW in the following calculations. Fig. 3 shows the variations of the turbulent dissipation and diapycnal mixing rates, and the Froude number with time at a depth of 94 m where the enhanced mixing is the most significant during the passage of the ISW on June 14, 1998. Before the arrival of the ISW, the Froude number is less than 1, the turbulent dissipation rate and the mixing rate are 10  10–10  8 W kg  1 and 1  10  9 –3.2  10  8 m2 s  1, respectively. These two variables increase dramatically as soon as the ISW arrives with a Froude number

Table 1 Comparison of the turbulent dissipation rate and the diapycnal mixing rate without ISW events in different sea areas.

Our results Carter et al. (2005) Nash and Moum (2001) MacKinnon and Gregg (2003) Zhang et al. (2005) Tian et al. (2009) Lu et al. (2009)

Sea area

Turbulent dissipation rate

Diapycnal mixing rate

Northern South China Sea Monterey Bay Oregon Shelf New England Shelf Northern South China Sea Both sides of the Luzon Strait Northern South China Sea

10  10–10  7 W kg  1 10  10–10  5 W kg  1

10  8–10  5 m2 s  1 10  7–10  5 m2 s  1 10  5–5  10  5 m2 s  1 10  6–10  3 m2 s  1 10  6–10  3 m2 s  1 10  4–10  1 m2 s  1 10  7–10  2 m2 s  1

10  9–10  5 W kg  1 10  8–10  7 W kg  1 10  9–10  7 W kg  1

J. Xu et al. / Continental Shelf Research 49 (2012) 34–43

37

Fig. 2. Comparison of the time-averaged vertical current shear (s  2) versus depth during the passage of the ISWs between the solution of the KdV equation (solid line) and the observations (dashed line) on May 17, May 19, May 24, June 11 and June 14, respectively.

Fig. 3. Variation of (a) the turbulent dissipation rate (W kg  1), (b) the diapycnal mixing rate (m2 s  1), and (c) the Froude number at a depth of 94 m with time on June 14, 1998 during the passage of an ISW. Here and subsequently, the time axis is in the format of hour:minute:second.

exceeding the critical value of unity, e.g., at the depth of 94 m, the maximum turbulent dissipation rate is 1.8  10  6 W kg  1, which increases by about three orders of magnitude; the maximum diapycnal mixing rate is 1.2  10  5 m2 s  1, which also increases

by three orders of magnitude. After the passage of the ISW, the mixing weakens, both the turbulent dissipation rate and the diapycnal mixing rate fall to a normal magnitude as that before the arrival of the ISW. The occurrence of the enhanced mixing

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J. Xu et al. / Continental Shelf Research 49 (2012) 34–43

during the passage of the ISW is corresponding to the variation of the Froude number. The above various parameters could only illustrate the variation of the enhanced mixing with time at a depth during the passage of ISWs, but whether the mixing rate increases at all depths or not is not explicit. Consequently, three moments are chosen to analyze the variations of the vertical current shear, the turbulent dissipation rate and the mixing rate with depth in the upper layer. Moment A is defined as the moment when the Froude number at the depth of the background main thermocline begins to change from less than 1 to greater than 1, which stands for the arrival of the ISW. Moment B is defined as the moment when the Froude number becomes the maximum, which indicates the passage of the ISW trough, while moment C is defined as the moment when the Froude number begins to change from greater than 1 to less than 1, which represents the tail end of the ISW. Moments A, B and C on June 14, 1998 are shown in Fig. 4a, and the buoyancy frequency corresponding to the passage of the ISW is presented in Fig. 4b. Additionally, the variations of the vertical current shear, the turbulent dissipation rate and the mixing rate versus depth at moments A, B and C are shown in Figs. 4c–e, respectively. Moreover, from Eqs. (13)–(15), the variations of the diapycnal mixing rate with depth and time, and the depth of corresponding disturbed thermocline (Fig. 5) are calculated. At moment A (Fig. 4c), the vertical current shear, the turbulent dissipation rate and the mixing rate only peak at a depth about 80 m, where these three parameters increase by three orders of magnitude. The maximum mixing rate appears at a depth of about 30 m above the disturbed thermocline. No significant enhanced mixing is observed at moment B (Fig. 4d), because the estimated amplitude of the ISW Z0 is about 93 m, thus the disturbed thermocline is at a depth of about 153 m, which is

beyond the range of our measurements. At moment C (Fig. 4e), the vertical current shear, the turbulent dissipation rate and the mixing rate increase at 44–56 m, 60–76 m and 90–100 m, and the mixing rate gets maximum at a depth of 98 m, about 20 m above the disturbed thermocline. Fig. 6 illustrates the variations of the mixing rate, the reciprocal of the gradient Richardson number and the Froude number. To measure the uncertainty leading from time variability in N, we also calculate the gradient Richardson number using the N profiles before, during and after the passage of the ISW, and it is found that the variation of the calculated gradient Richardson number is only about 5%, illustrating that the use of single density profile is allowable. Fig. 6 shows that the reciprocal of the gradient Richardson number tends to be greater than 4 when the mixing rate is large. Moreover, the enhanced mixing also occurs when the Froude number equals the critical value of unity. This seems to suggest that, the enhanced mixing only happened when the Froude number approximately equaled the critical value of unity, but it did not happen when the Froude number was much greater than 1 or less than 1. According to the former studies (Grue et al., 2000; Vlasenko and Hutter, 2001; Lamb, 2003), the gradient Richardson number is less than 1/4 seems to suggest that the enhanced mixing was caused by the shear instability, while the Froude number approximately equals to 1 seems to suggest that the enhanced mixing was caused by the convective instability. Based on the laboratory studies (Helfrich and Melville, 1986; Helfrich, 1992), a criterion for the breaking of the ISW when shoaling is that, breaking occurs at the site where the undisturbed lower-layer depth h2 is about 2–3 times the ISW amplitude Z0. Moreover, Vlasenko and Hutter (2002) documented a criterion for the breaking of the ISW when shoaling by model studies. They pointed out that a breaking event could arise if the ISW amplitude

Fig. 4. (a) Froude number near the main themocline versus time, (b) corresponding buoyancy frequency (s  1) versus depth, (c) vertical current shear (s  2) (dash line), turbulent dissipation rate (W kg  1) (solid line) and diapycnal mixing rate (m2 s  1) (dotted line) versus depth at moment A, here, logarithmic coordinate is used, (d) same as (c) but at moment B, and (e) same as (c) but at moment C on June 14, 1998 during the passage of the ISW.

J. Xu et al. / Continental Shelf Research 49 (2012) 34–43

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Fig. 5. Variation of the diapycnal mixing rate with depth and time (where the heavy solid line denotes the disturbed thermocline, and the vertical dotted lines represent moments A, B and C).

Fig. 6. Variation of (a) the diapycnal mixing rate (m2 s  1), (b) the reciprocal of the gradient Richardson number and (c) the Froude number with time on June 14, 1998.

Z0 was larger than 0.4h2. In our cases, the whole water depth is 472 m, h2 is 414 m, Z0 is about 93 m. Consequently, h2 is larger than 4 times of Z0, and Z0 is less than 0.4h2. Applying the above criteria, it is easy to find that the breaking event does not occur during the passage of the ISWs here, but since Z0/h2 is about 0.22, there appears to be some shear instability or overturning as concluded by the observation (Helfrich and Melville, 1986). As above, we also analyze the mixing versus depth in other ISW events. Figs. 7–10 show the variations of the vertical current shear, the turbulent dissipation rate and the diapycnal mixing rate versus depth at moments A, B and C in the other four ISW events. Besides, the depths of the disturbed thermocline at different moments are calculated (Table 2). It is found that the variation of the parameters on May 24 (Fig. 7) is similar to that on June 14. At moment A, the vertical current shear, the turbulent dissipation rate and the mixing rate increase at 20–24 m and 44–54 m by three orders, two orders and one order of magnitude, respectively, and the mixing rate gets maximum at a depth of 50 m, about 48 m above the disturbed thermocline. No significant enhanced mixing is observed at moment B, because the estimated amplitude of the ISW is about 82 m, thus the disturbed thermocline is at a depth of about 136 m, where is beyond our observation. At moment C, the vertical current shear, the turbulent

Table 2 Some mixing characteristics in different ISW events. Time

Moment

A

B

C

A

B

C

Amplitude Maximum thickness of the Depth where the upper layer (m) mixing rate is the maximum (m) May 17, 1998 66.31 May 19, 1998 57.04 May 24, 1998 82.05

100.56 99.30 98.1

121.31 107.04 136.04

114.92 107.33 120.2

80 62 50

102 94

84 80 110

June 11, 1998 59.25

66.38

110.25

103.56

55

102

82

dissipation rate and the mixing rate only peak at a depth about 110 m, with the maximum mixing rate at a depth of about 10 m above the disturbed thermocline. It is noticed that, in the above ISW events, there are several enhanced mixing peaks at different depths at moment A or C. However, in the other three ISW events (Figs. 8–10), the variation of mixing with depth exhibits a different pattern, i.e., at

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J. Xu et al. / Continental Shelf Research 49 (2012) 34–43

Fig. 7. Same as Fig. 4 but on May 24, 1998.

Fig. 8. Same as Fig. 4 but on May 17, 1998.

all of the three moments, the mixing enhanced merely at a depth. Fig. 8 shows that, on May 17, the vertical current shear and the turbulent dissipation rate increase by two orders and one order of

magnitude, respectively, and the mixing rate increases by six times. At moments A, B and C, the maximum mixing occurs at depths of 80 m, 102 m, and 84 m, about 20–30 m above the

J. Xu et al. / Continental Shelf Research 49 (2012) 34–43

41

Fig. 9. Same as Fig. 4 but on May 19, 1998.

Fig. 10. Same as Fig. 4 but on June 11, 1998.

disturbed thermocline. Figs. 9 and 10 show that, the variation of the vertical current shear, the turbulent dissipation rate and the mixing rate on May 19 and June 11 are similar to those on

May 17. Table 2 documents that the maximum mixing in these two ISW events occurs at about 10–30 m above the disturbed thermocline.

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J. Xu et al. / Continental Shelf Research 49 (2012) 34–43

temporally and spatially. It is found that, during the passage of ISWs, the variation of the time-averaged vertical shear has a good agreement with the KdV equation theory, suggesting that the timeaveraged mixing rate (or the vertical current shear) has a minimum near the background main thermocline. In the upper layer, when the ISWs arrive, the maximum turbulent dissipation rate and the diapycnal mixing rate can increase by three orders of magnitude, and the occurrence of the enhanced mixing during the passage of the ISW corresponds to the variation of the Froude number. In the upper layer, two types of the instantaneous enhanced mixing caused by ISWs are classified. Type-a enhanced mixing has several enhanced mixing peaks at different depths when the Froude number near the background main thermocline changes from less than 1 to greater than 1 or when it changes from greater than 1 to less than 1. Type-b enhanced mixing has only one enhanced mixing peak at a depth during the passage of ISWs. It shows that the mixing is highest at a depth about 10–50 m above the disturbed thermocline. The vertical current shear, the turbulent dissipation rate and the diapcynal mixing rate increase by 3–4 orders, 2–3 orders and 1–3 orders of magnitude, respectively. The enhanced mixing is coincident with a gradient Richardson number of less than 1/4, which implies that the shear instability is the main cause of the local enhanced mixing. Additionally, the enhanced mixing occurs when the Froude number approximately equals critical value of unity.

Acknowledgments Authors are indebted to the anonymous referees for important and helpful comments. This work was jointly supported by The National Basic Research Program (Nos. 2011CB013701 and 2013CB956101), the Knowledge Innovation Program of the Chinese Academy of Sciences (Grant No. SQ201107) and NSFC Grant No. 41025019. Fig. 11. Vertical current shear (s  2) of the fourth mode ISW versus depth computed by the KdV equation.

In summary, two types of enhanced mixing in the ISW events are categorized. Type-a enhanced mixing has several enhanced mixing peaks at different depths at moment A or C, e.g., on May 24 and June 14; type-b enhanced mixing has only one enhanced mixing peak at a depth at all moments in the other ISW events. Two reasons may cause the type-a enhanced mixing. First, typea enhanced mixing may be caused by the high-mode ISW. Fig. 11 displays the vertical current shear of the forth mode ISW computed by the KdV equation. It shows that, the forth mode ISW could cause several peaks in the vertical shear and thereafter the enhanced mixing at different depths. Type-b enhanced mixing mainly occurs merely at a depth may be due to the passage of a depression ISW in which the first mode wave is dominant. Second, type-a enhanced mixing may be caused by the strong shear instability when the large amplitude ISWs are about to arrive or leave. It is noted that, the estimated ISW amplitude on June 14 is larger than those in the other ISW events, thus when the large amplitude ISW propagates shoreward, the induced current field is more likely to become unstable and the shear instability is enhanced, thus the enhanced mixing is stronger in the tail of the ISW, which agrees with the observational result by Moum et al. (2003).

4. Conclusions Based on the limited observational current velocity, temperature and salinity data, the enhanced mixing caused by ISWs is discussed

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