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The vertical heat transport of internal solitary waves over the continental slope in the northern South China Sea
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Changrong LIANG1, 2, Xiaodong SHANG1, *, Guiying CHEN1
Acta Oceanologica Sinica | 2019, 38(3) : 36 - 44
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Acta Oceanologica Sinica | 2019, 38(3): 36-44
• Physical Oceanography, Marine Meteorology and Marine Physics •
The vertical heat transport of internal solitary waves over the continental slope in the northern South China Sea
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Changrong LIANG1, 2, Xiaodong SHANG1, *, Guiying CHEN1
Affiliations
  • 1 State Key Laboratory of Tropical Oceanography, South China Sea Institute of Oceanology, Chinese Academy of Sciences, Guangzhou 510301, China
  • 2 University of Chinese Academy of Sciences, Beijing 100049, China
Published: 2019-03-25 doi: 10.1007/s13131-019-1397-3
Outline
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An integrated analysis of internal solitary wave (ISW) observations obtained from two moorings over the continental slope in the northern South China Sea (SCS) leads to an assessment of the vertical heat transport of the ISWs. The clusters of ISW packets are phase-locked to the fortnightly cycle of the semidiurnal tide. The ISWs appear during large semidiurnal tides, and there is a period of 5–6 d when no ISWs are observed. The effect of the ISWs on the continental slope heat budget is observed. The ISWs can modify a local temperature field in which the temperature in the upper layer can be changed by O (100) °C after the ISWs passed the mooring. Both ISW-induced diffusion and ISW-induced advection contribute to the temperature variation. The estimates imply an average vertical heat flux of 0.01 to 0.1 MW/m2 in the ISWs in the upper 500 m of the water column. The vertical heat transport ranges from 0.56 to 2.83 GJ/m2 with a mean value of 1.63 GJ/m2. The observations suggest that the vertical heat transport is proportional to the maximum vertical displacement.

internal solitary wave  /  vertical heat transport  /  temperature variation  /  diffusion  /  advection  /  vertical heat flux
Changrong LIANG, Xiaodong SHANG, Guiying CHEN. The vertical heat transport of internal solitary waves over the continental slope in the northern South China Sea[J]. Acta Oceanologica Sinica, 2019 , 38 (3) : 36 -44 . DOI: 10.1007/s13131-019-1397-3
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1 Introduction
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Nonlinear internal solitary waves (ISWs) are a ubiquitous feature in the ocean. They carry large amounts of energy and momentum as they propagate (Klymak et al., 2006; Lien et al., 2005). The ISWs can reach the breaking limit as they shoal, producing enhanced turbulent mixing (Lien et al., 2014, 2012). Strong momentum and enhanced turbulent mixing induced by the ISWs suggest that the ISWs are a fundamental contributor to the redistribution of nutrients and heat. Elevated heat fluxes in the ISWs have been reported over the continental shelf (Moum et al., 2003; Inall et al., 2000; Shroyer et al., 2010). Inall et al. (2000) estimated the average heat flux across the thermocline to be 80 W/m2 over the Malin shelf during the large-amplitude high-frequency ISWs; Moum et al. (2003) reported an instantaneous heat flux in the ISWs of O (103) W/m2 over the continental shelf of Oregon; Shroyer et al. (2010) estimated the instantaneous heat flux in the ISWs to be 790 W/m2 over New Jersey’s shelf, which was one order of magnitude greater than the background value. These observations indicated that the enhancement of heat flux in the ISWs over the continental shelf is primarily attributed to the ISW-induced diffusion.
The South China Sea (SCS), which is one of the largest marginal seas of the Pacific, is well known as a location where the ISWs have been commonly observed. The ISWs originate in the Luzon Strait and propagate westward across the deep basin until they encounter the continental shelf (Guo and Chen, 2014; Ramp et al., 2004), which can be observed in Synthetic Aperture Radar (SAR) imagery (Hsu et al., 2000; Liu and Hsu, 2004). In addition to these ISWs originating in the Luzon Strait, the ISWs can also be generated locally at the shelf break by the evolution of the internal tides due to nonlinear and dispersive effects (Xu et al., 2010). Although there have been numerous studies of the ISWs in the northern SCS (Orr and Mignerey, 2003; Ramp et al., 2010; Alford et al., 2010, 2011; Bai et al., 2014; Chen et al., 2014), most studies have focused on the generation, characteristics, propagation patterns and energy contents of the ISWs, but few studies have focused on the vertical heat transport of the ISWs. Here we report the vertical heat transport of the ISWs over the continental slope in the northern SCS using data collected in autumn 2014. Our observations indicate that both ISW-induced advection and ISW-induced diffusion contribute to the redistribution of heat, and the magnitude of depth-integrated heat has a positive relationship with the maximum vertical displacement. We continue in Section 2 with a description of our experimental area and moored instrumentation. The results are presented in Section 3, which is divided into two parts. First, the arrivals of the ISWs are documented and their implied relationship with the internal tides is discussed. Second, we estimate the vertical heat transport of the ISWs and discuss the relationship between the vertical heat transport and the vertical displacement. A discussion and conclusions are provided in Sections 4 and 5, respectively.
2 Measurements
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On 1 August 2014 two moorings (A and B) were deployed over the continental slope in the northern SCS (Figs 1a and b). The deployment lasted for 59 d, from 1 August to 27 September 2014, providing a description of the surface and internal tides and, in particular, the velocity and temperature structures of the ISWs. Mooring B (20.84°N, 117.56°E) was located 22.13 km away from Mooring A (20.74°N, 117.75°E). The water depths of Moorings A and B were approximately 1 260 and 850 m, respectively. Mooring A was equipped with one upward-looking 75 kHz ADCP at 440 m depth, one downward-looking 75 kHz ADCP at 450 m depth, one downward-looking 150 kHz ADCP at 950 m depth, two Sea-Bird Electronics CTD sensors, 15 temperature sensors, and 14 conductivity/temperature (CT) sensors. The upward-looking and downward-looking 75 kHz ADCPs pinged and recorded data at 2 min interval with a vertical resolution of 16 m. The downward-looking 150 kHz ADCP pinged and recorded data at 1.5 min interval with a vertical resolution of 8 m. All of the CTD and temperature sensors sampled at 10 s interval, and the CT sensors sampled at 15 s interval. Mooring B was equipped with one upward-looking 75 kHz ADCP at 500 m depth, one downward-looking 75 kHz ADCP at 520 m depth, two Sea-Bird Electronics CTD sensors, 12 temperature sensors, and nine CT sensors. Both 75 kHz ADCPs pinged and recorded at data 2 min interval with a vertical resolution of 16 m. All of the CTD and temperature sensors sampled at 10 s interval, and the CT sensors sampled at 15 s interval. The ADCP relies on sufficient natural scatters in the water column to create a good return signal, but the ADCP cannot capture sufficient natural scatters every time. Data that comprised less than 80% good natural scatters were rejected, and the occasional unrealistic extreme values (e.g., speeds of being greater than 10 m/s) were removed. If the absent data points had good adjacent values in either time or space, then they were estimated using linear interpolation. Data from Mooring A were used to explore the characteristics of the ISWs and estimate the vertical heat transport of the ISWs, whereas data from Mooring B were combined to calculate the phase speed of the ISWs.
3 Results
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3.1 Arrival of internal solitary waves
We analyzed the scale and arrival of the ISWs using the data obtained from Mooring A. To clearly show the scale and arrival of the ISWs, we applied high-pass filtering of 1.0 h–1 to the temperature signal at 250 m. The high-pass filtered temperature fluctuations (Fig. 1c) clearly provide an overall impression of the scale and arrival of the ISWs. All of the observed ISWs were depression waves, such that a pronounced increase in temperature was observed as the ISWs passed the mooring. The largest temperature fluctuation induced by the ISWs was 8.5°C. Five clusters of the ISW packets were observed during the measurements, where the amplitudes of Cluster 2 waves were much greater than those of other cluster waves. The ISWs typically form from internal tides that are generated by tidal flow over topography in the Luzon Strait (Li and Farmer, 2011). To explore the relationship between the ISWs and the barotropic tides in the Luzon Strait, we obtained the barotropic tides in the Luzon Strait (20.5°N, 121.0°E) using the global inverse tide model (TPXO) (Egbert and Erofeeva, 2002), which provides the timing of diurnal and semidiurnal tides in the Luzon Strait during the period of observation. The distance between Mooring A and the Luzon Strait (20.5°N, 121.0°E) is approximately 341 km. With the mean phase speed of ISWs of 3.11 m/s (Table 1), we can estimate the time that is necessary for the ISWs to propagate from the Luzon Strait to Mooring A. The estimated propagation time is approximately 1.27 d. Figure 1d shows the resultant tides of tidal frequencies. The propagation time of the ISWs was offset. The fortnightly cycles were well-represented in both the resultant diurnal tide [u(O1)+u(K1)+u(P1)+u(Q1)] and the resultant semidiurnal tide [u(M2)+u(S2)+u(N2)+u(K2)]. A comparison of the high-pass filtered temperature fluctuations (Fig. 1c) to the resultant tides (Fig. 1d) clearly provides an overall impression of the arrival of the ISWs. The clusters of the ISW packets were clearly phase-locked to the fortnightly cycle of the semidiurnal tide. The ISWs appeared during large semidiurnal tides and there is a period of 5–6 d (during small semidiurnal tides) when no ISWs were observed.
To further explore the features of the ISWs, we plot samples of time series of the vertical velocity in Fig. 2. These time series span from 236 to 242 d (Fig. 1d, during large semidiurnal tides). There are no ISWs in 235 d (not shown), and only one ISW occurs in 236 d. As the semidiurnal tide became strong (Figs 1c and d), more ISWs occurred per day. As is shown in Fig. 2, three ISWs occurred each day in the following 4 d (237–240 d). The number of the ISWs decreases again as the semidiurnal tide became weak (241 and 242 d). For simplicity, we define the three ISWs that occurred in 1 d as S1, S2 and S3, respectively. S1 appeared in the morning (05:00–09:00 o’clock) and S2 appeared approximately 2 h after the appearance of S1. S2 had small amplitudes but were independent of S1. S3 appeared during the nighttime (20:00–22:00 o’clock). S3 was weaker than S1 but stronger than S2. S1 arrived approximately 30 min later each day, and S2 arrived approximately 15 min later each day. These time lags were smaller than those over the continental shelf that were reported by Ramp et al. (2004). More observations are needed to explain this difference.
3.2 Vertical heat transport of internal solitary waves
One of the ISWs from Mooring A is shown in Fig. 3, which provides more details about the current and temperature structures of the ISWs. This ISW arrived at Mooring A on 251.15 d (Fig. 1c, indicated by the arrow). Only zonal velocity is shown because the ISWs propagated principally westward and most of the velocities were contained in the zonal velocity. The ISW had opposing zonal currents in the upper (<225 m) and lower (>225 m) layers, with the maximum westward current in the upper layer reaching 1.4 m/s (Fig. 3a). The nodal point where the zonal velocity was 0 was at 225 m, which is deeper than those observed over the continental shelf (Lien et al., 2014). The vertical velocity (Fig. 3b) shows a classic first-mode depression wave structure with a sharp downward vertical velocity followed by an upward vertical velocity. We estimated the vertical displacement (δ) using vertical velocity data (Inall et al., 2001), which is defined as
$\delta \left({z, t} \right) = \mathop \int \nolimits_{{t_0}}^t {W_{\rm{f}}}\left({z, t} \right){\rm{d}}t, $
where t0=–90 min and Wf(z, t) is the high-pass filtered (1 h–1) vertical velocity signal at depth z. The results are shown in Fig. 3b. Large vertical displacements were observed between the two vertical pulses with the maximum vertical displacement (δmax) reaching 72 m. In total, 75 ISWs were encountered during the observation period. A summary of the maximum vertical displacement in the observed ISWs is given in Table 1. The maximum vertical displacement shows large variation; and these values range from 13.2 to 158.5 m, with a mean value of 70.8 m and a standard deviation of 35.8 m.
Figure 3c shows the isotherms of the ISW. The temperature sensors in the upper layer were pressed down to the deep water during the passage of the ISW as the mooring was bent over by drag forces, thus there are no temperature data in the upper layer during the passage of the ISW (the white patch in Fig. 3c). The depths of the temperature/CT sensors during the passage of the ISW were calculated based on the depths of the CTDs and the ADCPs. There are two cases for the sinking of the temperature/CT sensors. In the first case, we assume that the sinking of the temperature/CT sensors resulted from the tilting of the mooring. The depths that were calculated from this case were the lower limits of the temperature/CT sensors. In the second case, we assume that the sinking of the temperature/CT sensors resulted from the vertical sinking of the mooring. The depths calculated from this case were the upper limits of the temperature/CT sensors. The first case is more likely to be accurate. As indicated in Figs 3a and b, the horizontal velocity was much stronger than the vertical velocity in the upper 200 m. Thus upper instruments were advected horizontally by the horizontal velocity, which resulted in the tilt of mooring, rather than vertical depressed by the vertical velocity, and caused the mooring to sink vertically. Here we calculated the depths of the temperature/CT sensors during the passage of the ISW by assuming that the sinking of the temperature/CT sensors resulted from the tilting of the mooring, which provides the lower limits of the temperature/CT sensors.
Isotherms were first depressed downward by the downward vertical velocity and were then lifted up by the upward vertical velocity. The maximum isotherm displacement reached 109 m (Fig. 3c, indicated by the thick black curve). Figure 3c also shows the steady wave-like solutions of the Korteweg-deVries (KdV) equation (Moum et al., 2003; Choi and Camassa, 1999), $\zeta \left({x, t} \right) = a\;{\rm{sec}}{{\rm{h}}^2}\left[ {\left({x - ct} \right)/\text{λ} } \right]$, where a=109 m, is the wave amplitude; c=3.0 m/s, is the phase speed; and λ=1 277 m, is the half width of the wave. Moorings A and B are nearly located along the direction of propagation of the ISWs (Liu et al., 2004; Xu et al., 2016) and the distance between them was small. Therefore, the phase speed was roughly estimated by dividing the horizontal separation (22.13 km) between Moorings A and B by the corresponding elapsed time (1.98 h), and then subtracting the mean tidal speeds of O (0.1) m/s. The ISW traveled faster than those observed by Lien et al. (2014) in shallow water (<500 m), whose measured phase speeds of the ISWs were smaller than 2.5 m/s. The large phase speeds observed here are consistent with the theory (Small, 2001a, b ) that the phase speeds decrease as the ISWs shoal. The shape of the ISW is quite close to sech2 form (Fig. 3c, indicated by the pink curve), indicating that the ISWs can be described by the weakly nonlinear KdV equation. Different ISWs had different phase speeds, wave amplitudes, and half-widths. A summary of the phase speeds, the wave amplitudes, and the half-widths is given in Table 1. The phase speeds range from 2.55 to 3.82 m/s, with an average of 3.11 m/s. The small value (0.26 m/s) of standard deviation indicates that the phase speeds of the ISWs were relatively stable. The wave amplitude, instead, was more variable. These values range from 45 to 195 m with a mean value of 86 m and a standard deviation of 34.4 m. Evidence of variable wave amplitudes can also be observed in the time-series of high-pass filtered temperature fluctuations in Fig. 1c. The half width also shows variation, ranging from 795 to 2 568 m with a mean value of 1 382 m and a standard deviation of 415.2 m.
A prominent feature in Fig. 3c is that the observed isotherms after the passage of the ISW (t>25 min) were deeper than those before the ISW (t<–25 min), which implies an increase in the temperature after the ISW passed the mooring. The profiles of Tb(z) and Ta(z) are shown in Fig. 3d and their difference, ΔTab(z)=Ta(z)–Tb(z), is shown in Fig. 3e. Tb(z) was the average temperature at depth z between –90 and –25 min on the time axis in Fig. 3c, corresponding to the period when the temperature field was not influenced by the ISW and Ta(z) was the average temperature at depth z between 25 and 90 min, corresponding to the period when the ISW had passed the mooring. ΔTab(z) represented the temperature variation at depth of z induced by the ISW. ΔTab showed a decreasing trend with depth and became insignificant at approximately 500 m. The maximum of ΔTab occurred in the topmost layer with a value of 2.45°C. A small peak value of ΔTab was observed at 215 m.
An increase in the temperature after the passage of the ISW indicates that the heat is redistributed by the ISW. To quantify how much heat was transported into the lower layer by the ISW, we estimated the net heat transport of the ISW using:
$Q\left(z \right) = {\rho _{\rm{a}}}\left(z \right){c_{\rm{p}}}{T_{\rm{a}}}\left(z \right) - {\rho _{\rm{b}}}\left(z \right){c_p}{T_{\rm{b}}}\left(z \right), $
where ρb and ρa are the water densities; and cp=3.986 kJ/(kg·°C) is the specific heat that describes the amount of heat needed to raise the temperature of a certain mass by 1°C. The estimated Q induced by the ISW is shown in Fig. 3f. The downward-decreasing trend of Q is similar to that of ΔTab. A small peak value of Q was also observed at 215 m, corresponding to the peak value of ΔTab at 215 m (Fig. 3e). The heat transport was mainly limited in the upper ocean with 98% of Q occurring in the upper 500 m.
The heat flux during the passage of the ISW was estimated by integrating Q in the water column, ${J_{\rm{s}}}\left(z \right) = \frac{1}{{\Delta t}}{\mathop \int \nolimits_{{z_{\rm{b}}}}^z} Q\left(z \right){\rm{d}}z$, where Δt=50 min, represents the time that the ISW needed to pass the mooring and zb represents the ocean bottom. The profile of Js is shown in Fig. 3f. Js shows a downward-decreasing trend with most of the heat flux occurring in the upper 500 m. The values of Js reached O (105) W/m2 in the upper 200 m. Js represents the heat flux in one of the ISWs, but clusters typically comprised large numbers of the ISWs with different amplitudes. To estimate the ISW contribution to the heat flux over the continental slope, we estimate the average heat flux (Jsm) of the ISWs that were encountered during the observation. Profile of Jsm is shown in Fig. 4a. Jsm shows a decreasing trend with depth and most of the heat flux occurred in the upper 500 m. The divergence of heat flux in the ISWs is expressed through the one-dimensional balance $\Delta T = - \Delta t{\left({\rho {c_p}} \right)^{ - 1}}\left({{\rm{d}}J_{\rm{s}}^{\rm{m}}/{\rm{d}}z} \right)$. Profile of ΔT is shown in Fig. 4b. Large averaged heat flux could change the temperature in the upper 500 m by 0.2 to 1.5°C with a mean value of 0.8°C. This implies that the ISWs are a significant contributor to the redistribution of heat over the continental slope.
The total heat transports of the ISWs were estimated as ${E_Q} = {\mathop \int \nolimits_{{z_{\rm{b}}}}^{{z_{\rm{t}}}} }Q{\rm{d}}z$, where zt and zb represent the ocean surface and bottom, respectively. Q in each good temperature measurement depth bin was assumed to be constant with height over that depth bin. Here, we calculate EQ by integrating Q between 65 and 1 250 m because there were few data in the upper 65 m, thus EQ represents the total heat transport that was needed to achieve the temperature variations below 65 m. A summary of EQ in the observed ISWs is given in Table 1. EQ ranges from 0.56 to 2.83 GJ/m2 with a mean of 1.63 GJ/m2. EQ shows large variation, similar to δmax. To explore the relationship between EQ and δmax, a scatter plot between EQ and δmax is shown in Fig. 5. EQ displays a generally increasing trend with δmax. An empirical linear fit between EQ and δmax was obtained, EQ=αδmax+β, where α=10.3 MJ/m3 and β=0.88 GJ/m2, are the fitting parameters.
To assess the efficacy of the model of EQ=αδmax+β in predicting EQ, we tested the linear regressions with t-test (Rice, 2006). The two-tailed test P-value estimated from the raw data and fitted values is 0.834. This value is greater than 0.05, which suggests that the null hypothesis cannot be rejected. The coefficients of determination (R2) were also calculated to quantify how well the model can predict EQ. R2 is the ratio of the difference between the variance of the observed values and the variance of the residuals from the fit to the variance of the observed values (Rice, 2006). It can be interpreted as the proportion of the variability of the observed values that can be explained by the fitted values. The coefficient of determination between the bin-averaged data and the fitted values is 0.974, and the coefficient of determination between the raw data and the fitted values is 0.435.
4 Discussion
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In the above analysis, we show that the ISWs can cause large temperature variation in the upper ocean after they pass the mooring. The temperature variation induced by the ISWs can be described by the following time-dependent conservation equation (Pope, 2000):
$\text{∂}T/\text{∂}t = \nabla \cdot \left({\kappa \nabla T} \right) - \nabla \cdot \left({\vec vT} \right), $
where κ is the eddy diffusivity; ${\vec v}$ is the velocity field; $\nabla$ is the gradient operator; and $\nabla $· is the divergence operator. The temperature variation comprises diffusive and advective components. The first contribution, $\nabla$·(κ$ \nabla$T), describes the diffusion. The second contribution, –$\nabla $·(${\vec v}$T), describes the advection, which is a transport mechanism of a conserved property by a fluid due to the fluid’s bulk motion. Considering that diffusion is mainly dominant in the vertical direction and assuming that the velocity field describes an incompressible flow, then Eq. (2) can be simplified to
$\frac{{\text{∂}T}}{{\text{∂}t}} = \frac{\text{∂}}{{\text{∂}z}}\left({\frac{{{\kappa _z}\text{∂}T}}{{\text{∂}z}}} \right) - \left({U\frac{{\text{∂}T}}{{\text{∂}x}} + V\frac{{\text{∂}T}}{{\text{∂}y}} + W\frac{{\text{∂}T}}{{\text{∂}z}}} \right), $
where κz is the vertical eddy diffusivity; U, V and W are the zonal velocity, the meridional velocity, and the vertical velocity, respectively. Equation (3) implies that both advection and diffusion contribute to the temperature variation. Assuming that the advection term is 0 and the temperature variation just results from the diffusion, then Eq. (3) becomes the diffusion equation:
$\frac{{\text{∂}T}}{{\text{∂}t}} = \frac{\text{∂}}{{\text{∂}z}}\left({\frac{{{\kappa _z}\text{∂}T}}{{\text{∂}z}}} \right).$
The contribution of the ISW-induced diffusion to the temperature variation has been reported by previous researchers (i.e., Inall et al., 2000; Moum et al., 2003). In these observations, the contribution of advection to the temperature variation appears to be less important compared with the diffusion. Their observations show that the temperature variation can be achieved by solving the diffusion equation with the observed eddy diffusivity and temperature gradients, or the eddy diffusivity can be estimated by solving the diffusion equation with the temperature variation. Taking the ISW that is shown in Fig. 3 as an example, we assume that the temperature variation only resulted from diffusion and solve the diffusion equation numerically with the temperature profile Tb following Inall et al. (2000). The diffusion time is set to 50 min, which corresponds to the time that was needed for the ISW to pass the mooring. The estimated κz profile is shown in Fig. 4c. The result indicates that κz in the upper 500 m needs to be larger than 10–1 m2/s to achieve the temperature variation. However, the observations of Lien et al. (2012) indicate that the vertical eddy diffusivity of O (10–1) m2/s mainly occurred at the trapped core (in the upper 150 m) of a shoaling ISW. Our mooring was located over the continental slope. The ISWs arrived at the mooring as a nearly steady-state solitary depression wave. Vertical eddy diffusivity would not be larger than 10–1 m2/s throughout the upper 500 m. Evidence can also be found in the depth-time map of shear $S = {\left({\text{∂}U/\text{∂}z} \right)^2} + {\left({\text{∂}V/\text{∂}z} \right)^2}$ (Fig. 6a). Strong shear was mainly concentrated in the upper 150 m, whereas the shear below was weak and comparable to background values. These observations suggest that κz below 150 m should be smaller than 10–1 m2/s. However, the profile of κz that was calculated from the diffusion equation shows κz of O (10–1) m2/s below 150 m (Fig. 4c). This difference suggests that in addition to diffusion, the advection also contributed to the observed temperature variation.
Evidence for the contribution of the advection to the temperature variation can be found in the velocity vector field of the ISW (Fig. 6b). We transformed the temporal variation in the ISW observations into the wave’s spatial structure using a phase speed of 3.0 m/s. The velocity divergences $\nabla \cdot \vec v$ are also shown in Fig. 6b. The velocity divergences were estimated as $\text{∂}U/\text{∂}x + \text{∂}W/\text{∂}z$ because the ISW propagated principally westward and only $\text{∂}U/\text{∂}t$ can be converted into $\text{∂}U/\text{∂}x$ using the phase speed. This does not substantially impact our discussion because most of the horizontal velocities were contained in the zonal velocity during the passage of the ISW. It is apparent in Fig. 6b that the velocity divergences were approximately 0 for most of the depths during the observation period. The velocity divergences at some depths slightly deviated from 0, such as the velocity divergences in the upper 100 m, might be due to the absence of $\text{∂}V/\text{∂}y$. These observations indicated that $\nabla \cdot \vec v$=0 and the velocity field did not violate the conservation of mass.
The velocity field featured a “subsurface layer” (between the isotherms of 9 and 16°C) with relatively strong eastward velocity (Fig. 6b). Warm water was advected downward by the vertical velocity between –10 and 0 min (on the time axis), during which the warm water was also advected horizontally by the large eastward velocity in the subsurface layer. The vertical velocity changed direction at t=0 min and advected the warm water upward again between 0 and 10 min. However, the warm water could not be lifted up to its original depth by the upward vertical velocity. It was advected horizontally by the large eastward velocity before the vertical velocity lifted it because the upward vertical velocity was small and of short duration compared with the eastward velocity. The warm water that was advected horizontally by the eastward velocity led to a small peak value of ΔTab near the top of the subsurface layer. ΔTab below the subsurface layer was small because no large eastward velocity advected water horizontally and the water was again lifted by the upward vertical velocity. The velocity field slowly reverted to its original state between 10 and 25 min. Evidence of the contribution of the ISW-induced advection to the temperature variation was also observed in other ISWs (not shown).
To further explore the contribution of advection to the temperature variation, we quantified the changes in the vertical temperature gradient $\text{∂}T/\text{∂}z$ due to the passage of the ISW, which is shown in Fig. 7. $\text{∂}T/\text{∂}z$ in the upper 100 m was increased by approximately 0.05 after the passage (t>10 min) of the ISW, which might result from turbulent mixing since diffusion would redistribute the temperature field without moving the water. $\text{∂}T/\text{∂}z$ was also depressed downward after the passage of the ISW. As shown in Fig. 7 that the bottom of the large $\text{∂}T/\text{∂}z$ (>0.1°C/m) changed from a depth of approximately 100 m to a depth of approximately 110 m. This redistribution of $\text{∂}T/\text{∂}z$ mainly resulted from the advection. Both diffusion and advection contributed to the temperature variation in the upper 100 m. A different phenomenon occurred below 100 m. $\text{∂}T/\text{∂}z$ below 100 m suffered from the redistribution that was induced by the advection but not the diffusion (i.e., values of $\text{∂}T/\text{∂}z$ remained nearly unchanged), which is especially evident near the depth of the 16°C isotherm. $\text{∂}T/\text{∂}z$ near the depth of the 16°C isotherm was approximately 0.05°C/m and was depressed downward by approximately 20 m. This depression would increase the temperature by approximately 1°C to the observed ΔTab of 0.922°C. This suggests that the temperature variation below 100 m mainly resulted from the advection. Both vertical and horizontal velocities contributed to the redistribution of $\text{∂}T/\text{∂}z$. The warm water was first advected downward by the downward vertical velocity and was then lifted by the upward vertical velocity, during which the warm water was also advected by the horizontal velocity. The horizontal velocity trapped the warm water from being lifted, which led to the temperature variation. Similarly, the advection of the background horizontal temperature gradient ($\text{∂}{T_{\rm{b}}}/\text{∂}x$) might also contribute to the temperature variation since large horizontal velocity occurred during the passage of the ISW. Here we roughly estimated $\text{∂}{T_{\rm{b}}}/\text{∂}x$ with temperature data from Moorings A and B. $\text{∂}{T_{\rm{b}}}/\text{∂}x$ is given by $\left({\overline {{T_{\rm{A}}}} - \overline {{T_{\rm{B}}}} } \right)/\Delta d$, where $\overline {{T_{\rm{A}}}} $ and $\overline {{T_{\rm{B}}}} $ are the average temperatures at Moorings A and B, respectively; and Δd=22.13 km, is the horizontal separation between Moorings A and B. Taking a depth of 215 m as an example, we estimated $\text{∂}{T_{\rm{b}}}/\text{∂}x$. The result indicated that $\text{∂}{T_{\rm{b}}}/\text{∂}x$ at depth of 215 m was 1.38×10–6°C/m. Thus an average horizontal velocity of 0.5 m/s that lasted for 180 min yields a temperature variation of 0.008°C, which is small compared with the observed value of 0.922°C. This suggests that the contribution of horizontal advection of $\text{∂}{T_{\rm{b}}}/\text{∂}x$ to the temperature variation was small at depth of 215 m. Contribution of horizontal advection of $\text{∂}{T_{\rm{b}}}/\text{∂}x$ to the temperature variation was also small at other depths (not shown).
Our estimates of Js were calculated based on the temperature variation that was induced by the ISWs; thus, Js comprised the contributions of the advection and the diffusion. They were larger than those observed over the continental shelf (Moum et al., 2003; Inall et al., 2000; Shroyer et al., 2010). Inall et al. (2000) estimated the average heat flux across the thermocline to be 80 W/m2 over the Malin shelf; Moum et al. (2003) reported an instantaneous heat flux of O (103) W/m2 over the continental shelf of Oregon; Shroyer et al. (2010) estimated the instantaneous heat flux in the ISWs to be 790 W/m2 over New Jersey shelf. The larger heat flux in our observation can be attributed to a combination of factors. The ISW-induced advection is expected to be one of the factors. In previous observations over the continental shelf, the heat flux was primarily attributed to the ISW-induced diffusion. However, the ISW-induced advection also contributed to the heat flux in our observation. This difference might result from the properties of the ISWs. Previous observations were conducted over the continental shelf where the ISWs had shoaled. Small wavelength shear instabilities occurred in the ISWs, which caused the contribution of diffusion to the vertical heat transport to be more prominent than that of the advection. Our mooring was located over the continental slope. The ISWs were weakly non-linear and stable. Large velocities induced by the ISWs could advect the warm water downward, thus making an important contribution to the vertical heat transport. Unfortunately, we have no observed κz during the passage of the ISW to quantify how much of the heat flux was contributed by the ISW-induced advection and the ISW-induced diffusion, respectively. Additional data (i.e., microstructure data) are needed to solve this problem in the future.
5 Conclusions
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Moored data obtained between 1 August and 27 September 2014 were used to explore the characteristic of the ISWs and estimate the vertical heat transport of the ISWs over the continental slope in the northern SCS. The clusters of the ISW packets were phase-locked to the fortnightly cycle of the semidiurnal tide. The ISWs appeared during large semidiurnal tides and there is a period of 5–6 d (during small semidiurnal tides) when no ISWs were observed. Our observation indicates that the ISWs can effectively modify the local temperature field in which the temperature increased as the ISWs passed the mooring. The increase in the temperature that was induced by the ISWs decreased with increasing depth and most of the temperature variation occurred in the upper 500 m. The heat flux that was estimated based on the temperature variation reached 0.01–0.1 MW/m2 in the upper 500 m, which is one to three orders of magnitude larger than those observed over the continental shelf (Moum et al., 2003; Inall et al., 2000; Shroyer et al., 2010). The average heat flux in the ISWs would change the temperature in the upper 500 m by 0.2 to 1.5°C with a mean of 0.8°C, indicating that the ISWs are a significant contributor to the redistribution of heat in the upper ocean over the continental slope. Our observation suggests that both the ISW-induced diffusion and ISW-induced advection contributed to the heat flux. The diffusion and advection contributed to the temperature variation in the upper 100 m, and the advection made the domination contribution to the temperature variation below 100 m. The warm water was first advected downward by the downward vertical velocity and then lifted by the upward vertical velocity, during which the warm water was also advected by the horizontal velocity. The horizontal velocity trapped the warm water from being lifted to its original depth, which significantly improved the efficiency of the vertical heat transport. The estimated total heat transport, EQ, ranged from 0.56 to 2.83 GJ/m2 with a mean value of 1.63 GJ/m2. EQ was determined to be proportional to the maximum vertical displacement, such that EQ=αδmax+β. This model fitting provides a simple method for determining the vertical heat transport of the ISWs propagating over the continental slope in the northern SCS where only the vertical displacement (or velocity) is known. However, whether the model can be applied to other regions, such as the continental shelf, remains unknown. More observations are needed to robustly verify this model in the future.
Acknowledgements
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We thank all the crew of the survey ship from the South China Sea Institute of Oceanology, Chinese Academy of Sciences.
Funding
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  • The National Natural Science Foundation of China under contract Nos 41676022, 41630970 and 41521005; the National Programme on Global Change and Air-Sea Interaction under contract No. GASI-IPOVAI-04; the Open Project Program of State Key Laboratory of Tropical Oceanography under contract No. LTOZZ1801; the Instrument Developing Project of the Chinese Academy of Sciences under contract No. YZ201432.
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Year 2019 volume 38 Issue 3
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doi: 10.1007/s13131-019-1397-3
  • Receive Date：2017-10-20
  • Online Date：2026-03-31
  • Published：2019-03-25
Article Data
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  • Received：2017-10-20
  • Accepted：2017-11-11
Funding
The National Natural Science Foundation of China under contract Nos 41676022, 41630970 and 41521005; the National Programme on Global Change and Air-Sea Interaction under contract No. GASI-IPOVAI-04; the Open Project Program of State Key Laboratory of Tropical Oceanography under contract No. LTOZZ1801; the Instrument Developing Project of the Chinese Academy of Sciences under contract No. YZ201432.
Affiliations
    1 State Key Laboratory of Tropical Oceanography, South China Sea Institute of Oceanology, Chinese Academy of Sciences, Guangzhou 510301, China
    2 University of Chinese Academy of Sciences, Beijing 100049, China

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表12种不同金属材料的力学参数
科
Family		 属数
Number of
genus		 种数
Number of
species		 占总种数比例
Percentage of
total species (%)		 属
Genus		 种数
Number of
species		 占总种数比例
Percentage of total
species (%)
鹅膏菌科Amanitaceae 2 11 5.26 鹅膏菌属 Amanita 10 4.78
小菇科 Mycenaceae 2 12 5.74 丝盖伞属 Inocybe 5 2.39
多孔菌科 Polyporaceae 8 14 6.70 蜡蘑属 Laccaria 5 2.39
红菇科 Russulaceae 3 23 11.00 小皮伞属 Marasmius 6 2.87
小菇属 Mycena 11 5.26
光柄菇属 Pluteus 5 2.39
红菇属 Russula 17 8.13
栓菌属 Trametes 5 2.39
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