The Impact of Subtidal Circulation on Internal-Tide-Induced Mixing in the Philippine Sea

Colette G. Kerry University of Hawai‘i at Mānoa, Honolulu, Hawaii

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Brian S. Powell University of Hawai‘i at Mānoa, Honolulu, Hawaii

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Glenn S. Carter University of Hawai‘i at Mānoa, Honolulu, Hawaii

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Abstract

This study uses a primitive equation model to estimate the time-varying M2 internal tide dissipation in the Philippine Sea in the presence of the subtidal circulation. The time-mean diapycnal diffusivity due to the M2 internal tide is estimated to be 4.0–4.8 × 10−4 m2 s−1 at the Luzon Strait and 2–9 × 10−5 m2 s−1 in the Philippine Sea basin. The variability in internal tides and their interactions with the subtidal ocean circulation results in significant spatial and temporal variability in the energy available for mixing. The subtidal circulation influences internal-tide-induced mixing in two ways: by introducing variability in internal tide generation and by increased dissipation of baroclinic energy associated with greater velocity shear. Close to the generation site, mixing is dominated by high-mode internal tide dissipation, while in the far field the influence of the mesoscale energy on internal tide dissipation is significant, resulting in increased dissipation. This study presents model-based estimates of the important and relatively unknown effect of mesoscale circulation on internal-tide-induced mixing away from internal tide generation sites in a region of high eddy kinetic energy.

Corresponding author address: Colette Kerry, University of Hawai‘i at Mānoa, 1000 Pope Rd., Honolulu, HI 96822. E-mail: ckerry@hawaii.edu

Abstract

This study uses a primitive equation model to estimate the time-varying M2 internal tide dissipation in the Philippine Sea in the presence of the subtidal circulation. The time-mean diapycnal diffusivity due to the M2 internal tide is estimated to be 4.0–4.8 × 10−4 m2 s−1 at the Luzon Strait and 2–9 × 10−5 m2 s−1 in the Philippine Sea basin. The variability in internal tides and their interactions with the subtidal ocean circulation results in significant spatial and temporal variability in the energy available for mixing. The subtidal circulation influences internal-tide-induced mixing in two ways: by introducing variability in internal tide generation and by increased dissipation of baroclinic energy associated with greater velocity shear. Close to the generation site, mixing is dominated by high-mode internal tide dissipation, while in the far field the influence of the mesoscale energy on internal tide dissipation is significant, resulting in increased dissipation. This study presents model-based estimates of the important and relatively unknown effect of mesoscale circulation on internal-tide-induced mixing away from internal tide generation sites in a region of high eddy kinetic energy.

Corresponding author address: Colette Kerry, University of Hawai‘i at Mānoa, 1000 Pope Rd., Honolulu, HI 96822. E-mail: ckerry@hawaii.edu

1. Introduction

Predicting the global geography of diapycnal mixing in the ocean is important as it plays a key role in the meridional overturning circulation. Turbulent dissipation of internal tide energy in the deep oceans is estimated to provide approximately half of the mixing required to maintain the thermohaline circulation (Munk and Wunsch 1998; Niwa and Hibiya 2011). A global-averaged diapycnal diffusivity of 10−4 m2 s−1 is thought to be needed to maintain ocean stratification and sustain the meridional overturning circulation based on a vertical advective–diffusive balance (Munk 1966; Munk and Wunsch 1998). Early microstructure measurements in the 1970s and 1980s and direct dye release experiments in the 1990s (Ledwell et al. 1993; Munk and Wunsch 1998) found open-ocean diffusivity of 10−5 m2 s−1, an order of magnitude smaller. Enhanced mixing has been observed over regions of rough topography [e.g., Rudnick et al. 2003; Klymak et al. 2006 (for the Hawaiian Ridge); Polzin et al. 1997; Ledwell et al. 2000 (for the Mid-Atlantic Ridge)]; however, Rudnick et al. (2003) suggested that this local mixing at isolated ridges cannot be sufficient to achieve the average diffusivity of 10−4 m2 s−1 to close the large-scale budget of the abyssal ocean. Recent work by Waterhouse et al. (2014), compiling a global dataset of turbulent dissipation and diffusivity estimates, suggests that existing observations are on average consistent with the required global-averaged abyssal diffusivity.

Understanding the spatial distribution and temporal variability of mixing in the global oceans is important for developing realistic mixing parameterizations for global climate-scale circulation models. Parameterizations accounting for local internal-tide-driven mixing over internal tide generation sites have been implemented into global circulation models (Simmons et al. 2004b; Jayne 2009; Melet et al. 2013); however, the distribution of mixing associated with internal tide energy that radiates away from generation sites is largely unknown and is likely to be important for global climate predictions. Low-mode internal tides have been observed to propagate long distances across the oceans (Ray and Mitchum 1997; Ray and Cartwright 2001; Alford 2003) and contribute to mixing at locations far away from their generation sites. The mechanisms by which energy radiated as low-mode internal tides is transferred to higher wavenumbers, and ultimately to turbulent dissipation, are an ongoing question. Energy transfer to smaller scales can occur via wave–wave interactions (e.g., Muller et al. 1986), topographic scattering (e.g., Muller and Xu 1992; St. Laurent and Garrett 2002), and interaction with sheared currents. Internal tides may be scattered to higher modes at localized inhomogeneities in the background density field and at enhanced sheared currents (Olbers 1981) and by nonlinear interactions with vortical background flow (Buhler and McIntyre 2005; Dunphy and Lamb 2014). Refraction of internal tides upon interaction with mesoscale flows may also provide a mechanism for energy transfer into the internal wave continuum (Zaron and Egbert 2014). Redistribution of the low-mode energy flux to higher modes through interaction with the subtidal circulation provides a mechanism for driving mixing away from internal tide generation sites. Scattering to higher modes allows for greater vertical propagation of energy, such that the contribution to deep-ocean mixing may be significant. It has been suggested that elevated internal wave–induced mixing occurs in oceanic regions of enhanced mesoscale eddy energy; Rainville and Pinkel (2004) estimate elevated diapycnal diffusivity in the Kuroshio, and Whalen et al. (2012) infer heightened dissipation rates in areas of high eddy kinetic energy across the global oceans.

This study uses a modeling approach to investigate the impact of time-varying subtidal circulation and remotely generated internal tides on the dissipation of, and hence diapycnal diffusivity induced by, the principal lunar, semidiurnal M2 internal tides in the Philippine Sea: a region that experiences both strong internal tides and dynamic mesoscale circulation. Energetic internal tides are generated at the Luzon Strait (Ramp et al. 2004; Alford et al. 2011; Kerry et al. 2013, hereinafter KPC2013) and along the eastern margin of the Philippine Sea at the Mariana Island Arc (Zhao and D’Asaro 2011; KPC2013). The Philippine Sea is traversed by a band of enhanced eddy kinetic energy resulting from baroclinic instability associated with the Subtropical Countercurrent and the North Equatorial Current (NEC) (Qiu 1999; Qiu and Chen 2010). In the North Pacific Ocean, the eddy kinetic energy in the Philippine Sea is second only to the Kuroshio Extension, with values of 250–300 cm2 s−2 (Qiu and Chen 2010). The Kuroshio forms as the NEC impinges on the western boundary and flows northeastward along the east coast of Taiwan, after intruding into the Luzon Strait to varying extents (Rudnick et al. 2011). This region provides an ideal case study for the impact of subtidal circulation and remotely generated internal tides on internal tide energetics, an issue of global significance in the context of oceanic mixing.

A detailed analysis of the variability in generation and propagation patterns of the M2 internal tides in the Philippine Sea is presented in Kerry et al. (2014) based on a primitive equation model that simultaneously resolves the eddying general circulation and the M2 barotropic and baroclinic tides. Comparisons are made to KPC2013, in which the internal tides are simulated with a climatological-mean, horizontally uniform stratification in a domain encompassing both the Luzon Strait and Mariana Arc generation sites. With the addition of the subtidal circulation, the internal tide generation and propagation are each found to vary significantly in time and space and the average internal tide energetics differ considerably from the KPC2013 case that uses a quiescent, homogeneously stratified ocean. This paper is based on the same simulations described in Kerry et al. (2014), presents the time-varying baroclinic energy loss near the Luzon Strait generation site and in the Philippine Sea deep basin, and makes estimates of the associated turbulent diffusivities.

2. Model description

We use the Regional Ocean Modeling System (ROMS), a free-surface, hydrostatic, primitive equation ocean model solved on a curvilinear grid with a terrain-following vertical coordinate system, to simulate the eddying general circulation and the M2 barotropic and baroclinic tides in the Philippine Sea. To investigate the variability in the baroclinic tides generated at the Luzon Strait due to the time-varying circulation and stratification, and the varying influence of remotely generated internal tides from the Mariana Arc, we conduct simulations on an inner grid nested within a larger outer grid (Fig. 1).

Fig. 1.
Fig. 1.

Outer model domain is shown with model bathymetry. The inner domain used for the experiments is marked with the thick black line. The blue dashed lines show the areas a, b, and c for which dissipation and turbulent diffusivity are calculated and presented in Table 1. The magenta dashed lines show a subarea of area b, labeled area d, which is referred to in Fig. 6 and the corresponding discussion.

Citation: Journal of Physical Oceanography 44, 12; 10.1175/JPO-D-13-0249.1

The simulation configured for the outer grid uses boundary and initial conditions from the Mercator general ocean circulation model graciously provided by Mercator-Ocean of France, and the atmospheric forcing was provided by the National Centers for Environmental Prediction (NCEP)’s reanalysis atmospheric model (Kistler et al. 2001). The M2 tides are included by forcing at the four open boundaries with M2 tidal surface elevation and momentum from the Oregon State University Ocean Topography Experiment (TOPEX)/Poseidon Global Inverse Solution (TPXO7.1) barotropic tidal model (Egbert and Erofeeva 2002).

Both the outer and the inner grids have identical bathymetry and horizontal and vertical resolution. The model has a variable horizontal resolution, with 8 km over most of the domain, and a higher zonal resolution of 4.5 km over the Luzon Strait. This allows for improved bathymetric resolution, while minimizing pressure gradient errors in the region of steep topography. The model is configured with 25 vertical s layers distributed with a higher resolution in the upper 250 m of the water column. We perform three simulations on the nested inner domain to investigate the internal tides generated at the Luzon Strait including and excluding remotely generated internal tides from the Mariana Arc. These scenarios, outlined briefly below, are described in detail in Kerry et al. (2014).

  1. Full: The general ocean circulation and baroclinic tides are applied at the boundaries, and the barotropic tidal forcing is applied separately as harmonics, through nesting with the outer domain following the method for nesting tidal models described in Janekovic and Powell (2012). The Full simulation includes the influence of baroclinic tides generated at the Mariana Arc with varying subtidal dynamics.

  2. Luzon only: The boundary conditions taken from the outer domain are low-pass filtered to remove the baroclinic tides and the same barotropic forcing as in (i) is applied. As such, the internal tides generated outside of the inner domain are filtered out in this simulation.

  3. Constant remote flux: The boundary forcing as in (ii) is used, with a steady M2 baroclinic energy flux added to the eastern boundary condition taken from the M2 tidal simulation of the Mariana Arc described in KPC2013. This case excludes Mariana Arc generation site variability and represents propagation variability through the Philippine Sea.

Each scenario is integrated for 390 days, from 2 December 2009 to 27 December 2010, and the first 30 days are excluded from analysis for barotropic and baroclinic tide spinup. An overview of the consistency of the general circulation and the M2 tidal model with observations is presented in Kerry et al. (2014). The inferred dissipation and diffusivity from the Full simulation are compared to available observations where possible in the section below.

3. Results

a. Dissipation and diffusivity calculations

The conversion of barotropic tidal energy to baroclinic tides (hereafter referred to as generation) and their radiation away from the generation site can be described in terms of an energy budget, allowing estimation of the loss of baroclinic energy over a defined area. Baroclinic tidal energy generation C for a specific tidal frequency θ is given by
e1
where is the pressure perturbation at the bottom, and wbtθ is the vertical component of the barotropic tidal flow. In this work, we assume incompressibility, such that wbtθ = ubtθ · (−H). The pressure perturbation is given by
e2
where is the time-mean quantity. The baroclinicity condition requires a depth-averaged pressure perturbation of zero, such that
e3
The radiation of internal tides away from the generation site can be represented by the depth-integrated baroclinic energy flux, given by the time-averaged product of the pressure and velocity perturbations over a number of tidal cycles:
e4
The pressure perturbation is given by Eq. (2), and the velocity perturbation is given by
e5
where is the time-mean quantity, and by the baroclinicity condition
e6
Carter et al. (2008) define the baroclinic energy balance by partitioning the energy into generation C, tendency T, flux divergence ·Fbc, nonlinear advection A, and dissipation D. The baroclinic energy balance is defined as
e7
The tendency term describes the time rate of change of energy, and the advection term accounts for energy undergoing nonlinear transformations. Carter et al. (2008) show the tendency and advection terms are small for a numerical simulation of the Hawaiian Ridge using horizontally uniform stratification, justifying the use of the dominant baroclinic energy balance:
e8
Alford et al. (2011) employ this energy budget approach in the Luzon Strait and explicitly note that the dissipation D term accounts for all processes removing energy from the internal tide, including dissipation and nonlinear energy transfers.

We examine baroclinic energy budgets for the three cases (Full, Constant remote flux, and Luzon only) for three areas of the model domain (areas a, b, and c as defined in Fig. 1), characterizing the transfer of energy from the barotropic to the baroclinic tide, the radiation of baroclinic tidal energy, and the internal tide energy lost within the area. Area a encompasses the Luzon Strait generation site, and areas b and c are open-ocean areas of the western and central Philippine Sea, respectively. To estimate the magnitude and variability of the energy available for internal-tide-induced mixing in each area, we calculate the residual energy, given by C · Fbc, every 3 days averaged over the last five tidal cycles (62 h), representing the losses from the internal tide by dissipation, tendency, and nonlinear transfers. We do this by performing a harmonic analysis for M2 over each 62-h period and using the amplitudes and phases of the required variables to compute the baroclinic energy generation [Eq. (1)] and the baroclinic energy fluxes [Eq. (4)]. The equations are given in terms of amplitudes and phases in Kerry et al. (2014). Assuming the internal tide energy is slowly varying over the five tidal cycle period, the tendency term is small compared to the dissipation, and nonlinear transfers are likely to ultimately lead to dissipation (e.g., Glazman 1996), so it is reasonable to equate the residual energy to dissipation for our purposes. For area a, local generation is large compared to any incoming remotely generated baroclinic tidal energy and C · Fbc primarily represents the dissipation of locally generated internal tides. Areas b and c are deep with relatively flat topography, and internal tide generation is negligible. In these regions, the residual baroclinic energy describes the difference between the incoming and the outgoing internal tide energy.

The residual baroclinic energy for each area (D; W m−2) represents the spatially averaged internal tide energy loss per unit area describing the depth-integrated dissipation. The top portion of Table 1 shows the time-mean and standard deviation of the dissipation calculated every 3 days for each area for the three model scenarios and the values from KPC2013’s horizontally uniform stratification simulation. Note that the same explicit harmonic viscosity coefficient was specified for the harmonic mixing of horizontal momentum in all simulations (Full, Constant remote flux, Luzon only, and KPC2013). ROMS uses a third-order upstream advection scheme that reduces excessive dissipation and enhances the effective resolution (Shchepetkin and McWilliams 1998). Model estimates of dissipation are uncertain because of the parameterization of subgrid-scale dissipative processes, and the spatial sparsity of observations makes it difficult to verify model results. Dissipation may be underpredicted in the model as finite horizontal resolution limits the resolution of the higher, more easily dissipated, vertical modes. Model estimates of internal tide generation and local dissipation are also sensitive to bathymetric smoothing at the generation site (Di Lorenzo et al. 2006). For this study, a smoothing method has been applied in which a high priority is placed on maintaining topography (slopes and peak heights) important for internal tide generation while attempting to minimize horizontal pressure gradient errors associated with the terrain-following coordinate system. While the magnitudes of the dissipation values presented in this study are uncertain, comparisons between model scenarios showing the impact of the mesoscale circulation and remotely generated internal tides are useful and provide some important results.

Table 1.

Top portion shows the time-mean and standard deviation of spatially averaged dissipation rates (10−3 W m−2) computed over areas a, b, and c as defined in Fig. 1. KPC2013 is a horizontally uniform stratification simulation. Middle portion shows the corresponding time-mean turbulent diffusivity (10−5 m2 s−1) using method 1, including the range of values achieved given the estimated error bars on vertical decay scale ζ. Bottom portion shows the corresponding time-mean turbulent diffusivity (10−5 m2 s−1) using method 2.

Table 1.

The spatially averaged, depth-integrated dissipation values can be used to estimate depth-mean turbulent diffusivity (Kρ; m2 s−1) based on an assumption of the vertical distribution of dissipation through the water column. Following Osborn (1980), the turbulent diffusivity can be calculated by Kρ = Γϵ/N2, where Γ is the mixing efficiency, ϵ is the dissipation rate (W kg−1), and is the squared buoyancy frequency. We employ two different vertical profile shapes to provide estimates of turbulent diffusivities from the model dissipation estimates; method 1 uses an exponential profile with a chosen vertical decay scale from the ocean bottom, and method 2 assumes that the baroclinic energy loss occurs entirely in the upper 1000 m.

In method 1, we adopt vertical profiles of dissipation rate based on profile shapes estimated by St. Laurent et al. (2002) from observations by St. Laurent et al. (2001) and Moum et al. (2002). The dissipation rate is enhanced at the ocean bottom and decays vertically such that
e9
where ϵ0 is the maximum dissipation rate at the ocean bottom, z = −H, and ζ is the vertical decay scale. Vertical profiles of diffusivity can then be estimated from the dissipation estimate D by
e10
where F(z) is a function describing the dissipation rate vertical profile in Eq. (9) such that . St. Laurent et al. (2001) found markedly enhanced dissipation above rough topography of the Mid-Atlantic Ridge with levels above bathymetric slopes exceeding levels observed over crests and canyon floors. They estimated a vertical decay scale of 500 ± 100 m for observations taken over crests tops and canyon floors, while higher bottom dissipation rates decayed over a shorter scale of 150 ± 50 m over slopes in the Brazil basin. This dissipation profile shape [Eq. (9)] is formulated for high-mode dissipation at rough topography in the deep ocean and has been used in work by Simmons et al. (2004b), Jayne (2009), and Melet et al. (2013) to incorporate mixing parameterizations into global ocean circulation models. These three studies used a constant vertical decay scale across the global ocean of 500, 500, and 300 m, respectively.

To devise dissipation rate profiles for the Philippine Sea basin areas b and c, we use the mean depth of 5400 m and a vertical decay scale of 500 ± 100 m, as these relatively flat areas are analogous to the crest tops and canyon floors in St. Laurent et al. (2001). For area a, around the Luzon Strait, we use the mean depth of 2000 m and a vertical decay scale of 150 ± 50 m as was estimated for regions of sloping topography by St. Laurent et al. (2001). The dissipation rate profiles based on the time-mean spatially averaged dissipation for the Full case are shown in Fig. 2, given by ϵ = DF(z)/ρ(z). The dissipation rate near the bottom at the Luzon Strait region, between ~1400 and 2000 m, is consistent with the observed dissipation by Alford et al. (2011), but the exponential profile underestimates dissipation in the upper water column compared to their observations. Profiles for areas b and c are in agreement with observations in the abyssal Brazil basin (St. Laurent et al. 2001; Moum et al. 2002).

Fig. 2.
Fig. 2.

Dissipation rate profiles for method 1 diffusivity calculations, calculated from the time-mean, spatially averaged dissipation over the Luzon Strait region, (left) area a, and the western and central Philippine Sea basin, (right) areas b and c, for the Full case. For area a, a mean depth of 2000 m and a vertical decay scale of 150 m are used. For areas b and c, a mean depth of 5400 m and a vertical decay scale of 500 m are used.

Citation: Journal of Physical Oceanography 44, 12; 10.1175/JPO-D-13-0249.1

The vertically integrated average diffusivities, computed by Eq. (10), are presented in Table 1 (middle portion). We use a mixing efficiency of 0.2 (Osborn 1980) and density and buoyancy frequency profiles taken from the spatial and temporal mean from the model. The table also shows the range of diffusivities achieved by varying the vertical decay scale ζ within the range suggested by St. Laurent et al. (2001).

In method 2, we estimate turbulent diffusivities, assuming that the internal tide dissipation occurs entirely in the upper 1000 m. As presented in section 3c that follows, internal tide dissipation away from the generation site is significantly enhanced by the mesoscale circulation, and we suggest that this enhanced dissipation results from wave–mesoscale interaction associated with greater shear in the upper 1000 m. Using the depth-averaged squared buoyancy frequency N2 in the upper 1000 m of 3 × 10−5 s−2 from the model spatial- and temporal-mean stratification, the time-mean depth-averaged turbulent diffusivity is computed for each area for the three model scenarios and for KPC2013’s horizontally uniform stratification simulation. These diffusivities are presented in the bottom portion of Table 1.

The results in Table 1 are discussed for the region close to the Luzon Strait generation site, area a, and for the Philippine Sea basin, areas b and c, in the following sections.

b. Mixing near the generation site: The Luzon Strait

The mean depth-integrated dissipation over the Luzon Strait region, area a, for the Full case is 0.070 W m−2 (Table 1). Alford et al. (2011) present observations of depth-integrated dissipation at the Luzon Strait, computed based on Thorpe scales. Dissipation at their 19 stations ranges from 0.004 to 1.29 W m−2 with a median value of 0.166 W m−2. These values are for stations on or close to the ridges, where dissipation is likely to be highest, and include all tidal constituents. Our estimate accounts only for the M2 contribution, so by broad comparison our value of 0.070 W m−2 (2.5 times smaller than the median observed value) over the entire Luzon Strait region, area a, is congruous with the observed values. Our dissipation estimate is uncertain because of the parameterization of subgrid-scale dissipative processes in the model and may be an underestimate because of the smoothed topography and the lack of resolution of the higher modes. Strong internal tide dissipation at the Luzon Strait has been attributed to the breaking of lee waves at the steep ridges (Buijsman and Legg 2012), a process that is not resolved in the hydrostatic model.

For area a, the mean dissipation for the Full simulation including subtidal flow and remotely generated internal tides (70 × 10−3 W m−2) is only slightly greater than the value from the KPC2013 case (64 × 10−3 W m−2), indicating that the mesoscale circulation has a small influence on the strong local turbulent dissipation in this region. As seen in Fig. 3 (left panel), the spatially averaged time-mean vertical shear for area a from the Full simulation is greater in the upper 1000 m than the spatially averaged vertical shear for area a from KPC2013. Enhanced turbulence levels near internal tide generation sites are attributable to the dissipation of high-mode waves (e.g., St. Laurent and Garrett 2002), while low-mode internal waves carry the internal tide energy away from the generation site. This high-mode dissipation appears to dominate at the Luzon Strait, and the inclusion of the subtidal circulation, and hence enhanced shear in the upper ocean, has little impact on the local internal tide dissipation.

Fig. 3.
Fig. 3.

Spatially averaged time-mean vertical shear for the Luzon Strait region, (left) area a, and the Philippine Sea basin, (right) areas b and c, from the Full simulation and KPC2013.

Citation: Journal of Physical Oceanography 44, 12; 10.1175/JPO-D-13-0249.1

The spatial-mean dissipation over area a is closely coupled to the internal tide generation energy over time (shown in Fig. 4 for the Full-case simulation). The dissipation ranges from 0.05 to 0.10 W m−2 with the time-mean value of 0.070 W m−2 (black dashed line). This is consistent with the above result that baroclinic energy dissipation at the Luzon Strait is driven by the dissipation of the strong, locally generated internal tides, rather than the influence of the varying subtidal flow. The generation is greater in the KPC2013 simulation (16.97 GW, magenta dotted line) than the time-mean generation for the Full-case simulation (16.21 GW, magenta dashed line), and the spatially averaged dissipation over the Luzon Strait region is slightly less for KPC2013 at 0.064 W m−2 (black dotted line). The ratio of area-integrated internal tide dissipation to generation, q = D/C, is 0.36 for KPC2013 and 0.41 for the Full-case time-mean values. This suggests that the subtidal flow does play a minor role in increasing dissipation near the generation site, but the dominant influence is the internal tide generation energy level.

Fig. 4.
Fig. 4.

Spatial-mean dissipation and area-integrated generation over Luzon Strait region, area a, calculated every 3 days from the Full case. The time-mean dissipation and generation and the corresponding values from the KPC2013 simulation are shown.

Citation: Journal of Physical Oceanography 44, 12; 10.1175/JPO-D-13-0249.1

The longitudinal distribution of dissipation and generation over the Luzon Strait region is presented in Fig. 5. Energy budgets for the Full case were computed, every 3 days, over thin meridional areas that are one model grid cell wide and span the area a latitudes. Figure 5 (left panel) shows the time-mean generation (top) and dissipation (bottom) from these budgets. The temporal variability is shown by the standard deviations displayed as the shaded areas about the mean. The four peaks in generation represent the east- and west-facing slopes of each of the two ridges, as labeled in the figure. Time-mean generation over all four slopes is similar to the KPC2013 generation, with the largest difference being on the eastern slope of the eastern ridge where the subtidal circulation and remotely generated internal tides have the greatest influence (as shown in Kerry et al. 2014). Over the eastern ridge, the Full-case time-mean dissipation is similar to the KPC2013 dissipation, while over the western ridge, dissipation is enhanced in the presence of the subtidal flow despite similar generation energy. The right panel of Fig. 5 shows the time-mean eddy kinetic energy (EKE) computed using velocities averaged over the upper 500 m for the Full-case simulation. As seen in Fig. 3, 500 m is the depth range over which there is strong shear associated with the mesoscale circulation. The EKE is relatively low over the areas where most of the generation occurs on the eastern ridge, which is on the slopes directly to the east and west of the islands at ~20.5°N (see Fig. 5c in Kerry et al. 2014). The Kuroshio Loop Current enters the Luzon Strait to the south of these major east-ridge generation sites and exits the strait to the north. The time-mean EKE is greater directly over the generation region on the eastern slope of the western ridge that may help account for the enhanced dissipation.

Fig. 5.
Fig. 5.

(left) Spatial-mean generation (top) and dissipation (bottom) over meridional strips one grid cell wide over the Luzon Strait region (area a). Generation and dissipation are calculated every 3 days from the Full case. The solid lines show the time-mean values and the shaded areas about the means show the standard deviations. KPC2013 values are shown by the dashed lines. (right) Time-mean EKE in the upper 500 m (500-, 1000-, 1500-, and 2000-m depth contours are shown).

Citation: Journal of Physical Oceanography 44, 12; 10.1175/JPO-D-13-0249.1

Time-mean dissipation for the Constant-remote-flux case is of very similar magnitude to the Full case at the Luzon Strait, and the value for the Luzon-only case is 91% of the Full value (Table 1), suggesting that remotely generated waves from the Mariana Arc result in a small increase in the baroclinic energy dissipated within the Luzon Strait region. The variability in dissipation is lower for the Luzon-only case compared to the Full and Constant-remote-flux cases because of the significantly lower variability in internal tide generation as shown in Kerry et al. (2014).

The time-mean diffusivity for the Luzon Strait region for the Full case is estimated to be 48.4 × 10−5 m2 s−1 using the vertical dissipation rate profile assumed in method 1 and 40.0 × 10−5 m2 s−1 using method 2. The profile used in method 1 is formulated for high-mode dissipation over rough topography and is likely to be the most appropriate for this region, although it has too little dissipation in the upper water column compared to observations presented in Alford et al. (2011). A more appropriate profile could be formulated from such observations. The diffusivity in area a is approximately 5–7 times greater than in the open-ocean areas b and c when using method 1 for the computations and 20 times greater when using method 2.

Near the generation site, high-mode internal tides are prevalent, but dissipate quickly. In KPC2013, the first three modes were found to propagate into the Philippine Sea. How these low modes dissipate farther away from the generation region is important to the global energy budget.

c. Mixing in the far field: the Philippine Sea basin

Dissipation and diffusivity values for areas b and c presented in Table 1 represent large-scale spatial averages over the western and central regions of the Philippine Sea basin (Fig. 1). The inclusion of subtidal circulation increases turbulent dissipation in the Philippine Sea basin relative to KPC2013. The Full time-mean dissipation is 5 times greater than the KPC2013 case in area b and twice as great in area c. This suggests that dissipation of the low-mode internal tides that propagate into the Philippine Sea basin is enhanced by wave–mesoscale interactions. Figure 3 (right panel) shows that the spatially averaged time-mean vertical shear over areas b and c from the Full simulation is significantly greater in the upper 1000 m than the spatially averaged vertical shear from KPC2013 for the same region. Interaction of the internal tides with the sheared currents associated with the mesoscale circulation is likely to result in enhanced dissipation about the thermocline and may also result in scattering to more downward-propagating higher modes that may contribute to enhanced deep mixing. Numerical simulations by Dunphy and Lamb (2014) showed mode-1 internal tide energy was scattered to modes 2 and higher when passed through a mode-1 baroclinic eddy.

The temporal variability in internal tide dissipation to the east of the Luzon Strait generation region is examined by defining area d, shown in Fig. 1. This smaller area is chosen to investigate a potential relationship between mesoscale energy and internal tide dissipation away from the generation site because it is an area of high EKE compared to the rest of the deep Philippine Sea basin away from the western boundary current and is directly to the east of the Luzon Strait, in the path of the dominant eastward internal tide energy flux. Baroclinic energy budget calculations are performed every 3 days for the Full case. Figure 6 shows the spatial-mean dissipation and the total baroclinic energy entering area d. The time-mean dissipation (black dashed line) is 5.90 × 10−3 W m−2, an order of magnitude greater than the value for the KPC2013 simulation (black dotted line), while the baroclinic energy entering area d for KPC2013 is similar to the Full-case time mean (not shown). As compared to the simulation with a quiescent ocean, the inclusion of mesoscale circulation significantly increases internal tide dissipation in the model. This is in contrast to area a where dissipation is only slightly greater with the subtidal flow. The dissipation in area d varies significantly throughout the year from near zero to a factor of 3 greater than the temporal mean. Note that the spatial-mean dissipation occasionally is less than zero, which may be attributed to the tendency and nonlinear advection terms that are ignored. This indicates that our assumption that internal tide energy is slowly varying over the 62-h averaging period is not always valid. As seen in Fig. 6, the correlation between the dissipation and the incoming baroclinic energy is not as strong as between the dissipation and the internal tide generation in area a (Fig. 4). In area d, the varying subtidal circulation is also an important influence on the dissipation variability; changing mesoscale energy and horizontal and vertical shear are likely to affect internal tide dissipation, in addition to the amount of incoming internal tide energy. Teasing out these effects is not clear, however, because of the time-varying energy level entering the area. A simulation of a constant internal tide flux propagating through varying mesoscale fields may reveal more direct relationships between dissipation and mesoscale circulation energy and shear.

Fig. 6.
Fig. 6.

Spatial-mean dissipation and total incoming baroclinic energy for area d calculated every 3 days from the Full case. The time-mean dissipation and dissipation from the KPC2013 simulation are shown.

Citation: Journal of Physical Oceanography 44, 12; 10.1175/JPO-D-13-0249.1

Examining the longitudinal distribution of meridionally integrated baroclinic energy fluxes, dissipation, and EKE across the inner model domain (Fig. 7) shows the gradual decay of baroclinic energy away from the generation site (top panel), a decrease in dissipation east of the generation site to 124°E (middle panel), and a decrease in EKE (bottom panel). The top panel shows the time mean and standard deviations of the meridionally integrated energy fluxes from the Full case, calculated every 3 days for the year-long simulation, over the latitudinal range of areas b and c, 17.7°–22.9°N. The standard deviation in the energy fluxes increases with distance from the generation site as a result of variability in the dissipation of the baroclinic energy. The energy flux from KPC2013 is shown by the dashed line in Fig. 7. Decay of the baroclinic tidal energy is significantly less in KPC2013 (despite identical model parameters), consistent with the lower dissipation as discussed above. The difference in the meridionally integrated energy flux as compared to the subtidal solution increases with distance from the generation site. For KPC2013, the meridionally integrated fluxes are eastward at 136°E (near the eastern extent of the inner domain) as the energy from the Luzon Strait dominates over the westward flux from the Mariana Arc. In the Full case, the time-mean flux is approximately zero at 136°E. With the increased decay of the baroclinic energy fluxes due to the subtidal flow, the internal tides generated at the Luzon Strait have lost energy as compared to the internal tides from the closer Mariana Arc at this longitude, such that the westward and eastward energy fluxes are approximately equal.

Fig. 7.
Fig. 7.

(top) Zonal baroclinic energy fluxes integrated over the meridional range of areas b and c (17.7°–22.9°N) shown for the Philippine Sea basin (122.5°–136 °E). Fluxes are calculated every 3 days from the Full case. The black solid line shows the time-mean values, and the shaded area about the mean shows the standard deviations. Corresponding meridionally integrated fluxes from the KPC2013 simulation are shown by the dashed line. (middle) Spatial-mean dissipation over meridional strips one grid cell wide over the meridional range 17.7°–22.9°N shown for the Philippine Sea basin. Dissipation is calculated every 3 days from the Full case. The blue solid line shows the time-mean values, and the shaded area about the mean shows the standard deviations. Corresponding dissipation from the KPC2013 simulation is shown by the dashed line. (bottom) Spatial-mean EKE in the upper 500 m over the same meridional strips; time mean shown by the black solid line and standard deviations by the gray shaded area.

Citation: Journal of Physical Oceanography 44, 12; 10.1175/JPO-D-13-0249.1

As in Fig. 5, Fig. 7 (middle panel) shows the time-mean dissipation averaged over the meridional “strips” that are one model grid cell wide and span the latitudinal range of areas b and c, 17.7°–22.9°N. Energy budgets were computed every 3 days, and the standard deviations are shown by the shaded area about the mean. Dissipation is greatest close to the Luzon Strait generation site and decreases sharply to the east as the high-mode internal tides dissipate rapidly. The decrease in baroclinic energy flux (top panel) is more gradual as the less dissipative low-mode internal tides dominate the total energy flux propagating away from the generation site, as was shown in KPC2013. The Full-case dissipation directly east of the generation site decreases more sharply compared to KPC2013 as the high modes are likely to dissipate more quickly in the presence of the energetic subtidal flows here. The lower modes also experience greater dissipation across the domain with mesoscale flows. Full-case dissipation remains relatively high over the region of elevated meridionally averaged EKE between the strait and 126°E, east of which both the dissipation and EKE decrease. The dissipation peaks again at 128°E, associated with a small increase in baroclinic energy due to internal tides generated to the north on the East China Sea shelf. The elevated dissipation in the east of the model domain may be due to proximity to the Mariana Arc and dissipation of the high-mode internal tides generated there. Enhanced dissipation may also occur here because of the topographic scattering to higher modes by the ridge that runs approximately north–south near 136°E, as described by St. Laurent and Garrett (2002) and Johnston et al. (2003). This ridge does not generate significant internal tides (KPC2013), but its associated rough topography may cause scattering. This suggestion is supported by the greater diffusivities in area c for the Full and Constant-remote-flux cases compared to the Luzon-only case, as discussed below.

Remotely generated internal tides from the Mariana Arc also increase dissipation in area b, although to a lesser extent than the subtidal flow (Table 1). Dissipation in area b for the Luzon-only case (ignoring remote tides from the Mariana) is 69% of the Full value, but is 3.5 times greater than the KPC2013 value. Spatially averaged dissipation in area c is smaller than those in area b for all cases that include subtidal flow. The ratio of dissipation in area c to dissipation in area b is 0.77, 0.71, and 0.55 for the Full, Constant-remote-flux, and Luzon-only cases, respectively. The internal tides reaching area c from the distant Luzon Strait become mode-1 dominant (KPC2013), which is not as dissipative and accounts for the lower diffusivity in area c as compared to area b for the Luzon-only case. In the KPC2013 simulation, dissipation in area c exceeds that in area b, suggesting that, in the absence of subtidal flow, dissipation is enhanced in area c because of the greater high-mode internal tide energy. These high-modes may come from the Mariana Arc generation site; in KPC2013, significant mode-2 energy reaches the eastern boundary of area c. However, these high modes may not reach area c in the more dissipative Full and Constant-remote-flux simulations, and topographic scattering of the low-mode flux from the Mariana Arc to higher modes at the ridge near the eastern boundary of area c may be responsible for the enhanced dissipation in this area. The dissipation value in area c for the KPC2013 simulation is slightly greater than the time-mean value for the Luzon-only case, but is a factor of 0.54 of the Full-case time-mean value. These results suggest that in area c both the subtidal circulation and the internal tides generated at the Mariana Arc equally contribute to the dissipation of the internal tide.

Variability in dissipation over the year is similar for the Full and Constant-remote-flux cases in area b, while in area c the time-varying generation at the Mariana Arc in the Full case results in greater variability in dissipation than the Constant-remote-flux case (Table 1). For the Luzon-only case, dissipation varies less in both areas, which is consistent with the significantly lower variability in internal tide generation as shown in Kerry et al. (2014).

The spatial- and temporal-mean turbulent diffusivities for the Full case are 9.4 × 10−5 and 7.0 × 10−5 m2 s−1 for areas b and c, respectively, using method 1 and 2.2 × 10−5 and 1.7 × 10−5 m2 s−1 using method 2. Diffusivity estimates for KPC2013 are 1.8 × 10−5 and 3.8 × 10−5 m2 s−1 for areas b and c using method 1 and 0.44 × 10−5 and 0.91 × 10−5 m2 s−1 using method 2. The vertical distribution of dissipation is not well known, but the increased depth-integrated dissipation in the presence of significantly elevated shear in the upper 1000 m (Fig. 3) suggests that, as well as enhanced dissipation near the ocean bottom as described by method 1, dissipation is also likely to occur in the upper ocean associated with greater shear about the thermocline (e.g., method 2). The actual dissipation rate profile would include both bottom-enhanced dissipation and enhanced upper-ocean dissipation, and the depth-averaged diffusivities computed using the two profile methods are likely to provide lower- and upper-bound estimates on the diffusivity values.

The diffusivity estimates can be compared to the value of 1 × 10−5 m2 s−1 that has been the generally accepted typical open-ocean diffusivity away from topography (e.g., Gregg 1989; Ledwell et al. 1993; Kunze and Toole 1997; Munk and Wunsch 1998). Ledwell et al. (1993) reported diapycnal diffusivity levels of approximately 1 × 10−5 m2 s−1 for an open-ocean region averaged over hundreds of kilometers and 5 months, and Polzin et al. (1997) estimated similar diapycnal diffusivities above smooth abyssal plains in the deep Brazil basin and over the South American continental rise. In Hawaii, measured diffusivity decayed away from the ridge to this background level of 1 × 10−5 m2 s−1 (Rudnick et al. 2003; Klymak et al. 2006). Waterhouse et al. (2014) report globally averaged depth-averaged diapycnal diffusivity is O(10−4) m2 s−1 below 1000-m depth and is O(10−5) m2 s−1 above 1000 m and note that the distribution is extremely patchy in space. Although our dissipation and diffusivity calculations are uncertain, the enhanced eddy kinetic energy and the strong internal tides that propagate into the Philippine Sea region may result in higher diffusivity for the region compared to less energetic regions of the global oceans. Rainville and Pinkel (2004) measure shear variance in the Kuroshio and, assuming that dissipation varies as shear variance squared, estimate 4–9 times more dissipation in the current than offshore in the open ocean. Mesoscale variability in their study region (at the beginning of the Kuroshio Extension) is similar to that in the Philippine Sea (Qiu and Chen 2010), and we estimate 2–5 times greater diffusivity in the Philippine Sea for the Full case compared to KPC2013.

4. Discussion

In this work, we find that dissipation close to the internal tide generation site is largely unaffected by the mesoscale circulation, while dissipation in the far field is considerably enhanced in the presence of the eddying subtidal circulation. While the reliability of estimates of internal tide dissipation from numerical models is unclear as mixing processes are parameterized, the increased far-field dissipation with the inclusion of subtidal flows compared to the quiescent ocean simulation supports the suggestion of enhanced internal-tide-induced mixing in regions of elevated eddy kinetic energy. This is a key result toward understanding the spatial variability in diapycnal diffusivity in the global oceans and the mechanisms for internal-tide-induced turbulence from both locally and remotely generated internal tides. These results are consistent with the study by Whalen et al. (2012), which infers dissipation rates across the global oceans using strain information from Argo profiles and finds elevated dissipation rates both at regions of rough topography and in areas of high eddy kinetic eddy. Scattering of low-mode internal tide energy to higher modes through interaction with the subtidal circulation provides a mechanism for deep-ocean mixing away from internal tide generation sites. The distribution of diapycnal mixing is spatially varying and complex (Simmons et al. 2004b; St. Laurent and Simmons 2006; Waterhouse et al. 2014), and the impact of the mesoscale circulation on internal wave dissipation is likely to contribute to this nonuniform mixing distribution.

The significantly greater dissipation away from the internal tide generation site in the simulations that include subtidal circulation, compared to KPC2013, can be attributed to the increased velocity shear associated with the mesoscale circulation. Factors that affect the dissipation of energy in numerical models include numerical dispersion and the choice of parameterization for the mixing of momentum, in which mixing is directly related to horizontal and vertical shear. In all simulations the same harmonic viscosity coefficient was specified for the harmonic mixing of horizontal momentum. KPC2013 performed a sensitivity analysis on the harmonic viscosity parameter and found the results were not sensitive to this explicit diffusion for simulations with a quiescent ocean. With the same explicit diffusion for the parameterization of horizontal mixing applied, the increase in dissipation away from the internal tide generation site in the presence of the subtidal flow must be attributed to increased velocity shear and therefore increased explicit diffusion, as well as increased implicit subgrid-scale dissipation. The ROMS advection scheme is designed to effectively preserve the distribution of the advected scalar fields (potential vorticity and material concentrations) by detecting grid points where the values of the quantity are overshot during the advection step and iteratively diffusing the overshooting excess (Shchepetkin and McWilliams 1998). Where energy is transferred toward smaller scales that eventually cannot be resolved by the grid, the energy must be dissipated in the model, thereby simulating subgrid-scale dissipation.

Measurements of the rate of decay of internal tide energy away from the generation sites provide insight into the magnitude of energy that is available for mixing, but there interpretation is complicated by the spatial inhomogeneity of internal tide energy fluxes. This spatial inhomogeneity was seen in Kerry et al. (2014) and results from interference of waves from multiple generation sites (Rainville et al. 2010; Zaron and Egbert 2014) and constructive and destructive interference resulting from interaction with mesoscale eddies (Dunphy and Lamb 2014). Johnston et al. (2011) compared observations of internal tide beams near Monterey Bay to a numerical model that did not include mean or mesoscale flows and found that the small-scale features of the internal tide beams in the model did not experience the dissipation or dephasing found in the observations. Simulations using the Princeton Ocean Model without subtidal circulation by Rainville et al. (2010) were found to overestimate the high-mode internal tide energy. Niwa and Hibiya (2004) found that additional damping in the horizontal was required for their model, using uniform horizontal stratification, to achieve agreement of surface amplitudes with TOPEX/Poseidon satellite data in the Philippine Sea. Simulations including subtidal dynamics, such as the study presented here, using an advanced advection scheme may be useful tools to estimate internal tide energetics; however, direct measurements are required to validate this. Our values only include the M2 contribution. Jan et al. (2008) estimated similar internal tide generation energy for the O1, K1, and M2 constituents at the Luzon Strait, and generation energy for S2 of about 13% of the M2, so the actual contribution from the internal tides could be approximately 3 times greater.

The purpose of this study was to compare the impact of the eddying subtidal circulation on the depth-integrated internal tide dissipation in the Philippine Sea, and the results suggest that the lateral distribution of mesoscale eddy kinetic energy is likely to affect the lateral distribution of mixing. Because of the complexity of the generation and dissipation processes of internal tides, the vertical structure of the mixing is also likely to be complex and spatially varying. Indeed, observations show significant variability in the vertical distribution of mixing across the global oceans (e.g., St. Laurent et al. 2001; Klymak et al. 2006; Polzin 2009; Alford et al. 2011; Waterhouse et al. 2014). Two different assumptions of the vertical dissipation rate profile were made to provide estimates of depth-averaged diapycnal diffusivity from the model dissipation estimates. The first method assumed enhanced dissipation near the ocean bottom with exponential decay with depth above the bottom, formulated by St. Laurent and Garrett (2002) to describe the dissipation of high-mode internal waves at rough topography in the deep ocean. The second method assumes that the internal tide energy is dissipated entirely in the upper 1000 m. The increased dissipation away from the internal tide generation site in our simulations that include mesoscale circulation is related to enhanced shear, most of which is in the upper 1000 m. The processes through which the subtidal flow facilitates transfer of internal tide energy to small-scale turbulence are unclear; the eddying mesoscale circulation may cause enhanced internal tide dissipation about the thermocline because of the interaction with sheared currents and may also cause scattering to higher modes that propagate downward where they dissipate at rough topography. We do not attempt to study the vertical distribution of mixing or suggest the most appropriate choice of vertical profile, but assume simple profile shapes to provide a range of depth-averaged diffusivity estimates from our dissipation estimates. These values allow easier comparison with literature on oceanic mixing. Melet et al. (2013) show that the ocean state shows significant sensitivity to the vertical profile of internal-tide-driven mixing implemented in an ocean general circulation model. Improved mixing profile estimates, which are likely to be laterally varying, should be devised from observations and further study into the vertical structure of internal tide–eddy interactions.

In this study, we present spatially averaged dissipation estimates over the Luzon Strait internal tide generation region and the western and central Philippine Sea regions to investigate the effect of mesoscale circulation on the magnitude and variability of internal-tide-induced mixing. The lateral variability over smaller spatial scales, and its significance for global ocean model mixing parameterizations, is largely unknown and requires further study. While the inclusion of subtidal circulation significantly enhances dissipation in the simulations presented in this study, it is difficult to distinguish the direct effect of changing mesoscale energy on internal tide dissipation, as internal tide generation and propagation patterns are also varying. More idealized model studies could be more effective at isolating the effects of subtidal circulation on a constant low-mode internal tide flux, for example. This study however provides an estimate of the mean and variability of internal tide energetics in the Philippine Sea and makes a useful comparison to a model simulation using horizontally uniform stratification, a simplification that is often made in internal tide modeling studies.

5. Conclusions

Using a numerical model that simultaneously resolves the eddying ocean circulation and the M2 tides, we estimate the time-varying turbulent diffusivities due to the M2 internal tide contribution over three areas: the Luzon Strait and the deep-ocean basin regions of the western and central Philippine Sea. At the Luzon Strait (area a), the time-mean turbulent diffusivity including subtidal flows and remotely generated internal waves (Full case) is found to be 4.0–4.84 × 10−4 m2 s−1, which is 5–20 times greater than the estimated diffusivity in the Philippine Sea basin for the same simulation. We infer that the dissipation of internal tide energy at the Luzon Strait is dominated by dissipation of the strong, locally generated internal tides, with the mesoscale flows having a small influence.

The estimates of mean turbulent diffusivity due to the M2 internal tides in the deep-ocean region of the Philippine Sea (areas b and c, Full case) are 2–9 × 10−5 m2 s−1 for the Full case. In the western Philippine Sea (area b), the mesoscale circulation plays an important role in the internal tide dissipation, which is enhanced by a factor of 5 when the subtidal circulation is considered, as compared to the horizontally uniform stratification case in KPC2013. In the central Philippine Sea (area c), the dissipation is enhanced by a factor of 2 compared to the KPC2013 simulation. We suggest that enhanced mixing is due to increased velocity shear associated with the mesoscale circulation. The subtidal circulation may cause enhanced dissipation due to interaction with sheared currents in the upper ocean and may cause scattering of the low-mode internal tides to higher modes, which have greater downward propagation of energy and may contribute to deep-ocean mixing. Internal tides generated at the Mariana Arc are found to increase diffusivity in the deep-ocean region, with a particularly important impact in the central Philippine Sea (area c).

This study supports previous findings that significantly enhanced mixing is likely to occur over rough topography where energetic internal tides are generated (Polzin et al. 1997; Ledwell et al. 2000). The results also suggest that open-ocean regions with elevated eddy kinetic energy such as the Philippine Sea may have higher diffusivity as compared to less energetic regions of the world’s oceans (Whalen et al. 2012). Our results support the suggestion by Liang and Thurnherr (2012) that, in addition to topographic roughness and tidal forcing, parameterizations of deep-ocean mixing should also take the energy associated with the subtidal circulation into account. The increase in dissipation with mesoscale circulation is an important result, but direct measurements are required to validate the magnitude of the model diffusivity estimates. The Philippine Sea may make an important contribution to the global mixing budget, being both a region of strong internal tides and enhanced eddy kinetic energy. Other notable regions around the globe where significant internal tide generation correspond to regions of enhanced eddy kinetic energy include the east coast of Australia, the southeastern tip of Africa, and the Kuroshio Extension off the east coast of Japan (Simmons et al. 2004a; Jia et al. 2011).

The spatial and temporal variability in internal tides is affected by the subtidal ocean circulation as well as remotely generated internal tides, as examined in Kerry et al. (2014) and is found to result in significant variability in the energy available for mixing. The subtidal circulation influences internal-tide-induced mixing in two ways: first, by introducing variability in internal tide generation that has a direct effect on the baroclinic energy made available for turbulent mixing. Second, interactions of the internal tides with the mesoscale circulation influence the dissipation of baroclinic energy. Close to the generation site, dissipation is dominated by the high-mode internal tide dissipation, while in the far field the influence of the mesoscale energy is significant. Understanding the variability of internal-tide-induced mixing is a key to making sense of sparse observations of ocean mixing and developing improved parameterizations for climate-scale models. This study provides a step toward understanding the space–time distribution of energy available for global mixing and highlights the importance of considering the subtidal flow and background internal wave field in estimating internal-tide-induced mixing.

Acknowledgments

The authors thank Mercator-Ocean of France for the model data used to provide the boundary conditions for the ROMS solutions presented. The authors also thank Dr. Ivica Janeković of the Rudjer Bošković Institute for assistance with creating the model grid. Dr. Kerry and Dr. Powell were supported by ONR Grant N00014-09-1-0939. Dr. Carter was supported by ONR Grant N00014-10-1-0334.

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    • Export Citation
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    • Export Citation
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    • Export Citation
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    • Search Google Scholar
    • Export Citation
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    • Search Google Scholar
    • Export Citation
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    • Search Google Scholar
    • Export Citation
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    • Search Google Scholar
    • Export Citation
  • Rudnick, D. L., and Coauthors, 2011: Seasonal and mesoscale variability of the Kuroshio near its origin. Oceanography, 24, 5263, doi:10.5670/oceanog.2011.94.

    • Search Google Scholar
    • Export Citation
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    • Search Google Scholar
    • Export Citation
  • Simmons, H. L., R. W. Hallberg, and B. K. Arbic, 2004a: Internal wave generation in a global baroclinic tide model. Deep-Sea Res. II, 51, 3043–3068, doi:10.1016/j.dsr2.2004.09.015.

    • Search Google Scholar
    • Export Citation
  • Simmons, H. L., S. R. Jayne, L. C. St. Laurent, and A. J. Weaver, 2004b: Tidally driven mixing in a numerical model of the ocean general circulation. Ocean Modell., 6, 245263, doi:10.1016/S1463-5003(03)00011-8.

    • Search Google Scholar
    • Export Citation
  • St. Laurent, L. C., and C. Garrett, 2002: The role of internal tides in mixing the deep ocean. J. Phys. Oceanogr., 32, 28822899, doi:10.1175/1520-0485(2002)032<2882:TROITI>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • St. Laurent, L. C., and H. Simmons, 2006: Estimates of power consumed by mixing in the ocean interior. J. Climate, 19, 48774890, doi:10.1175/JCLI3887.1.

    • Search Google Scholar
    • Export Citation
  • St. Laurent, L. C., J. M. Toole, and R. W. Schmitt, 2001: Buoyancy forcing by turbulence above rough topography in the abyssal Brazil basin. J. Phys. Oceanogr., 31, 34763495, doi:10.1175/1520-0485(2001)031<3476:BFBTAR>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • St. Laurent, L. C., H. L. Simmons, and S. R. Jayne, 2002: Estimating tidally driven mixing in the deep ocean. Geophys. Res. Lett., 29, 2106, doi:10.1029/2002GL015633.

    • Search Google Scholar
    • Export Citation
  • Waterhouse, A. F., and Coauthors, 2014: Global patterns of diapycnal mixing from measurements of the turbulent dissipation rate. J. Phys. Oceanogr., 44, 18541872, doi:10.1175/JPO-D-13-0104.1.

    • Search Google Scholar
    • Export Citation
  • Whalen, C. B., L. D. Talley, and J. A. MacKinnon, 2012: Spatial and temporal variability of global ocean mixing inferred from Argo profiles. Geophys. Res. Lett., 39, L18612, doi:10.1029/2012GL053196.

    • Search Google Scholar
    • Export Citation
  • Zaron, E. D., and G. D. Egbert, 2014: Time-variable refraction of the internal tide at the Hawaiian Ridge. J. Phys. Oceanogr., 44, 538557, doi:10.1175/JPO-D-12-0238.1.

    • Search Google Scholar
    • Export Citation
  • Zhao, Z., and E. D’Asaro, 2011: A perfect focus of the internal tide from the Mariana Arc. Geophys. Res. Lett., 38, L14609, doi:10.1029/2011GL047909.

    • Search Google Scholar
    • Export Citation
  • Fig. 1.

    Outer model domain is shown with model bathymetry. The inner domain used for the experiments is marked with the thick black line. The blue dashed lines show the areas a, b, and c for which dissipation and turbulent diffusivity are calculated and presented in Table 1. The magenta dashed lines show a subarea of area b, labeled area d, which is referred to in Fig. 6 and the corresponding discussion.

  • Fig. 2.

    Dissipation rate profiles for method 1 diffusivity calculations, calculated from the time-mean, spatially averaged dissipation over the Luzon Strait region, (left) area a, and the western and central Philippine Sea basin, (right) areas b and c, for the Full case. For area a, a mean depth of 2000 m and a vertical decay scale of 150 m are used. For areas b and c, a mean depth of 5400 m and a vertical decay scale of 500 m are used.

  • Fig. 3.

    Spatially averaged time-mean vertical shear for the Luzon Strait region, (left) area a, and the Philippine Sea basin, (right) areas b and c, from the Full simulation and KPC2013.

  • Fig. 4.

    Spatial-mean dissipation and area-integrated generation over Luzon Strait region, area a, calculated every 3 days from the Full case. The time-mean dissipation and generation and the corresponding values from the KPC2013 simulation are shown.

  • Fig. 5.

    (left) Spatial-mean generation (top) and dissipation (bottom) over meridional strips one grid cell wide over the Luzon Strait region (area a). Generation and dissipation are calculated every 3 days from the Full case. The solid lines show the time-mean values and the shaded areas about the means show the standard deviations. KPC2013 values are shown by the dashed lines. (right) Time-mean EKE in the upper 500 m (500-, 1000-, 1500-, and 2000-m depth contours are shown).

  • Fig. 6.

    Spatial-mean dissipation and total incoming baroclinic energy for area d calculated every 3 days from the Full case. The time-mean dissipation and dissipation from the KPC2013 simulation are shown.

  • Fig. 7.

    (top) Zonal baroclinic energy fluxes integrated over the meridional range of areas b and c (17.7°–22.9°N) shown for the Philippine Sea basin (122.5°–136 °E). Fluxes are calculated every 3 days from the Full case. The black solid line shows the time-mean values, and the shaded area about the mean shows the standard deviations. Corresponding meridionally integrated fluxes from the KPC2013 simulation are shown by the dashed line. (middle) Spatial-mean dissipation over meridional strips one grid cell wide over the meridional range 17.7°–22.9°N shown for the Philippine Sea basin. Dissipation is calculated every 3 days from the Full case. The blue solid line shows the time-mean values, and the shaded area about the mean shows the standard deviations. Corresponding dissipation from the KPC2013 simulation is shown by the dashed line. (bottom) Spatial-mean EKE in the upper 500 m over the same meridional strips; time mean shown by the black solid line and standard deviations by the gray shaded area.

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