Jody M. Klymak

The formation and fate of internal waves in the South China Sea

Internal gravity waves, the subsurface analogue of the familiar surface gravity waves that break on beaches, are ubiquitous in the ocean. Because of their strong vertical and horizontal currents, and the turbulent mixing caused by their breaking, they affect a panoply of ocean processes, such as the supply of nutrients for photosynthesis, sediment and pollutant transport and acoustic transmission; they also pose hazards for man-made structures in the ocean. Generated primarily by the wind and the tides, internal waves can travel thousands of kilometres from their sources before breaking, making it challenging to observe them and to include them in numerical climate models, which are sensitive to their effects. For over a decade, studies have targeted the South China Sea, where the oceans’ most powerful known internal waves are generated in the Luzon Strait and steepen dramatically as they propagate west. Confusion has persisted regarding their mechanism of generation, variability and energy budget, however, owing to the lack of in situ data from the Luzon Strait, where extreme flow conditions make measurements difficult. Here we use new observations and numerical models to (1) show that the waves begin as sinusoidal disturbances rather than arising from sharp hydraulic phenomena, (2) reveal the existence of >200-metre-high breaking internal waves in the region of generation that give rise to turbulence levels >10,000 times that in the open ocean, (3) determine that the Kuroshio western boundary current noticeably refracts the internal wave field emanating from the Luzon Strait, and (4) demonstrate a factor-of-two agreement between modelled and observed energy fluxes, which allows us to produce an observationally supported energy budget of the region. Together, these findings give a cradle-to-grave picture of internal waves on a basin scale, which will support further improvements of their representation in numerical climate predictions.

Energy Flux and Dissipation in Luzon Strait: Two Tales of Two Ridges

AbstractInternal tide generation, propagation, and dissipation are investigated in Luzon Strait, a system of two quasi-parallel ridges situated between Taiwan and the Philippines. Two profiling moorings deployed for about 20 days and a set of nineteen 36-h lowered ADCP–CTD time series stations allowed separate measurement of diurnal and semidiurnal internal tide signals. Measurements were concentrated on a northern line, where the ridge spacing was approximately equal to the mode-1 wavelength for semidiurnal motions, and a southern line, where the spacing was approximately two-thirds that. The authors contrast the two sites to emphasize the potential importance of resonance between generation sites. Throughout Luzon Strait, baroclinic energy, energy fluxes, and turbulent dissipation were some of the strongest ever measured. Peak-to-peak baroclinic velocity and vertical displacements often exceeded 2 m s−1 and 300 m, respectively. Energy fluxes exceeding 60 kW m−1 were measured at spring tide at the wester...

Speed and Evolution of Nonlinear Internal Waves Transiting the South China Sea

Abstract In the South China Sea (SCS), 14 nonlinear internal waves are detected as they transit a synchronous array of 10 moorings spanning the waves’ generation site at Luzon Strait, through the deep basin, and onto the upper continental slope 560 km to the west. Their arrival time, speed, width, energy, amplitude, and number of trailing waves are monitored. Waves occur twice daily in a particular pattern where larger, narrower “A” waves alternate with wider, smaller “B” waves. Waves begin as broad internal tides close to Luzon Strait’s two ridges, steepening to O(3–10 km) wide in the deep basin and O(200–300 m) on the upper slope. Nearly all waves eventually develop wave trains, with larger–steeper waves developing them earlier and in greater numbers. The B waves in the deep basin begin at a mean speed of ≈5% greater than the linear mode-1 phase speed for semidiurnal internal waves (computed using climatological and in situ stratification). The A waves travel ≈5%–10% faster than B waves until they reach...

Direct Breaking of the Internal Tide near Topography: Kaena Ridge, Hawaii

Abstract Barotropic to baroclinic conversion and attendant phenomena were recently examined at the Kaena Ridge as an aspect of the Hawaii Ocean Mixing Experiment. Two distinct mixing processes appear to be at work in the waters above the 1100-m-deep ridge crest. At middepths, above 400 m, mixing events resemble their open-ocean counterparts. There is no apparent modulation of mixing rates with the fortnightly cycle, and they are well modeled by standard open-ocean parameterizations. Nearer to the topography, there is quasi-deterministic breaking associated with each baroclinic crest passage. Large-amplitude, small-scale internal waves are triggered by tidal forcing, consistent with lee-wave formation at the ridge break. These waves have vertical wavelengths on the order of 400 m. During spring tides, the waves are nonlinear and exhibit convective instabilities on their leading edge. Dissipation rates exceed those predicted by the open-ocean parameterizations by up to a factor of 100, with the disparity in...

Internal Hydraulic Jumps and Overturning Generated by Tidal Flow over a Tall Steep Ridge

Abstract Recent observations from the Hawaiian Ridge indicate episodes of overturning and strong dissipation coupled with the tidal cycle near the top of the ridge. Simulations with realistic topography and stratification suggest that this overturning has its origins in transient internal hydraulic jumps that occur below the shelf break at maximum ebb tide, and then propagate up the slope as internal bores when the flow reverses. A series of numerical simulations explores the parameter space of topographic slope, barotropic velocity, stratification, and forcing frequency to identify the parameter regime in which these internal jumps are possible. Theoretical analysis predicts that the tidally driven jumps may occur when the vertical tidal excursion is large, which is shown to imply steep topographic slopes, such that dh/dxN/ω > 1. The vertical length scale of the jumps is predicted to depend on the flow speed such that the jump Froude number is of order unity. The numerical results agree with the theoreti...

Energy Transport by Nonlinear Internal Waves

Wintertime stratification on Oregon’s continental shelf often produces a near-bottom layer of densefluid that acts as an internal waveguide on which nonlinear internal waves propagate. Shipboard profiling and bottom lander observations capture disturbances that exhibit properties of internal solitary waves, bores and gravity currents. Wave-like pulses are highly turbulent (instantaneous bed stresses are 1 N m 2 ), resuspending bottom sediments into the water column and raising them 30 + m above the seafloor. The waves’ cross-shelf transport of fluid counters the time-averaged Ekman transport in the bottom boundary layer. In the nonlinear internal waves we have observed, the kinetic energy is roughly equal to the available potential energy and is O(0.1) MJ per m of coastline. The energy transported by these waves includes a nonlinear advection term huEi that is negligible in linear internal waves. Unlike linear internal waves, the pressure-velocity energy flux hupi includes important contributions from nonhydrostatic effects and surface displacement. It is found that, statistically, huEi ’ 2hupi. Vertical profiles indicate that up(z) is more important in transporting energy near the seafloor while uE(z) dominates farther from the bottom. With the wave speed, c, estimated from weakly nonlinear wave theory it is verified experimentally that the total energy transported by the waves, hupi + huEi ’ chEi. The high but intermittent energyflux by the waves is, in an averaged sense, O(100) W per m of coastline. This is similar to independent estimates of the shoreward energy flux in the semidiurnal internal tide at the shelfbreak.

Tidally Generated Turbulence over the Knight Inlet Sill

Very high turbulent dissipation rates (above «5 1024 Wk g 21) were observed in the nonlinear internal lee waves that form each tide over a sill in Knight Inlet, British Columbia. This turbulence was due to both shear instabilities and the jumplike adjustment of the wave to background flow conditions. Away from the sill, turbulent dissipation was significantly lower ( «5 1027 to «5 1028 Wk g 21). Energy removed from the barotropic tide was estimated using a pair of tide gauges; a peak of 20 MW occurred during spring tide. Approximately twothirds of the barotropic energy loss radiated away as internal waves, while the remaining one-third was lost to processes near the sill. Observed dissipation in the water column does not account for the near-sill losses, but energy lost to vortex shedding and near-bottom turbulence, though not measured, could be large enough to close the energy budget.

The Breaking and Scattering of the Internal Tide on a Continental Slope

AbstractA strong internal tide is generated in the Luzon Strait that radiates westward to impact the continental shelf of the South China Sea. Mooring data in 1500-m depth on the continental slope show a fortnightly averaged incoming tidal flux of 12 kW m−1, and a mooring on a broad plateau on the slope finds a similar flux as an upper bound. Of this, 5.5 kW m−1 is in the diurnal tide and 3.5 kW m−1 is in the semidiurnal tide, with the remainder in higher-frequency motions. Turbulence dissipation may be as high as 3 kW m−1. Local generation is estimated from a linear model to be less than 1 kW m−1. The continental slope is supercritical with respect to the diurnal tide, implying that there may be significant back reflection into the basin. Comparing the low-mode energy of a horizontal standing wave at the mooring to the energy flux indicates that perhaps one-third of the incoming diurnal tidal energy is reflected. Conversely, the slope is subcritical with respect to the semidiurnal tide, and the observed ...

Seasonality in submesoscale turbulence

Although the strongest ocean surface currents occur at horizontal scales of order 100 km, recent numerical simulations suggest that flows smaller than these mesoscale eddies can achieve important vertical transports in the upper ocean. These submesoscale flows, 1–100 km in horizontal extent, take heat and atmospheric gases down into the interior ocean, accelerating air–sea fluxes, and bring deep nutrients up into the sunlit surface layer, fueling primary production. Here we present observational evidence that submesoscale flows undergo a seasonal cycle in the surface mixed layer: they are much stronger in winter than in summer. Submesoscale flows are energized by baroclinic instabilities that develop around geostrophic eddies in the deep winter mixed layer at a horizontal scale of order 1–10 km. Flows larger than this instability scale are energized by turbulent scale interactions. Enhanced submesoscale activity in the winter mixed layer is expected to achieve efficient exchanges with the permanent thermocline below.

A modified law-of-the-wall applied to oceanic bottom boundary layers

[1] Near the bottom, the velocity profile in the bottom boundary layer over the continental shelf exhibits a characteristic law-of-the-wall that is consistent with local estimates of friction velocity from near-bottom turbulence measurements. Farther from the bottom, the velocity profile exhibits a deviation from the law-of-the-wall. Here the velocity gradient continues to decrease with height but at a rate greater than that predicted by the law-of-thewall with the local friction velocity. We argue that the shape of the velocity profile is made consistent with the local friction velocity by the introduction of a new length scale that, near the boundary, asymptotes to a value that varies linearly from the bottom. Farther from the boundary, this length scale is consistent with the suppression of velocity fluctuations either by stratification in the upper part of the boundary layer or by proximity to the free surface. The resultant modified law-of-the-wall provides a good representation of velocity profiles observed over the continental shelf when a local estimate of the friction velocity from coincident turbulence observations is used. The modified law-ofthe-wall is then tested on two very different sets of observations, from a shallow tidal channel and from the bottom of the Mediterranean outflow plume. In both cases it is argued that the observed velocity profile is consistent with the modified law-of-the-wall. Implicit in the modified law-of-the-wall is a new scaling for turbulent kinetic energy dissipation rate. This new scaling diverges from the law-of-the-wall prediction above 0.2D (where D is the thickness of the bottom boundary layer) and agrees with observed profiles to 0.6D.