Subhas K. Venayagamoorthy

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.

On the turbulent Prandtl number in homogeneous stably stratified turbulence

In this paper, we derive a general relationship for the turbulent Prandtl number Pr t for homogeneous stably stratified turbulence from the turbulent kinetic energy and scalar variance equations. A formulation for the turbulent Prandtl number, Pr t , is developed in terms of a mixing length scale L M and an overturning length scale L E , the ratio of the mechanical (turbulent kinetic energy) decay time scale T L to scalar decay time scale T ρ and the gradient Richardson number Ri. We show that our formulation for Pr t is appropriate even for non-stationary (developing) stratified flows, since it does not include the reversible contributions in both the turbulent kinetic energy production and buoyancy fluxes that drive the time variations in the flow. Our analysis of direct numerical simulation (DNS) data of homogeneous sheared turbulence shows that the ratio L M /L E ≈ 1 for weakly stratified flows. We show that in the limit of zero stratification, the turbulent Prandtl number is equal to the inverse of the ratio of the mechanical time scale to the scalar time scale, T L /T ρ . We use the stably stratified DNS data of Shih et al. (J. Fluid Mech., vol. 412, 2000, pp. 1―20; J. Fluid Mech., vol. 525, 2005, pp. 193―214) to propose a new parameterization for Pr t in terms of the gradient Richardson number Ri. The formulation presented here provides a general framework for calculating Pr t that will be useful for turbulence closure schemes in numerical models.

On the formation and propagation of nonlinear internal boluses across a shelf break

High-resolution two- and three-dimensional numerical simulations are performed of first-mode internal gravity waves interacting with a shelf break in a linearly stratified fluid. The interaction of nonlinear incident waves with the shelf break results in the formation of upslope-surging vortex cores of dense fluid (referred to here as internal boluses) that propagate onto the shelf. This paper primarily focuses on understanding the dynamics of the interaction process with particular emphasis on the formation, structure and propagation of internal boluses onshelf. A possible mechanism is identified for the excitation of vortex cores that are lifted over the shelf break, from where (from the simplest viewpoint) they essentially propagate as gravity currents into a linearly stratified ambient fluid.

Numerical simulations of the interaction of internal waves with a shelf break

The energetics of the interaction of internal gravity waves with a shelf break is investigated by means of high-resolution two-dimensional numerical simulations, with an emphasis on understanding the partitioning of the internal wave energy over the course of the interaction process and the subsequent dynamics of the onshore propagating internal waves. Some of the energy is dissipated as a result of the instabilities associated with breaking, while the remaining energy is either reflected back away from or transmitted onto the shelf. We employ an analysis of the distribution of the energy flux across the shelf break taking into account the contributions from nonhydrostatic as well as nonlinear effects to quantify the percentage of energy flux that is transmitted onto the shelf, as well as the percentages of reflected and dissipated energy fluxes, from an incoming wave field. For a given frequency of an incoming wave, we vary the amplitude of the wave to vary the incident energy flux, and we simulate condi...

Lagrangian mixing in decaying stably stratified turbulence

Direct numerical simulations are used to study mixing and dispersion in decaying stably stratified turbulence from a Lagrangian perspective. The change in density of fluid particles owing to small-scale mixing is extracted from the simulations to provide insight into the mixing process. These changes are driven by temporally and spatially intermittent events that are strongly suppressed as the stratification increases and overturning motions disappear. This occurs for times

Relevance of the Thorpe length scale in stably stratified turbulence

Nt \,{>}\, 2\upi

Biases in Thorpe-Scale Estimates of Turbulence Dissipation. Part I: Assessments from Large-Scale Overturns in Oceanographic Data

, i.e. after one buoyancy period, where

A unifying framework for parameterizing stably stratified shear-flow turbulence

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The quest for an unambiguous parameterization of mixing efficiency in stably stratified geophysical flows

is the buoyancy frequency. The role of small-scale mixing processes in the density (or buoyancy) flux is analysed. After an initial transient, we find that diapycnal displacements due to mixing dominate the dispersion of fluid particles, even in weak stratification. The relationship between the diapycnal diffusivity and vertical dispersion coefficients is found to be strongly dependent on stratification. Models for the mixing following fluid particles are investigated. The time scale for the density changes due to small-scale mixing is shown to be approximately independent of

A simple turbulence model for stably stratified wall‐bounded flows

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