The Impact of Topographic Steepness on Tidal Dissipation at Bumpy Topography

Young Yi,Robert Nazarian,Sonya Legg

doi:10.3390/fluids2040055

Abstract

Breaking internal waves are an important contributor to mixing in the stratified ocean interior. We use two-dimensional, nonhydrostatic numerical simulations to examine the breaking of internal waves generated by tidal flow over sinusoidal bottom topography. We explore the sensitivity of the internal wave breaking to the topographic steepness and Coriolis frequency, focusing on the vertical structure of kinetic energy dissipation and the ratio of local dissipation to the barotropic-to-baroclinic energy conversion. When the tidal frequency is twice the local Coriolis frequency, wave breaking above the topography is driven by wave–wave interactions which transfer wave energy from the tidal forcing frequency to the inertial frequency. The greater shear associated with the inertial frequency waves leads to enhanced dissipation in a thick layer above the topography. The topographic steepness strongly modulates this dependence of dissipation on Coriolis frequency; for some steep sinusoidal topographies, most wave energy propagates downward into the topographic troughs, eliminating the possibility for significant breaking above the topographic peaks. Current parameterizations of tidal dissipation in use in global ocean models need to be adapted to include the dependence of the local dissipation on both the Coriolis frequency and the topographic steepness.

Highlights

Tidal flow over sea-floor topography in a buoyancy-stratified ocean can lead to the generation of internal waves at the tidal frequency, known as internal tides [1]
Since linear internal tide theory predicts that much of the tidal-energy conversion over these hills is supplied from the barotropic tidal flow along the direction with greater topographic variations [6,35], two-dimensional simulations are a reasonable first choice to examine this topography while minimizing computational cost
Having noted that parametric subharmonic instability (PSI) dominates the dissipation of the internal tide for f = ω0 /2, and the magnitude of this dissipation increases as the topographic length scale decreases for subcritical topography, we examine the tidal dissipation as a function of increasing topographic steepness, γ

Summary

Introduction

Tidal flow over sea-floor topography in a buoyancy-stratified ocean can lead to the generation of internal waves at the tidal frequency, known as internal tides [1]. These waves propagate both vertically and horizontally, carrying wave energy away from their generation site [2]. That energy can be used for turbulent mixing of heat and salt This mixing across density surfaces (diapycnal mixing) has an important role in large-scale ocean circulation, providing a mechanism for mixing heat down from the upper ocean, thereby lightening the deepest abyssal waters [3]. A parameterization commonly used in current climate models [4] represents this tidally-driven mixing in terms of the local dissipation of the internal tides near the generation site: e=

Methods

Results

Conclusion