The Impact of Topographic Steepness on Tidal Dissipation at Bumpy Topography

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.

Impact of Background Geostrophic Currents With Vorticity on Resonant Triad Interaction Over Mid‐Ocean Ridges

“…This is due to the generation of subharmonic waves along the IT beams. For runs with BGCs of positive relative vorticity, all energy dissipation peaks at the center of the ridge, agreeing with the results shown in Figures 7b, 7d The vertical profiles of the dissipation rate are shown in Figure 8 as a function of depth, which is essential for the improvement of the "vertical distribution function" in the corresponding parameterization (Mackinnon et al, 2017;Yi et al, 2017). We also calculate the energy dissipation rate induced by the subharmonic waves and ITs from the filtered velocity fields to illustrate their contributions quantitatively.…”

“…of run CE3 (Figure 3g). Because the effective Coriolis frequency is generally equal to ω 0 /2 around the crest of the ridge in run CE3, intense RTI occurs (Nikurashin & Legg, 2011;Richet et al, 2018;Yang et al, 2018;Yi et al, 2017). As shown in Figure 3g, the subharmonic waves are more powerful than those in the other two runs (CE1 and CE2), accompanied with strong baroclinic currents over the crest of the ridge.…”

“…where subscripts 0, 1, and 2 denote the ITs and two subharmonic waves, respectively (Phillips, 1966;Mc-Comas & Bretherton, 1977;Maurer et al, 2016). RTI can occur over both small-scale rough topography (Nikurashin & Legg, 2011;Yi et al, 2017) and isolated mid-ocean ridges (Liang & Wunsch, 2015;Wang et al, 2021) in the ocean. RTI results in enhanced energy dissipation, because the generated subharmonic waves have smaller vertical scales and stronger shears (Liang & Wunsch, 2015;Nikurashin & Legg, 2011;Richet et al, 2018;Staquet & Sommeria, 2002;Wang et al, 2021).…”

On the Magnitude of Canyon‐Induced Mixing

“…Diapycnal mixing, or mixing across density surfaces, is important in sustaining the large‐scale circulation of the ocean (Bryan, 1987; Wunsch & Ferrari, 2004). While there are a host of physical processes through which diapycnal mixing may occur, the breaking of tidally generated internal waves (internal tides) has been shown to be an efficient mechanism for diapycnal mixing in the ocean (Egbert & Ray, 2000; de Lavergne et al., 2019; Munk & Wunsch, 1998; Polzin et al., 1997; Vic et al., 2019; Whalen et al., 2012; Waterhouse et al., 2014; Yi et al., 2017). These waves efficiently transmit energy over ocean basins (Zhao et al., 2016), and deposit this energy to turbulent mixing where they break.…”

Control of the abyssal ocean overturning circulation by mixing-driven bottom boundary layers

“…At even larger scales, the entire life-cycle of the internal wave field can be simulated (again using an LES closure to arrest the turbulent cascade to unresolved small scales): conversion of the barotropic tide into internal tides at rough topography, internal wave propagation, wave-wave interactions, reflection, and breaking (Nikurashin and Legg, 2011;Yi et al, 2017;Jalali and Sarkar, 2017). All of these past studies, however, are inherently transient exercises since there is no forcing that restores the stratification; tidally-driven turbulence homogenizes the near-bottom layers until eventually the stratification becomes too weak to support propagating internal waves, i.e.…”