Near-inertial dissipation due to stratified flow over abyssal topography

Abstract

Linear theory for steady stratified flow over topography sets the range for topographic wavenumbers over which freely propagating internal waves are generated, and the radiation and breaking of these waves contribute to energy dissipation away from the ocean bottom. However, previous numerical work demonstrated that dissipation rates can be enhanced by flow over large scale topographies with wavenumbers outside of the lee wave radiative range. We conduct idealized 3D numerical simulations of steady stratified flow over 1D topography in a rotating domain and quantify vertical distribution of kinetic energy dissipation. We vary two parameters: the first determines whether the topographic obstacle is within the lee wave radiative range and the second, proportional to the topographic height, measures the degree of flow non-linearity. For certain combinations of topographic width and height, breaking occurs in pulses every inertial period, such that kinetic energy dissipation develops inertial periodicity. In these simulations, kinetic energy dissipation rates are also enhanced in the interior of the domain. In the radiative regime the inertial motions arise due to resonant wave-wave interactions. In the small wavenumber non-radiative regime, instabilities downstream of the obstacle can facilitate the generation and propagation of non-linearly forced inertial motions, especially as topographic height increase. In our simulations, dissipation rates for tall and wide non-radiative topography are comparable to those of radiative topography, even away from the bottom, which is relevant to the ocean where the topographic spectrum is such that wider abyssal hills also tend to be taller.

The Impact of Representations of Realistic Topography on Parameterized Oceanic Lee Wave Energy Flux

“…(2020) considered this “cap” approximation for flow around an isolated seamount, showing that linear theory applied to the “cap” only could be used to estimate energy flux. For periodic topography, Zemskova and Grisouard (2021) note from idealized simulations that topography with wavelength outside of the radiating range can generate propagating lee waves due to a reduced effective topographic width when flow blocking takes place.…”

Energy Sinks for Lee Waves in the Northern South China Sea

“…The second regime ( Fr = 0.3–0.7; Case 3) develops with the generation of inertial frequency harmonics. In this regime, the rapid growth of IOs could significantly modify the wave vertical scales and promote wave breaking (Nikurashin & Ferrari, 2010b; Zemskova & Grisouard, 2021). The growth of IOs dissipates a significant amount of E IW below HAB = 400 m (Figure 13c; Figure 15c), and leaves only about one third of the E IW radiating into the shear zone.…”

“…In addition, the R IW may be potentially dependent on the Froude number Fr = Nh / U b where h is the root‐mean‐squared height of the topography and U b is the bottom flow speed. Inertial oscillations (IOs) can be triggered by wave breaking in a rotating frame and the rapid growth of IOs under large Fr condition could significantly modify the wave vertical scales and promote wave breaking (Nikurashin & Ferrari, 2010b; Zemskova & Grisouard, 2021). This indicates that lee waves generated in a large Fr environment tend to dissipate close to the rough topography and consequently they are less likely to interact with mean flows and be re‐absorbed by mean flows.…”

Influence of Lee Wave Breaking on Far‐Field Mixing in the Deep Ocean

“…Over a sufficiently long period, the response mechanism fully develops, which can efficiently contribute to the growth of NIWs. Built on the findings of Nikurashin and Ferrari (2010), a recent numerical study confirmed the formation of NIWs in the local field and showed that changes in both topographic height and width can facilitate their growth (Zemskova & Grisouard, 2021). If the topography is taller or narrower, the fluid movement squeezing against the abrupt, steep topography becomes faster, leading to a greater horizontal velocity gradient.…”