Internal Lee Waves Generated by Shear Flow Over Small-Scale Topography

When the bottom current flows over a small-scale topographic feature (with characteristic horizontal scale of 0.1-10.0 km), it generates internal lee waves. These lee waves furnish the energy cascade from mesoscale to dissipative scale, resulting in enhanced turbulent mixing. The existing lee wave theory and parameterization are mostly based on uniform background flow. We improve the linear lee wave theory by considering shear background flow and viscous and diffusive effects, which are ubiquitous in the ocean. In particular, the introduction of vertical viscous and diffusive terms effectively improves the problem of critical layer (where the wave frequency is close to the Coriolis frequency) for linear lee waves under weakly dissipative limit. Then, the influences of different types of shear flow on the frequency, vertical wavelength, group velocity, energy flux, energy density, energy dissipation and irreversible mixing of lee waves are explored through both theory and numerical simulation. A bottom-up decreasing background flow can enhance energy dissipation and irreversible mixing below the critical layer. However, in the real ocean, the dissipation and mixing caused by a decreasing background flow may be weaker than that caused by an increasing background flow in a depth integrated sense, especially when considering a bounded domain. Additionally, the theory of wave action conservation in the absence of dissipation, which is commonly used as a criterion in research of internal waves propagating in varying background fields, is extended to a modified wave action equation considering dissipation, which may potentially improve the lee wave parameterization in the future.

Automated summary

This study improves the linear lee wave theory by considering shear background flow and viscous and diffusive effects. The influences of different types of shear flow on various aspects of lee waves are explored. It is found that a bottom-up decreasing background flow can enhance energy dissipation and irreversible mixing, but in a depth integrated sense, the dissipation and mixing caused by a decreasing background flow may be weaker than that caused by an increasing background flow.