Oceanic Waves

Background

Lee waves are an example of internal gravity waves forced by stably stratified flow over bathymetry. Oceanic internal lee waves have horizontal wavelengths between O(1–10) km that bridge mesoscale currents and small-scale turbulence and play a central role in the ocean’s energy cascade. Their generation exerts wave drag on balanced flow and extracts mesoscale energy, and their propagation transports this energy through wave-fluxes. When they break, they convert energy downscale to turbulent dissipation and mixing, maintaining the ocean’s stratification and, in turn, contributing to the large-scale circulation. 

For the global energy budget (FIG. 1), roughly 1 terawatt of wind-work drives the ocean circulation, out of which 15–75% is used for lee-wave generation. A common assumption in recent ocean modeling literature is that this lee-wave generation is all lost to turbulent dissipation in a one-way forward energy cascade (from large to small scale; marked by the red dashed arrow in FIG. 1). However, this can be challenged by the fact that lee waves and their generating currents can exchange energy through wave-mean interaction and this exchange can be two-way. Thus, lee-wave generation may be partially reabsorbed back to bottom-intensified currents, which unveils a backward energy cascade (from small to large scale; marked by the green arrow in FIG. 1). Wave action conservation suggests that, in a steady flow, wave action A = E / ωL is conserved rather than wave energy E. As Doppler-shift alters waves’ Lagrangian frequency ωL = |ωE − kU| (where Eulerian frequency ωE is invariant, k is the along-stream topographic wavenumber, and U is flow velocity), shear will result in energy exchange between waves and the mean flow.

Problem Statement

Key Findings

• For monochromatic topography with |kU|≈ 0.9N (where k is the along-stream topographic wavenumber, U is the near-bottom flow speed, and N is the buoyancy frequency), Reynolds-decomposed energy budget analysis is consistent with wave action conservation predictions, confirming that only 14% of the upward lee-wave energy flux is dissipated, while up to 50% is reabsorbed into the sheared mean flow. Thus, reabsorption needs to be taken into account as a possible mechanism for reducing the lee-wave dissipative sink for balanced circulation.

• For broadband topography at mid- and high latitudes, the integrated dissipative fraction is 90–95%, suggesting that reabsorption is not sufficient to explain the observed turbulence shortfall in the Southern Ocean.

• A new parameterization for lee-wave energy sinks into reabsorption and dissipation as a function of lee-wave generation frequency is proposed, independent of the strength of turbulent parameterization. 

• This research quantifies lee waves’ role in dissipating versus redistributing balanced energy and advance parameterizations of drag and mixing for balanced flow interacting with topography for oceanic general circulation models.