arXiv subjects

Miles A. Sundermeyer

Publications and source records attributed to Miles A. Sundermeyer.

2 recordsLinked to original sources

arXiv2026

Toward a Universal Framework for the Internal Gravity Wave Spectrum

The Garrett-Munk (GM) spectrum has long provided a canonical model of the oceanic internal gravity wave field. However, it relies on hydrostatic assumptions and idealized stratification that limit its applicability where non-hydrostatic dynamics, vertical boundary effects, or non-monotonic stratification are important. Here we develop a generalized framework for the internal wave spectrum based on non-hydrostatic vertical modes formulated in horizontal wavenumber-vertical mode space. Energetic orthogonality among wave modes requires that such a formulation be cast in horizontal wavenumber space rather than frequency space. In this formulation, the deformation radius associated with each vertical mode provides a proxy for distinguishing hydrostatic and non-hydrostatic regimes. Vertical modes are obtained numerically from the fixed-K Sturm-Liouville problem, allowing arbitrary stratification and multiple turning depths. Combined with a generalized spectral function, the formulation yields expected distributions of horizontal kinetic, vertical kinetic, and potential energy as functions of depth, frequency, and horizontal wavenumber. Example applications illustrate departures from GM theory associated with boundary effects and non-hydrostatic dynamics, including improved representation of vertical variance and high-frequency vertical kinetic energy, while reproducing observed features of horizontal wavenumber spectra.

physics.flu-dyn↗

arXiv2020

A generalized wave-vortex decomposition for rotating Boussinesq flows with arbitrary stratification

The linear wave and geostrophic (vortex) solutions are shown to be a complete basis for physical variables $(u,v,w,ρ)$ in a rotating non-hydrostatic Boussinesq model with arbitrary stratification. As a consequence, the fluid can be unambiguously separated into linear wave and geostrophic components at each instant in time, without the need for temporal filtering. The fluid can then be diagnosed for temporal changes in wave and geostrophic coefficients at each unique wavenumber and mode, including those that inevitably occur due to nonlinear interactions. We demonstrate that this methodology can be used to determine which physical interactions cause the transfer of energy between modes by projecting the nonlinear equations of motion onto the wave-vortex basis. In the particular example given, we show that an eddy in geostrophic balance superimposed with inertial oscillations at the surface transfers energy from the inertial oscillations to internal gravity wave modes. This approach can be applied more generally to determine which mechanisms are involved in energy transfers between wave and vortices, including their respective scales. Finally, we show that the nonlinear equations of motion expressed in a wave-vortex basis are computationally efficient for certain problems. In cases where stratification profiles vary strongly with depth, this approach may be an attractive alternative to traditional spectral models for rotating Boussinesq flow.

physics.flu-dyn↗