Internal wave energy flux from density perturbations in nonlinear stratifications

TL;DR

This paper develops methods to compute internal wave energy flux in stratified oceans with variable buoyancy frequency, enabling analysis of energy transfer from density perturbations in realistic ocean conditions.

Contribution

It introduces analytic and computational techniques to determine energy flux from density data for arbitrary stratification profiles, extending previous methods limited to constant N.

Findings

Methods agree with direct numerical simulations

Applicable to real ocean data with variable stratification

Provides MATLAB tool for practical implementation

Abstract

Internal gravity wave energy contributes significantly to the energy budget of the oceans, affecting mixing and the thermohaline circulation. Hence it is important to determine the internal wave energy flux $\mathbf{J} = p \, \mathbf{v}$, where $p$ is the pressure perturbation field and $\mathbf{v}$ is the velocity perturbation field. However, the pressure perturbation field is not directly accessible in laboratory or field observations. Previously, a Green's function based method was developed to calculate the instantaneous energy flux field from a measured density perturbation field $\rho(x,z,t)$, given a $constant$ buoyancy frequency $N$. Here we present methods for computing the instantaneous energy flux $\mathbf{J}(x,z,t)$ for a spatially varying $N(z)$, as in the oceans where $N(z)$ typically decreases by two orders of magnitude from shallow water to the deep ocean. Analytic methods are presented for computing $\mathbf{J}(x,z,t)$ from a density perturbation field for $N(z)$ varying linearly with $z$ and for $N^2(z)$ varying as $\tanh (z)$. To generalize this approach to $arbitrary$ $N(z)$, we present a computational method for obtaining $\mathbf{J}(x,z,t)$. The results for $\mathbf{J}(x,z,t)$ for the different cases agree well with results from direct numerical simulations of the Navier-Stokes equations. Our computational method can be applied to any density perturbation data using the MATLAB graphical user interface EnergyFlux.