On the interpretation of energy and energy fluxes of nonlinear internal waves: an example from Massachusetts Bay

Abstract

A self-consistent formalism to estimate baroclinic energy densities and fluxes resulting from the propagation of internal waves of arbitrary amplitude is derived using the concept of available potential energy. The method can be applied to numerical, laboratory or field data. The total energy flux is shown to be the sum of the linear energy flux $\int u'p'\,{\rm d}z$ (primes denote baroclinic quantities), plus contributions from the non-hydrostatic pressure anomaly and the self-advection of kinetic and available potential energy. Using highly resolved observations in Massachusetts Bay, it is shown that due to the presence of nonlinear internal waves periodically propagating in the area, $\int u'p'\,{\rm d}z$ accounts for only half of the total flux. The same data show that equipartition of available potential and kinetic energy can be violated, especially when the nonlinear waves begin to interact with the bottom.