Recent direct observations of the rate of kinetic energy dissipation, ε, tend to vary systematically with buoyancy frequency, N. This note presents arguments leading to an expected relationship between these two parameters. We first suggest that the classical separation of velocity field into “turbulent” and “mean” (including internal waves) is inappropriate for a stratified system such as the ocean, in which nonlinear forces and buoyant restoring forces act over a wide range of space-time scales. Reconsidering the steady-state kinetic energy equation without this separation, we obtain ε ∝ N1.0 or ε ∝ N1.5, where the ambiguity in exponent is associated with uncertainty with regard to the appropriate form for the vertical velocity variance of the internal wave field. With similar assumptions in the steady-state equation for available potential energy (APE) it is shown that the rate of dissipation of APE, γ, also varies as γ ∝ N1.0 or γ ∝ N1.5, where ambiguity in exponent again derives from internal wave vertical velocity variance. If, in addition, the flux Richardson number is independent of N, the vertical eddy diffusivity for mass Kp associated with internal wave mixing varies as Kp ∝ N–1.0 or Kp ∝ N–0.5.
Gargett, Ann E., and Greg Holloway. 1984. "Dissipation and diffusion by internal wave breaking." Journal of Marine Research 42, (1). https://elischolar.library.yale.edu/journal_of_marine_research/1706