The Poisson Link Between Internal Wave and Dissipation Scales in the Thermocline Part I. Probability Density Functions and the Poisson Modeling of Vertical Strain

Abstract

The irregular nature of vertical density profiles is a ubiquitous characteristic of the ocean thermocline. This distortion can be quantified by tracking a set of constant-density (isopycnal) surfaces over time. Examination of 30,000 km of vertical density profile data from seven Pacific Ocean sites indicates that the statistics of isopycnal vertical separation follow the Gamma probability distribution, the continuous representation of a Poisson process. All aspects of this process are specified by a single parameter, κ0, of order .5-2 m-1 across the Pacific. When vertical wavenumber spectra of vertical strain are nondimensionalized by κ0, the variability in these pan-Pacific spectra reduce from a factor of 20 to a factor of two.Given that numerous dimensionless metrics such as the Richardson Number, Froude Number, Burger Number, etc., are required to specify dynamical balances in the sea, it’s intriguing that a single-parameter model describes all aspects of the statistics of vertical strain over the range of scales ~2-200 m. While both internal wave and vortical motions are present in the data, the waves dominate the strain signal at these sites. The high wavenumber cut-off in the strain spectrum is set by the nonsinusoidal waveform of short vertical scale internal waves. As large-scale numerical models improve in resolution, they should replicate this Poisson structure in order to properly model plankton variability, vertical diffusion, horizontal dispersion, sound propagation, and other fine-scale phenomena.