Vertical dispersion of inertial waves in the upper ocean

Abstract

A linear model of the vertical dispersion of near‐inertial waves is developed. A porosity distribution near the bottom of the computational domain minimizes bottom reflections and simulates an ocean of infinite depth. The model is used to show that the vertical dispersion of near‐inertial waves in the upper ocean may, under certain conditions, contribute significantly to the observed rapid decay of inertial oscillations in the surface layer. The kinetic energy of inertial oscillations at mid‐latitudes decays with an e folding time scale of 10 days or less, when the parameter λ(km)/N(cph)d(m) is less than or of the order of unity, where λ is the wavelength of the wind‐generated near‐inertial waves, N is the Väisälä frequency in the upper pycnocline, and d is the surface layer thickness. At the top of the pycnocline the model predicts a velocity maximum, which develops as energy propagates downward, out of the surface layer. However, when the upper pycnocline is sufficiently peaked, a resonant frequency interference effect is predicted. This effect modulates the dissipation of surface layer inertial oscillations, and their magnitude after a storm need not decay monotonically. We also make qualitative comparisons with deep‐ocean current meter observations taken during the Mixed Layer Experiment (MILE) and with shallow water (105 m) observations taken in the Baltic Sea.