A Numerical Investigation of Resonant Inertial Response of the Ocean to Wind Forcing

Abstract

A one-dimensional model of upper-ocean vertical mixing is used to investigate the ocean's response to idealized atmospheric storms over short (1–2 day) timescales. Initial ocean conditions are based on observations from the northeast Pacific. When the wind rotation is resonant at the inertial frequency, the surface input of kinetic energy to the currents, KE0, is maximized, as are the net changes in inertial kinetic energy, potential energy, and sea surface temperature. The KE0 is a key air–sea interaction parameter because of its strong dependence on the time histories of the wind forcing and surface current, and because some of this kinetic energy input can go to increasing potential energy when dissipated in regions of large buoyancy gradients below the mixed layer. Energy input and the ocean response are rapidly reduced for less inertial winds, indicating that the upper ocean has highly tuned inertial resonant responses. The degree of tuning is highest for the inertial kinetic energy response, followed by KE0 input, the potential energy, and temperature responses. For storms of varying strength, duration, shape, and wind rotation, about 20% of the final inertial current energy is found beneath the mixed layer, regardless of the stratification. The magnitude of inertial current response depends on KE0 and wind rotation, but not stratification, and is approximately 0.532 KE0[1–e−2.81], where Γ is a function of wind rotation that varies from 1 for purely inertial winds to 0 for winds with no energy at the inertial frequency. Changes in potential energy and surface temperature depend mainly on KE0 and stratification, but not systematically on wind rotation other than as accounted for in KE0. Initial currents can modulate KE0 and the responses significantly; the modulation varies roughly linearly with initial current speed, consistent with a simple scale analysis. Modulation of each measure of ocean response is similar, so that there is little effect on general relationships formed by normalizing the responses with KE0, except for certain special phase relationships between the initial current direction and wind direction. Parameterizations of KE0 and of the mechanical production of turbulent kinetic energy should include both wind speed (or friction velocity) and rotation of the wind.