Berkeley Fluids Seminar
University of California, Berkeley
Bring your lunch and enjoy learning about fluids!
Wednesday, April 20, 2016
240, Bechtel Hall, 13:00-14:00
Dr. Jin-Han Xie (Physics, UC Berkeley)
Interactions between inertial waves and mesoscale mean flow in the ocean
Abstract: Wind forcing of the ocean generates a spectrum of inertia-gravity waves that is sharply peaked near the local inertial (or Coriolis) frequency. The corresponding near-inertial waves (NIWs) make a dominant contribution to the vertical velocity and vertical shear in the ocean; they therefore play an important role for mixing, biological productivity, pollutant dispersion and, arguably, the thermohaline circulation. By applying a form of Whitham averaging to the variational formulation of the primitive equations for a rotating stratified fluid, we derive a model which couples the dynamics of both NIW and mesoscale mean flow. The wave equation recovers an asymptotic model proposed by Young and Ben Jelloul (YBJ). It describes the slow evolution of NIWs that results from weak dispersion and from their interactions with the quasitwo-dimensional vortical motion. Our procedure provides a direct route to the YBJ equation and elucidates its variational structure and conservation laws. The effect NIWs on the quasiqeostrophic mean flow is governed by a material invariant equation, where the new conserved quantity consists of the classic quasi-qeostrophic potential vorticity and quadratic NIW effects. The preservation of a Hamiltonian structure by this wave-mean coupled model enables the longtimeproperty study and an energy transfer mechanism – stimulated NIW generation, which is important to ocean energetics – is proposed.