# Atmosphere Ocean Science Colloquium

#### Interactions between near-inertial waves and mesoscale mean flow in the ocean

**Speaker:**
Jin-Han Xie, CIMS

**Location:**
Warren Weaver Hall 1302

**Date:**
Wednesday, October 11, 2017, 3:30 p.m.

**Synopsis:**

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 both rotating stratied uid and shallow

water system, we derive models which couples the dynamics of both NIW and mesoscale mean

ow. 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 quasi-two-dimensional vortical motion. Our procedure provides a direct

route to the YBJ equation and elucidates its variational structure and conservation laws. The

eect NIWs on the quasi-qeostrophic mean ow is governed by a material invariant equation,

where the new conserved quantity consists of the classic quasi-qeostrophic potential vorticity and

quadratic NIW eects. The preservation of a Hamiltonian structure by this wave-mean coupled

model enables the long-time property study and an energy transfer mechanism { stimulated

NIW generation, which is important to ocean energetics { is proposed. Adding viscosity to the

shallow water model is also discussed