Trapped Quasi-Inertial Waves in Shear Oceanic Currents

M. V. Kalashnik^{a, b}

^a Obukhov Institute of Atmospheric Physics, Russian Academy of Sciences, Moscow, Russia

^b Scientific Production Enterprise Taifun, Obninsk, Russia

e-mail: kalashnik-obn@mail.ru

Received July 6, 2012; in final form, May 20, 2013

Abstract—We studied trapped long quasi-inertial waves in horizontally inhomogeneous flows with low
Rossby numbers. A simple heuristic derivation of two equations for the wave amplitude is presented. These
equations are true for strong and weak density stratifications. A spectral problem is formulated to find the fre-
quencies of trapped waves based on the amplitude equations. Exact solutions of the hyperbolic problem for a
free hyperbolic shear layer are found. It is shown that the location of the trapping area principally depends on
the stratification. If the buoyancy frequency is greater than the inertial frequency, trapping occurs in the region
of anticyclonic velocity shear; if the buoyancy frequency is smaller than the inertial frequency, trapping occurs
in the region of cyclonic velocity shear. Thus, in the first case, the frequencies of the trapped waves are smaller
than the inertial frequency, while, in the second case, they are greater. The intense wave activity observed in the
regions of oceanic fronts and jet currents can be related to the existence of trapped waves.

DOI: 10.1134/S0001437014020106

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