Inertial oscillation, inertial wave and initial value problem in rotating annular channels

Abstract

Inertial oscillations, inertial waves and the initial value problem in a rotating annular channel are investigated for an arbitrarily small but fixed Ekman number E. We first derive the inviscid solution of inertial oscillations and inertial waves, as well as an asymptotic expression for the viscous decay factors valid for the inertial modes of a broad range of frequencies that are required for an asymptotic solution of the initial value problem. A time-dependent asymptotic solution of the initial value problem subject to a physically acceptable initial condition is then obtained. We also perform a fully numerical analysis to estimate the viscous decay factors and to simulate time-dependent solutions of the initial value problem, showing satisfactory quantitative agreement between the asymptotic analysis and the fuller numerics.

Keywords:

• Inertial wave
• Initial value problem
• Rotating channels

Acknowledgements

X. Liao is supported by NSFC grant/10633030, MOSTC863/2006AA01A125, STCSM/08XD14052 and CAS grant/KJCX2-YW-T13 and K. Zhang is supported by UK NERC and STFC grants. The numerical computation is supported by SSC.