Inertial oscillations, with frequency f (f is the Coriolis parameter) are not an uncommon phenomen in the oceans. Their detection in the Earth's atmosphere has been aided by hourly wind data from the NOAA Wind Profiler Network. Selected stations in the Great Plains reveal their existence in the lower troposphere up to 20 percent of the time over a four year period. The present investigation provides a theoretical depiction of the mutual interaction between inertial oscillations and frontogenesis. The development is general: it could apply to either oceanic or atmospheric events.
The basic model is two-dimensional, inviscid and nonlinear. The flow is contained between rigid lids at the top and the bottom. The critical assumption that provides an analytically tractable problem is that the flow is characterized by zero potential vorticity. This assumption implies that the temperature or the density is only a function of X = x + v/f, where x is the cross-front horizontal coordinate, and v is the along-front velocity (a function of the horizontal and vertical coordinates and time).
The principal results that will be displayed are 1) the nonlinear solution exhibits frontogenesis in the presence of inertial oscillations, and 2) two end states are possible. Either the relative vorticity becomes infinite in a finite time, a frontal discontinuity, or the solution is represented as the sum of a steady geostrophic part and a time dependent inertial oscillation. In the second case, frontogenesis occurs in the first half-cycle of the oscillation; then it reverses and the initial state is recovered at the end of the period. The initial conditions determine which end state will be realized: the initial relative vorticity must exceed a critical value for a discontinuity to occur. Other characteristic of the solution, including the partition of energy between the geostrophic flow and the inertial oscillations, will be presented. Lastly, the relevance of the present model to atmospheric and oceanic flows will be noted.
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12th Conference on Atmospheric and Oceanic Fluid Dynamics