The Time Behavior of the Probability Density Function of Some Simplified Atmospheric Flows

Abstract

A three-component barotropic flow is considered to study the time behavior of the joint probability density function of spectral amplitudes. The beta effect is included by allowing the phase of the waves to be a linear time function. Analytic and numerical integrations are obtained for cases with and without beta. It is found that the addition of the beta effect produces important changes in the behavior of the probability function, particularly for long times. Initial correlations between the wave components are allowed and found to have some impact on the second moments of the distribution for the first two days. After this time, the nonlinearities build correlations such that the fields are independent of the initial correlation values.