Gaussianity of internal waves

Abstract

Present theories of nonlinear interactions within a random internal wave field depend upon the assumption of quasi-Gaussian statistics; i.e., the nonlinearities are assumed to be perturbations on a Gaussian base state. Examination of horizontal current, temperature, and vertical displacement data has been ambiguous as to the correctness of this assumption. This report describes the time variability of the probability distribution of the east and north velocity components and the up (vertical displacement) variable of the internal wave experiment (IWEX ); the goal is to test for the Gaussianity of internal waves. In order to use the classical chi-square and the two-tailed Kolmogorov-Smirnov goodness-of-fit tests the correlation or spectral structure of the data must be considered. Starting with artificially generated Gaussian random time series that are white in frequency space, the Gentleman and Sande (1966) method is used to incorporate desired spectral shapes into the series, which are then used to find, for the two goodness-of-fit tests, new confidence levels that recognize the presence of an internal wavelike correlation structure in the data. The degree of Gaussianity of the east, north, and up variables throughout IWEX is discussed in this light and compared with results of previous investigations. It is concluded from the IWEX data that temperature and displacement are more likely to be Gaussian than are current data, that small kurtosis is characteristically associated with non-Gaussian current data, that negative skewness contributes to non-Gaussian temperature/displacement data, and that bursts of high variance may precede times of non-Gaussian behavior. No consideration was given to the frequency domain behavior of the data other than to the overall spectral shape for use in generating the artificial data. In this sense, then, this report is a preliminary study only, because the temporal evolution of the statistics of the various frequency bands in the internal wave field is the underlying question of importance.