Abstract
A consistent hydrodynamic model is developed for the effects of a stochastic field of internal waves in the deep ocean on sound-speed and current fluctuations. A scaling is used which reflects the preponderance of energy contained in internal waves of long horizontal wavelengths and near-inertial periods. An approximate solution to the consistent boundary-value problem for vertical eigenfunctions is obtained by a WKB(J) expansion. Expressions are found for internal-wave fluctuations as superpositions of deterministic functions multiplied by random variables, for which particular probability distributions are not assumed. Using specific forms of Brunt–Vaisala frequency and internal-wave energy-density spectrum for illustration, formulas for covariances, variances, confidence intervals, correlation coefficients, and correlation scales are obtained for acoustically pertinent fluctuations. As a result of the consistent treatment of vertical variations throughout the model, many properties of the statistical quantities, such as vertical nonstationarity of the variances, upper and lower correlation depths, and horizontal correlation length, are demonstrated and physically interpreted.
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