On an inverse problem of ship-induced internal waves

An inverse problem for trapped internal waves is considered in an attempt to provide a practical tool for estimating the density stratification in the sea from the wake pattern behind a moving vessel. The ambient stratification is represented by Barber's (1993) exponential series and the coefficients are found by matching the first mode dispersion relation to the one found from the wake data. A fast algorithm for calculating the dispersion relation is derived. It is shown that when the series converges with a low number of coefficients, the inverse profile is adequate, as happens for example for typical sea loch profiles. In more general circumstances the predicted maximum stratification still provides a reasonable approximation as a result of Barber's (1993) theorem.