Interference and Transmission of locally forced internal waves in non-uniform stratifications

Abstract

Several studies have investigated the effect of constructive or destructive interference on the transmission of internal waves that propagate through non-uniform stratifications. Such studies have been performed for internal waves that are spatiotemporally harmonic. To understand the effect of spatiotemporal localization, this thesis presents a theoretical and experimental study of the transmission of two-dimensional internal waves that are generated by a boundary forcing that is localized in both space and time. This is done by considering an idealized problem and applying a weakly viscous semi-analytic linear model to it. After validation with a numerical model, the semi-analytic model allows us to perform parametric studies. Using theoretical studies, we show that localization leads to the disappearance of transmission peaks and troughs that would otherwise be present for a harmonic forcing. The laboratory experiments that we perform provide a clear indication of this physical effect. Based on the group velocity and angle of propagation of the internal waves, a practical criteria that assesses when the transmission peaks or troughs are evident, is obtained. It is found that there is a significant difference in the predicted energy transfer due to a harmonic and non-harmonic forcing which has direct implications to various physical forcings such as a storm over the ocean.