Propagation of obliquely incident water waves over a trench. part 2. currents flowing along the trench

Several methods based on matched eigenfunction expansions are developed to study the diffraction of a linear, steady train of waves in finite water depth by a combination of straight depth discontinuities and colinear vortex sheets, where the vortex sheets represent a first approximation to a thin shear layer between regions of dissimilar ambient current velocity. Special attention is paid to the case of a current flowing along a submerged trench, and predictions of reflection and transmission are seen to be highly sensitive to the magnitude and direction of the ambient current.