TABLE OF CONTENTS In the nearshore region, the most important currents are horizontal and they have horizontal extensions (length scales) that are of the order of a wave length or much larger. Due to turbulence from various sources and the mechanisms responsible for generating the currents, they may show vertical variations in the horizontal velocity, typically in magnitude, but often the direction of the velocity is also varying over the vertical.
The presence of currents changes the waves. However, as with depth refraction, the lowest order effect turns out to be in the dispersion relation through changes in the speed of wave propagation. Because those kinematic properties do not depend on the wave amplitude] we are, in parallel with the depth refraction] able to analyze the propagation patterns in linear waves on currents separately from the analysis of the dynamics which provides the information about the amplitude variations.
A common assumption is also that we analyze the effect the current has on the waves but assume the currents remain unchanged the waves. This of course is a simplification that is discussed extensively in the chapters about wave induced currents and nearshore circulation.
In the following, we first analyze the local effects of the simplest case, a wave motion on a steady current, uniform both over depth and in the horizontal plane. Then give a brief overview of the local effects of depth varying currents] and finally briefly discuss extension of the geometric optics approximation to the...
