Gravity waves in flowing water

Abstract

Some particular cases of the effect of a non-uniform current on two-dimensional gravity waves are considered. For linear waves on a current varying as the one-seventh power of the depth, the velocity of propagation can be found as a power series in the square root of the Froude number. For the non-linear solitary and cnoidal waves, both the profile and the velocity are found to depend on the value at the free surface of the current and its first derivative.