Some Surface Effects on Gravity Waves in a Viscous Fluid

Abstract

The complex dispersion relation for gravity waves in a viscous fluid of infinite depth was computed by Chandrasekhar¹. He assumed a stress-free surface, which may be expressed by

$$\frac{{\partial \text{u}}} {{\partial \text{Y}}} + \frac{{\partial \text{v}}} {{\partial \text{X}}} = 0,\,\,\,\,\,Y = 0$$

valid in linear theory. Two-dimensional motion is considered, where x is a horizontal coordinate along the undisturbed fluid surface, and y is a vertical coordinate opposite gravity. g denotes gravitational acceleration, while u and v are horizontal and vertical velocity components.