Stokes Waves in Water of Finite Depth

TL;DR

This paper investigates Stokes waves in finite-depth water, analyzing how physical quantities change with wave steepness and examining stability conditions and complex singularities.

Contribution

It extends previous methods to finite-depth water, providing new insights into wave behavior, stability, and singularities for varying steepness levels.

Findings

Physical quantities vary with wave steepness in finite-depth water.

The Taylor sign condition is examined for these waves.

Complex singularities outside the domain are analyzed.

Abstract

Periodic water waves of permanent form traveling at constant speed, the so-called Stokes waves, are studied in water of fixed finite depth using methods previously used in water of infinite depth. We apply our methods to waves of varying steepness over a range of fixed depths in order to determine how a number of physical quantities related to the waves change as the steepness of the waves increases. Finally, we examine the Taylor sign condition for these waves, as well as the complex singularities outside of their domain of definition when the waves are considered as a function of a conformal variable.