STABLE AND UNSTABLE MODES IN A WAVE-CURRENT SYSTEM HAVING UNIFORM VORTICITY

Sea waves interacting with a surface current whose undisturbed velocit y profile is linear form a physical system that is practically importa nt and moreover easy to treat mathematically since the dispersion equa tion becomes an algebraic equation The present paper emphasizes which information about fundamental wave modes that can be obtained from gra phical solutions of the dispersion equation. Use of Taylor's nondimens ional variables Y = U/c and Z = hg/U-2 makes it possible to show in a very clear way how the flow becomes unstable within a certain wave num ber band. The instability is reminiscent of the Kelvin-Helmholtz insta bility, but occurs even for a homogeneous fluid.