A numerical study of the effect of free surface and water depth on the stability of wakes: Use of GDQ formulation

Abstract

The instability character of a wake in the presence of a free surface is examined by a recently developed GDQ (generalized differential quadrature) numerical method. It is shown that at low Froude number the wake near a free surface is convectively unstable, but when the Froude number is increased further it becomes absolutely unstable. The effect of water depth on the stability property of the wake flow is also investigated. It is found that the influence of water depth on the critical point of instability is limited to at most 20% variation in the complex frequency, while the change in temporal growth rate is also limited to about 20%. © 1997 by John Wiley & Sons, Ltd.