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Gravity Waves in a Heterogeneous Incompressible Fluid (Classic Reprint) (Inglés) Tapa blanda – 15 jun 2012


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Introduction Me will consider some tuo diraenslonal flows of an Incompressible heterogeneous ideal fluid of finite depth with a free surface. Let the coordinate axes be chosen so that when the fluid is at rest it occupies the strip -h y0, -ok xoo, of tjfie x-y planej the liney =0 corresponds to the undisturbed free surface, andy =-h to the rigid bottom. The density, p, of the fluid when at rest is assumed to depend on yonly, and in order for the equilibrium to be stable, p= p(y) must be a monotonic nonincreasing function of y. The fluid is then said to be stably stratified. The study of heterogeneous fluids was begun byS tokes (I8I4.7) who considered infinitesimal gravity vjaves in a fluid consisting of two layers of different density. This was later generalized to any niomber of layers by VJ ebb and by Greenhill (see [2 Ja 231, 233) For a fluid of nlayers wth a free surface, this problem leads to the following conclusions. There aren critical velocities, -U 1U o... UCO :foJ snj velocity between 0and U, nx Ti do n-x there aren possible waves; betx;een Ut and U2 there are n-1 possible waves; and so on, vuitil for UU no waves are possible. The shortest wave for any given speed is similar to the surface wave in a homogeneous medium. All the other vjaves are internal waves, having one or more nodes below the free surface. As the velocity approaches one of the critical speeds from beloxij, the length of the longest wave Increases monotonically to 00. Some interest in the problem derives from the fact that under appropriate circumstances internal gravity waves can be very large and their effect quite noticeable, as, for example, in the case of dead water resistance (see [2], 231, 219).
(Typographical errors above are due to OCR software and don't occur in the book.)

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