Generation of Periodic Internal Waves by an Oscillating Strip of Finite Width

摘要: The traditional approach to the calculation of inter-nal-wave generation, which is based on use forceand mass sources with parameters adopted from thehomogeneous-liquid theory, enables one determine afar field accurate empirical constants [1–3]. Amethod for constructing solutions a linearizedproblem that exactly satisfy boundary conditions, wasproposed in [4, 5]. As wave source, part an infiniteplane positioned at arbitrary angle ϕ horizon-tal and executing periodic oscillations frequency ω was considered. A finite-width strip oscillating alongits surface emits unimodular bimodal beams into aliquid constant buoyancy N ; beamstravel θ = horizontal. In anarbitrary case ( ≠ ), when all separate theemitting surface, pattern particle-dis-placement amplitudes are consistent measure-ments [6, 7]. critical two wavebeams propagate along plane separating liquid,the calculations result overstated values sepa-rated-beam give no way finding adja-cent-beam [5, critical-angle isof particular interest problems geophysicalhydrodynamics [8] calls special consideration.In present paper, solution more physi-cally-based problem internal-wave generation by afinite-width constructed entirerange variation slope including criti-cal one.A system two-dimensional equations motionfor exponentially stratified incompressible liquid inthe Boussinesq approximation [1] brought fol-lowing equation stream function Ψ emit-ωNarcsin---- ting-surface axes coordinate ξ , ζ ) (see figure): (1) Here, ∆ + ν kinematic viscosity.The gravity g opposite z -axis; relationbetween systems x isshown figure.The adhesion conditions emitting surface(which width inclined its surface) thedamping perturbations infinity constitute theboundary velocity u