Process of the Formation of Internal Waves Initiated by the Start of Motion of a Body in a Stratified Viscous Fluid

Abstract

The mechanism of formation of three-dimensional internal gravity waves initiated by the start of motion of a disk of given diameter and finite thickness in the horizontal direction along the disk symmetry axis from right to left at a given uniform velocity in an incompressible viscous linearly density-stratified fluid is first considered in detail. The consideration is carried out on the basis of numerical solution of the system of Navier—Stokes equations in the Boussinesq approximation and visualization of the three-dimensional vortex structure of the flow calculated. The obtained fields of the velocity vectors and pressure perturbations possess horizontal and vertical symmetry planes passing through the disk symmetry axis. The process of formation of flow in the upper half-space caused by the shear and gravitational instabilities is described. In this process, two horizontal vortex filaments are initially formed between the back disk face and the place of pulsed start and then transformed into legs of the hairpin vortex loop whose head is located to right of the start point. Thereafter, vortex rings are periodically formed above the start point during half the buoyancy period of fluid. The left-hand halves of the rings are transformed into half-waves occupying space between the disk and the start point.