The solution of a problem of stratified fluid dynamics and its stabilization as t → ∞

Near-field internal wave beams in two dimensions

“…(2017) and Boury, Peacock & Odier (2019) for a horizontal wave generator and Beckebanze, Raja & Maas (2019) for a vertical wave generator. To some extent this can also be seen in the inviscid calculations of Gabov (1985) for a horizontal plate, Gabov & Pletner (1985) for an inclined plate, Gabov & Krutitskii (1987) for a vertical plate and Gabov & Pletner (1988) for a horizontal disc, although only Gabov & Pletner (1985) considered the determination of the multivalued functions explicitly.…”

An explicit solution of the pseudo‐hyperbolic initial boundary value problem in a multiply connected region

“…The analogue of the Neumann boundary condition corresponds to the specification of normal velocities for a stream function. Hence, the Dirichlet boundary condition on r' coincides with the boundary condition in [6,8,11,12] where normal velocities are given on one plate in terms of a stream function. The analogue of the Neumann boundary condition on r2 coincides with the boundary condition in [22,29] where pressure is given on one plate in terms of a stream function.…”

“…The specification of normal velocities corresponds to the first boundary condition for a stream function and to the analogue of the second boundary condition for a potential function. As mentioned above, the previous problems on oscillations of one plate [6,8,11,12,16,22,29] were formulated in terms of a stream function. Problems in [6, 8, 11, 12, 161 have been studied with the specification of normal velocities on the plate, therefore, with the first boundary condition.…”

“…In [6,8,11,12,16,29] the exact solutions of non-stationary boundary value problems on small oscillations of one plate in an unbounded stratified and rotational fluid have been obtained. In doing so, the pressure or the normal velocities were specified on both sides of the plate.…”

“…The derivation of the equation of gravity-gyroscopic waves (1.1) is given in the point 1 of the appendix for the convenience of readers. One can note that in some papers gravity-gyroscopic waves are called gravity-inertial waves.In [6,8,11,12,16,29] the exact solutions of non-stationary boundary value problems on small oscillations of one plate in an unbounded stratified and rotational fluid have been obtained. In doing so, the pressure or the normal velocities were specified on both sides of the plate.…”