Development of the wave motion induced by near-bottom periodic disturbances in a two-layer shear current

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The behavior of wave motion arising in an ideal incompressible homogeneous fluid under switching-on periodic bottom disturbances is studied in the linear approximation for the two-dimensional non-stationary problem. In the undisturbed state, the velocities of two-layer fluid flow are linear functions of the vertical coordinate in each of the layers with different gradients and coincide on the boundary of the layers. The upper boundary of fluid can be either free or bounded by the rigid cover. The dispersion dependences and the group velocities of the appearing wave modes are determined. The vertical displacements of the free surface and the interface between the layers are calculated. A comparison with the solution for a single-layer fluid is carried out.

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Sobre autores

I. Sturova

Lavrentyev Institute of Hydrodynamics of the Siberian Branch of the Russian Academy of Sciences

Autor responsável pela correspondência
Email: sturova@hydro.nsc.ru
Rússia, Novosibirsk

Bibliografia

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2. Fig. 1. Flow diagram in an undisturbed state: a – two–layer liquid; b - single-layer liquid.

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3. Fig. 2. Areas of unstable values of wave numbers depending on the velocity of the shear flow V0: 1, 2 – cases 1 and 2.

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4. Fig. 3. Dispersion dependences (a, c) and group velocities (b, d): curves 1-3 correspond to the mode number for case 1 (a, b) and case 2 (c, d). Curves 4 show the dispersion dependence and group velocity of a single wave mode in the considered cases for a two-layer liquid under pressure a solid lid.

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5. Fig. 4. Elevations of the free surface (a, b) and the interface of the layers (c–e) at t = 12 c for case 1 (a, c, e) and case 2 (b, d, e) in the presence of a free surface (a–d) and a solid cover (e, e). Vertical arrows indicate the positions of the wavefronts for different modes.

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6. Fig. 5. Dispersion dependences (a) and group velocities (b): 1 – n = 1 and n = 3 for a two–layer liquid in case 1; 2 and 3 - modes n = 1 and n = 2 for a single-layer liquid in cases 3 and 4, respectively.

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7. Fig. 6. Vertical displacements of the free surface (a, c, e, w) and on the horizon y = - H1 (b, d, e, h) at t = 12 c for a single-layer liquid, cases 3-6, respectively. Vertical arrows indicate the positions of the wavefronts for various models.

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