Simulation of the Flow Velocity Field on the Free Surface of a Stratified Fluid

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Abstract

The paper considers the problem of simulation of the velocity field on the free surface of an ideal stratified fluid generated by internal gravitational waves that reached the surface. The buoyancy frequency may vary with depth. The computer program has been written that allows calculating all components of the velocity field on the surface. It is shown that the calculation results for the vertical velocity component are consistent with the known asymptotics obtained in the far-field approximation for the cases of uniform and rectilinear motion of a point mass source horizontally (by B. Voisin) or at a fixed angle to the horizon (by M.M. Scase and S.B. Dalziel) in a uniformly stratified fluid.

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About the authors

D. Yu. Knyazkov

Ishlinsky Institute for Problems in Mechanics of the RAS

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Email: knyaz@ipmnet.ru
Russian Federation, Moscow

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Supplementary files

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2. Fig. 1. The area of Ω

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3. Fig. 2. Scheme for calculating the asymptotics of the velocity field during horizontal motion of a mass source from [13]

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4. Fig. 3. Simulation of horizontal motion in an ideal uniformly stratified fluid, N = 0.8. The velocity of motion V = 1 m/s, the vertical component of the velocity of the fluid vz (x, 1, z) is shown in the vertical section y = 1. Travel time T = 125 s for (a). The numerical solution (a) and the analytical approximation (b) are shown

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5. Fig. 4. Scheme for calculating the asymptotics of the velocity field when a mass source is moving at an angle to the horizon from [14]

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6. Fig. 5. Simulation of the propagation of internal waves from a mass source that moves uniformly and rectilinearly at a fixed angle γ = 30° to the horizon, N = 0.8. The velocity of motion V = 1 m/s, the vertical component of the velocity of the liquid vz (x, 1, z) is shown in the vertical section y = 1. Travel time T = 139.3 s. The numerical solution (a) and the analytical approximation (b) are shown

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7. Fig. 6. The magnitude of the vertical velocity component vz on the free surface (a) and in the liquid column (b) at time t = 175 s

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8. Fig. 7. The flow field (vx, vy) on the free surface z = H at time t = 175 s: the x-component (a) and the y-component (b) are shown

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