Influence of ice compression on components of the velocity of motion of liquid under the ice cover in a traveling periodic flexural gravity wave of finite amplitude

The equations describing parametric instabilities of a finite-amplitude internal gravity wave in an inviscid Boussinesq fluid are studied numerically. By improving the numerical approach, discarding the concept of spurious roots and considering the whole range of directions of the Floquet vector, Mied's work is generalized to its full complexity. In the limit of large disturbance wavenumbers, the unstable disturbances propagate in the directions of the two infinite curve segments of the related resonant-interaction diagram. They can therefore be classified into two families which are characterized by special propagation directions. At high wavenumbers the maximum growth rates converge to limits which do not depend on the direction of the Floquet vector. The limits are different for both families; the disturbance waves propagating at the smaller angle to the basic gravity wave grow at the larger rate.

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A transit through the trapping and blocking of flexural-gravity wave: Impact of two-dimensional current and in-plane compression

Physics of Fluids ◽

10.1063/5.0066115 ◽

2021 ◽

Vol 33 (11) ◽

pp. 116603

Author(s):

S. Das ◽

S. Saha

Keyword(s):

Gravity Wave ◽

Two Dimensional ◽

Wave Impact ◽

Plane Compression ◽

Flexural Gravity Wave

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Velocities of motion of liquid particles under the floating ice cover in the case of propagation of periodic waves of finite amplitude

Physical Oceanography ◽

10.1007/s11110-011-9100-z ◽

2011 ◽

Vol 21 (1) ◽

pp. 13-22 ◽

Cited By ~ 1

Author(s):

Ant. A. Bukatov ◽

And. A. Bukatov

Keyword(s):

Ice Cover ◽

Finite Amplitude ◽

Periodic Waves

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Flexural gravity wave motion over poroelastic bed

Wave Motion ◽

10.1016/j.wavemoti.2016.02.002 ◽

2016 ◽

Vol 63 ◽

pp. 135-148 ◽

Cited By ~ 7

Author(s):

S. Das ◽

H. Behera ◽

T. Sahoo

Keyword(s):

Gravity Wave ◽

Wave Motion ◽

Flexural Gravity Wave

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Flexural Gravity Wave Scattering Due to Variations in Bottom Topography

Volume 4: Ocean Engineering; Ocean Renewable Energy; Ocean Space Utilization, Parts A and B ◽

10.1115/omae2009-79191 ◽

2009 ◽

Author(s):

D. Karmakar ◽

J. Bhattacharjee ◽

T. Sahoo

Keyword(s):

Gravity Wave ◽

Water Waves ◽

Wave Scattering ◽

Bottom Topography ◽

Single Step ◽

Energy Relation ◽

Wide Spacing ◽

Expansion Formulae ◽

Flexural Gravity Wave ◽

Multiple Step

Oblique flexural gravity wave scattering due to abrupt change in bottom topography is investigated under the assumption of linearized theory of water waves. The problem is studied first for single step in case of finite water depth whose solution is obtained based on the expansion formulae for flexural gravity wavemaker problem and corresponding orthogonal mode-coupling relation. The results for the multiple step topography are obtained from the result of single step using the method of wide-spacing approximation. Energy relation for oblique flexural gravity wave scattering due to change in bottom topography is used to check the accuracy of the computation. Using shallow water approximation the wave scattering due to multiple step topography is derived considering the continuity of mass and energy flux. In this case also the result for single step topography is obtained and then using the wide-spacing approximation the result for multiple steps are derived. Numerical results for reflection and transmission coefficients and deflection of ice sheet are obtained to analyze the effect of multiple step topography on the propagation of flexural gravity waves.

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