Boundary layer theory modified for analysis of wave flow on the surface of a viscous liquid finite-thickness layer resting on a hard bottom |
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Authors: | A I Grigor’ev D M Pozharitsky and S O Shiryaeva |
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Institution: | 1.Demidov State University,Yaroslavl,Russia |
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Abstract: | The theory of a boundary layer that is adjacent to the surface of an indefinitely deep viscous liquid and caused by its periodic
motion is modified for analysis of finite-amplitude flow motion on the charged surface of a viscous conductive finite-thickness
liquid layer resting on a hard bottom (the thickness of the layer is comparable to the wavelength). With the aim of adequately
describing the viscous liquid flow, two boundary layers are considered: one at the free surface and the other at the hard
bottom. The thicknesses of the boundary layers are estimated for which the difference between an exact solution and a solution
to a model problem (stated in terms of the modified theory) may be set with a desired accuracy in the low-viscosity approximation.
It is shown that the presence of the lower (bottom) boundary layer should be taken into account (with a relative computational
error no more than 0.001) only if the thickness of the viscous layer does not exceed two wavelengths. For thicker layers,
the bottom flow may be considered potential. In shallow liquids (with a thickness of two tenths of the wavelength or less),
the upper (near-surface) and bottom layers overlap and the eddy flow entirely occupies the liquid volume. As the surface charge
approaches a value that is critical for the onset of instability against the electric field negative pressure, the thicknesses
of both layers sharply grow. |
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