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- W955781220 abstract "Investigation of small normal oscillations of viscous incompressible liquid partially filling a vessel is connected with construction of solutions for a spectral boundary problem of the form 1 $$begin{array}{*{20}{c}} { - frac{1}{H}nabla V + nabla p = lambda V, div V = 0 in Omega , V = 0 on S, mathop{smallint }limits_{sum } h dS = 0,} {{{V}_{z}} = - lambda h,frac{{partial V}}{{partial z}} + frac{{partial {{V}_{z}}}}{{partial x}} = 0,frac{{partial {{V}_{y}}}}{{partial z}} + frac{{partial {{V}_{z}}}}{{partial y}} = frac{2}{H}frac{{partial {{V}_{z}}}}{{partial z}} - p + h = 0 on sum ,} end{array} $$ where Ω is the domain filled with liquid, S is the solid wall of the container, Σ is the non-perturbed free surface of the liquid, V(x,y,z) is a velocity vector for particles of the liquid, p(x,y,z) is pressure inside of the liquid, h(x, y) is deviation with respect to the vertical of the free surface of the liquid, λ is the frequency parameter, $$H = {{g}^{{1/2}}}{{L}^{{3/2}}}{{v}^{{ - 1}}} $$ the Galilei number, g is the free fall acceleration, L is the characterictic length of the domain, v is the coefficient of kinematical viscosity, (x,y,z) is the Gartesian coordinate system, the z axis being directed upward vertically and Σ lying on the plane z = 0." @default.
- W955781220 created "2016-06-24" @default.
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- W955781220 date "1992-01-01" @default.
- W955781220 modified "2023-10-18" @default.
- W955781220 title "Approximate Method of Investigation of Normal Oscillations of Viscous Incompressible Liquid in Container" @default.
- W955781220 doi "https://doi.org/10.1007/978-3-0348-8627-7_8" @default.
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