Under-ice seiches |
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| Authors: | V N Zyryanov |
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| Institution: | 1.Water Problems Institute,Russian Academy of Sciences,Moscow,Russia |
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| Abstract: | A closed, ice-covered water body containing water with homogeneous density distribution is considered. No-slip conditions
are specified for flow velocity at the lower ice boundary and on the bed. Two variants of boundary conditions are considered
on the side boundary: the boundary is either a solid vertical wall with a finite liquid depth or the liquid wedges out to
zero depth values. Ice either is attached fast to the shore or is separated from it by an open-water zone. A basic fourth
order equation is derived for the amplitude of ice oscillations. The introduction of friction results in the appearance of
reduced depth. Eigenvalue problem is considered for evaluating seiche periods. For the case when the liquid wedges out at
the shore, the basic equation becomes singular at water body boundaries. A lake with a longitudinal depth profile, which can
be approximated by a parabola, is considered. The solution is found by the method of matched asymptotic expansions. In the
inner domain, beyond the boundary layers, the equation is reduced to Legendre equation, which yields a new relationship for
the spectrum of seiche oscillations both in the presence of ice and in an open lake with varying depth. Boundary layers appear
at the margins of the lake, where the liquid wedges out; a solution is found for these layers. |
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