Wave scattering by narrow cracks in ice sheets floating on water of finite
depth.
D.V. Evans & R. Porter (submitted to J. Fluid Mech.)
An explicit solution is provided for the scattering of an
obliquely-incident flexural-gravity wave by a narrow straight-line crack
separating two semi-infinite thin elastic plates floating on water of
finite depth. By first separating the solution into the sum of symmetric
and anti-symmetric parts it is shown that a simple form for each part can
be derived in terms of a rapidly-convergent infinite series multiplied
by a fundamental constant of the problem. This constant is itself
simply determined by applying an appropriate edge condition. Curves of
reflection and transmission coefficients are presented showing how they
vary with plate properties and angle of incidence. It is also shown that
in the absence of incident waves and for certain relations between their
wavelength and frequency, symmetric edge waves exist which travel along
the crack and decay in a direction normal to the crack.
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