Propagation of solitary waves in curved shallow water channels
of constant depth
and width is investigated by carrying out numerical simulations based on
the
generalized weakly nonlinear and weakly dispersive Boussinesq model. The
objective is to
investigate the effects of channel width and bending sharpness on the transmission
and reflection of long waves propagating through significantly curved channels.
Our
numerical results show that, when travelling through narrow channel bends
including
both smooth and sharp-cornered 90°-bends, a solitary wave is transmitted
almost
completely with little reflection and scattering. For wide channel bends,
we find that,
if the bend is rounded and smooth, a solitary wave is still fully transmitted
with little
backward reflection, but the transmitted wave will no longer preserve the
shape of
the original solitary wave but will disintegrate into several smaller waves.
For solitary
waves travelling through wide sharp-cornered 90°-bends, wave reflection
is seen to
be very significant, and the wider the channel bend, the stronger the reflected
wave
amplitude. Our numerical results for waves in sharp-cornered 90°-bends
revealed a
similarity relationship which indicates that the ratios of the transmitted
and reflected
wave amplitude, excess mass and energy to the original wave amplitude,
mass and
energy all depend on one single dimensionless parameter, namely the ratio
of the
channel width b to the effective wavelength λe.
Quantitative results for predicting wave transmission and reflection based
on
b/λe are presented.