Propagation of solitary waves in curved shallow water channels
of constant depth
and width is investigated by carrying out numerical simulations based on
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.
numerical results show that, when travelling through narrow channel bends
both smooth and sharp-cornered 90°-bends, a solitary wave is transmitted
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
backward reflection, but the transmitted wave will no longer preserve the
the original solitary wave but will disintegrate into several smaller waves.
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
amplitude. Our numerical results for waves in sharp-cornered 90°-bends
similarity relationship which indicates that the ratios of the transmitted
wave amplitude, excess mass and energy to the original wave amplitude,
energy all depend on one single dimensionless parameter, namely the ratio
channel width b to the effective wavelength λe.
Quantitative results for predicting wave transmission and reflection based
b/λe are presented.