Perpustakaan Digital ITB

We examine the waveforms of linear waves over a fully submerged, arbitrarily periodic bed, using the recent Floquet theory for gravity waves and extending it to the regime of capillary-gravity waves. The exact solutions illustrate the complex features of waveform geometry that are frequency dependent, including the modulation of propagating waveforms in space-time, spatially modulated standing waveforms, asymmetric waveforms over a symmetric bed profile, and high-curvature wave-crest forms. These features are in contrast to the trivial and invariant sinusoidal waveform of the ordinary linear waves on a flat bed, but reminiscent of nonlinear waveforms. The effect of surface tension is seen to counteract wave scattering by topography, tending to restore the waveform towards a symmetric and sinusoidal geometry. These features are the general characteristics of linear waves over a periodic bed since they are the properties of eigenmodes, and can inspire andguide applications.