Frequency Downshifting in Wave Spectra in Coastal Zone and Its Influence on Mudbank Formation

The evolution of wind waves in coastal zones leads to changes in the shape of the wave spectrum. Along the coast of Kerala, due to the presence of mudbanks during the southwest monsoon, we could observe downshifting of the peak frequency in the wave spectral data. The present study aims at proving the mechanism of frequency downshifting and possible influence of the downshifting process on mudbank formation. The results of SWASH (Simulating WAves till SHore) modeling and bispectral analysis shows that frequency downshifting occurs due to the difference nonlinear triad interactions of the main frequency peak of the wave spectrum with frequencies of the infragravity range independent of the viscosity of the medium. The increase in wave dissipation accelerates frequency downshifting additionally, decreasing the wave energy in the main peak frequency. It is shown that frequency downshifting can be one of the possible wave mechanisms of mudbank formation due to essentially different wave attenuation coefficients at the beginning and end of this process. For muddy cohesive sediments, it will lead to formation with an erosive profile at first and then an accumulative profile, i.e., mudbank formation.

Nonlinear evolution of the modulational instability under weak forcing and damping

The evolution of modulational instability, or Benjamin-Feir instability is investigated within the framework of the two-dimensional fully nonlinear potential equations, modified to include wind forcing and viscous dissipation. The wind model corresponds to the Miles' theory. The introduction of dissipation in the equations is briefly discussed. Evolution of this instability in the presence of damping was considered by Segur et al. (2005a) and Wu et al. (2006). Their results were extended theoretically by Kharif et al. (2010) who considered wind forcing and viscous dissipation within the framework of a forced and damped nonlinear Schrödinger equation. The marginal stability curve derived from the fully nonlinear numerical simulations coincides with the curve obtained by Kharif et al. (2010) from a linear stability analysis. Furthermore, it is found that the presence of wind forcing promotes the occurrence of a permanent frequency-downshifting without invoking damping due to breaking wave phenomenon.

Experimental evidence of stable wave patterns on deep water

Recent predictions from competing theoretical models have disagreed about the stability/instability of bi-periodic patterns of surface waves on deep water. We present laboratory experiments to address this controversy. Growth rates of modulational perturbations are compared to predictions from: (i) inviscid coupled nonlinear Schrödinger (NLS) equations, according to which the patterns are unstable and (ii) dissipative coupled NLS equations, according to which they are linearly stable. For bi-periodic wave patterns of small amplitude and nearly permanent form, we find that the dissipative model predicts the experimental observations more accurately. Hence, our experiments support the claim that these bi-periodic wave patterns are linearly stable in the presence of damping. For bi-periodic wave patterns of large enough amplitude or subject to large enough perturbations, both models fail to predict accurately the observed behaviour, which includes frequency downshifting.