Possible management of near shore nonlinear surging waves through bottom boundary conditions

Abstract

Instead of taking the usual passive view for warning of near shore surging waves including extreme waves like tsunamis, we aim to study the possibility of intervening and controlling nonlinear surface waves through the feedback boundary effect at the bottom. It has been shown through analytic result that the controlled leakage at the bottom may regulate the surface solitary wave amplitude opposing the hazardous variable depth effect. The theoretical results are applied to a real coastal bathymetry in India.

Free surface lump wave dynamics of a saturated superfluid 4 He film with nontrivial boundary condition at the substrate surface

“…As the simplest case we consider f = constant, which means there is a constant downward superfluid velocity at the bottom surface. For unforced KP-I equation (when f=0), the 3D plot of the lump solution (27) in the X−Y plane at a given time is shown in figure 2. We can see that the lump wave decreases rapidly as  ¥ X Y , showing it's localized nature.…”

“…The standard trivial bottom boundary condition is used in the derivation of long wave, small amplitude nonlinear integrable equations like KdV, KP equations etc in hydrodynamic systems. In [26,27], such bottom boundary condition is changed to include a weak leakage effect in order to study the solitary wave dynamics. In this work, we consider a very weak yet finite downward localized superfluid flow into the substrate.…”

Free surface lump wave dynamics of a saturated superfluid Helium film with nontrivial boundary condition at the substrate surface

“…Again in the same procedure we can get V 2 (X, Y, T ) in the next order as V 2 = 1 2 V 0XX . Thus we now have the solution of the forced KP-I equation (20) as…”

“…We consider, (20) is to be solved with the initial condition U (X, Y, 0, 0) = g(X, Y ). In [33], authors have discussed in detail how the initial conditions and the forcing function must be related.…”

“…In shallow water long wave systems in (1+1) dimensions, we have considered such nontrivial bottom boundary conditions in [19,20]. Phase and amplitude modifications of solitary waves in such cases as the solutions of perturbed KdV equation has been obtained analytically.…”