The interaction of oblique flexural gravity waves with a small bottom deformation on a porous ocean-bed: Green’s function approach

Wave resonances and hydroelastic wave motion

“…The convergence of the integrals in equations (3.34) and (3.35) are evident from the compact support nature of B(x). The above-mentioned expressions for reflection and transmission coefficients with U = 0 exactly match with Mohapatra [21]. To study Bragg resonance, the shape function of the form of sinusoidal ripples on the porous seabed is considered and is given by…”

“…The convergence of the integrals in equations (3.34) and (3.35) are evident from the compact support nature of Bfalse(xfalse). The above-mentioned expressions for reflection and transmission coefficients with U=0 exactly match with Mohapatra [21]. To study Bragg resonance, the shape function of the form of sinusoidal ripples on the porous seabed is considered and is given by Bfalse(xfalse)={asin⁡false(pxfalse),if b1≤x≤b2;0,otherwise;with b1=−n0kwπ, b2=m0kwπ, kw=1/p, false(m0+n0false)/2 is the number of ripples, a and p are respectively, the amplitude and wavenumber of the sinusoidal ripple.…”

“…and .32) where Ω z = (Dk 4 + 1)F(k, z ) and Ω 2 3 = (Dk 4 + 1)((k 2 tanh kh − Gk)/(k − G tanh kh)). Using the above derived Green function, the contour integration technique and Green's identity in the fluid region [21], the first order velocity potential is derived as…”

“…The occurrence of the Bragg resonance is proved for the incident wave with a wavelength approximately equal to twice the integral multiple of the bottom wavelength [18]. Bragg resonance is also shown for the wave scattering problem due to the small undulated bottom [19], porous undulated bottom [20,21] and undulated bottom in the presence of floating elastic plates [22].…”