Research Projects

The effect and importance of density stratifications (M-R. Alam, Y. Liu and D. K. P. Yue, J. Fluid Mech. (2009), Vol. 624, pp. 191-224) and non-uniform but periodic bottom profiles (Jie Yu and Louis N. Howard, J. Fluid Mech. (2012), vol. 712, pp. 451-470) has been analyzed by a few researchers. It is observed that in the water wave scattering problems, the effect of density contrast with non-uniform & non-periodic bottom profiles naturally arises (J. Yu and L. R. M. Maas, J. Fluid Mech. (2016), vol. 794, pp. 700-718). The wave blocking and negative energy waves (Das et al. (2018), Boral et al. (2022)) occur in the presence of opposing current. Although these scenarios are partially addressed, it is interesting to analyze the non-periodic and non-uniform bottom undulation in a multi-layer fluid system. Hence, the present proposal shall address the following: (i) the density constarts (unstable and stable fluid layers), (ii) non-periodic, arbitrary bottom profiles- in applications to model the situations like Tsunami and wave scattering near and far away from the bay area, (iii) Blocking dynamics, energy transfer and negative energy waves, (iv) time-domain simulations of viscous model in unstable stratification. The governing boundary value problem shall be solved: (a) by linearizing the equations, (b) weakly non-linear, and (c) full non-linear simulations using some analytical and semi-analytical techniques.