Estimation of energy loss of internal solitary waves over an isolated obstacle

Simulations of internal solitary waves (ISW) of the first mode over the isolated obstacles of various shapes:  triangles, semicircle and rectangles of different lengths are presented.  The influence of height, length and shape of the obstacle on the transformation of ISW and energy dissipation was investigated. A two-layer free surface water system with upper and bottom layer thicknesses h₁ and h₂ and densities ρ₁ and ρ₂, respectively, and water depth H was considered.  It was carried out set of 42 numerical experiments with both ISW of elevation and depression types. The results of simulation were compared with the results of laboratory experiments. It is shown that the blocking parameter B  [1] (that is a dimensionless parameter equal to the ratio of the lower layer above the obstacle to the wave amplitude) is useful for describing the type of interaction and estimation of energy loss.  The transformation of large amplitude ISW over a triangular obstacle differs from the corresponding interaction with the semicircle obstacle. Internal boluses formed in the case of semicircle or rectangle obstacle are 1.5 - 2 times larger than in the case of a triangular obstacle. As a result, energy dissipation and corresponding mixing in the case of ISW transformation over semicircle and a rectangular obstacle is greater than in the case of a triangular ones. Maximum energy losses can reach 42% in the case of a rectangular obstacle. Energy losses increase with increasing length of the obstacle. Thus, we can conclude that topographic effects, namely the influence of shape and geometric characteristics of underwater obstacles have a significant impact on the dissipation of mechanical energy. 

 

[1]  T. Talipova , K. Terletska, V. Maderich, I. Brovchenko, K. T. Jung, E. Pelinovsky and R. Grimshaw  Internal solitary wave transformation over the bottom step: loss of energy. // Phys. Fluids, 2013, 25, 032110