Head-on collision of the second mode internal solitary waves

Abstract

Second mode internal waves are widespread in offshore areas, and they frequently follow the first mode internalwaves on the oceanic shelf. Large amplitude internal solitary waves (ISW) of second mode containing trappedcores associated with closed streamlines can also transport plankton and nutrients. An interaction of ISWs withtrapped cores takes place in a specific manner. It motivated us to carry out a computational study of head-oncollision of ISWs of second mode propagating in a laboratory-scale numerical tank using the nonhydrostatic 3Dnumerical model based on the Navier-Stokes equations for a continuously stratified fluid.Three main classes of ISW of second mode propagating in the pycnocline layer of thickness h between homogeneousdeep layers can be identified: (i) the weakly nonlinear waves (ii) the stable strongly nonlinearwaves with trapped cores and (iii) the shear unstable strongly nonlinear waves (Maderich et al., 2015). Fourinteraction regimes for symmetric collision were separated from simulation results using this classification:(A) an almost elastic interaction of the weakly nonlinear waves (B) a non-elastic interaction of waves withtrapped cores when ISW amplitudes were close to critical non-dimensional amplitude a/h (C) an almost elasticinteraction of stable strongly nonlinear waves with trapped cores (D) non-elastic interaction of the unstablestrongly nonlinear waves.ith closed streamlines can also transport plankton and nutrients. An interaction of ISWs withtrapped cores takes place in a specific manner. It motivated us to carry out a computational study of head-oncollision of ISWs of second mode propagating in a laboratory-scale numerical tank using the nonhydrostatic 3Dnumerical model based on the Navier-Stokes equations for a continuously stratified fluid.Three main classes of ISW of second mode propagating in the pycnocline layer of thickness h between homogeneousdeep layers can be identified: (i) the weakly nonlinear waves (ii) the stable strongly nonlinearwaves with trapped cores and (iii) the shear unstable strongly nonlinear waves (Maderich et al., 2015). Fourinteraction regimes for symmetric collision were separated from simulation results using this classification:(A) an almost elastic interaction of the weakly nonlinear waves (B) a non-elastic interaction of waves withtrapped cores when ISW amplitudes were close to critical non-dimensional amplitude a/h (C) an almost elasticinteraction of stable strongly nonlinear waves with trapped cores (D) non-elastic interaction of the unstablestrongly nonlinear waves.