Speaker: Pierre-Yves Passaggia (UNC Chapel Hill)
Title : Nonlinear internal solitary waves and their stability in shallow and deep water
Abstract : The transfer of energy from large to small scales in density stratified flows such as the oceans, lakes and the atmosphere is known to be driven in large part by internal gravity waves. One particularly energetic type of internal wave is the Internal Solitary Wave (ISW). Near-surface ISWs of depression have been observed in the northern south china sea with amplitudes in excess of 240 meters in the deep ocean (Huang et al., Nature 2016), and equally notable, wave height five times larger than the pycnocline depth in coastal regions (Stanton & Ostrovsky, GRL, 1998). In this talk, recent experimental observations of nonlinear ISWs in deep water will be presented. In particular, evidence of nonlinear internal waves in the case of a continuous stratifications with thick interfaces in the deep regime will be presented. These experiments were performed in a wave tank in excess of 2 meters deep allowing for reaching large Reynolds number where viscous and surfactant effects at the surface become negligible. Combined measurements of velocity and density will be compared with solutions of the Dubreil-Jacotin-Long (DJL) equation and show excellent agreements. In the second part of the talk, the dynamics of perturbations to large-amplitude ISWs with thin interfaces and internal waves with trapped cores will be analyzed by means of optimal transient growth methods. Optimal perturbations are computed through direct-adjoint iterations of the Navier-Stokes equations linearized around inviscid, steady ISWs obtained from the (DJL) equation. The unstable dynamics are shown to be dominated by the transient growth of small-amplitude perturbations located upstream the ISW, in the pycnocline. An application to the field observation of Moum et al. (JPO, 2003) over the Oregon shelf shows excellent quantitative agreements for both the ISW and the perturbation dynamics. These results will finally be discussed in the case of internal waves with trapped cores where different dynamics arise.