Incomplete Similarity of Internal Solitary Waves with Trapped Core

Thursday, 18 December 2014
Volodymyr Maderych1, Kyung Tae Jung2, Katheryna Terletska3, Igor Brovchenko3 and Tatyana Talipova4, (1)National Academy of Sciences of Ukraine, Kiev, Ukraine, (2)KIOST Korea Institute of Ocean Science and Technology, Ansan, South Korea, (3)Institute of Mathematical Machine and Systems Problems NASU, Kiev, Ukraine, (4)Institute of Applied Physics RAS, Nizhny Novgorod, Russia
The dynamics and internal structure of internal solitary waves with trapped core propagating in a thin pycnocline near the bottom or surface for a wide range of wave amplitude and stratification are studied numerically in the frame of the Navier-Stokes equations for the laboratory and ocean scales. It is shown that the most important characteristics of the dynamics of waves are the local Froude number Frm, calculated as the ratio of the maximum local velocity to the phase velocity of the waves, the minimum Richardson number Rimin and the effective Reynolds number Reeff , defined as the ratio the product of the phase velocity c of the waves and the wave amplitude a to the kinematic viscosity. Depending on the parameter values Frm and Rimin three main classes of ISW propagating in the pycnocline layer over or under homogeneous deep layer can be identified: (i) the weakly nonlinear waves at Rimin >1, Frm < 1; (ii) the stable strongly nonlinear waves with trapped cores at Rimin 0.15 and Frm ~1.2; and (iii) the unstable strongly nonlinear waves at Rimin <0.1 and Frm ~ 1.25. On the whole, the results of experiments and numerical simulations showed complete similarity in all range of the phase velocity and wavelength at large Reeff . The experimental and computed dependence of horizontal size of the trapped core on the height of the trapped core also demonstrate self-similarity of the trapped core shape. However, incomplete similarity of Rimin is found when dependence on viscosity remains at large Reeff which implies the viscosity effect on the stability of ISW. This dependence is approximated by power law Rimin~(a / h)-1.19 Reeff -1.19. With time a wave damping occurs, thus Rimin is growing following this self-similar dependence.