Large-amplitude internal solitary waves and intrusive currents in a pycnocline: A computational study

Large-amplitude internal solitary waves and intrusive currents, generated by the collapse of a mixed fluid region in a stratified pycnocline, are studied numerically. The main method of analysis is based on direct numerical simulation of the incompressible Navier-Stokes equations in the Boussinesq approximation.; The internal structure of large-amplitude mass-transporting solitary waves, propagating along the pycnocline in a deep channel in two dimensions, is visualized using a particle tracking technique. For larger wave amplitudes and Reynolds numbers an entrainment pattern develops, which is shown to be associated with the overturning of isopycnals at the bulge boundary and the generation of negative vorticity inside. The results illustrate that large-amplitude collapse-generated solitary waves are not vortex-pairs. The results also suggest that there is no clear boundary between mass-transporting solitary waves and intrusive gravity currents.; The dependence of the wavespeed and wavelength on wave amplitude is measured in numerical experiments for a wide range of amplitudes and compared to laboratory data and analytical theories. A good agreement with the experimental data is obtained. For very large wave amplitudes the curves for wavespeed and wavelength tend to approach the asymptotic two-fluid self-similar solution's behaviour.; Numerical experiments on the head-on collision of solitary waves are performed. Computed results show that large-amplitude mass-transporting waves are not solitons in the classical sense, since they are changed after collision. The negative phase shift after the collision is accurately measured.; An alternative numerical approach, based on finding inviscid steady-state solutions of Long's equation, is used to supplement the results of direct numerical simulations and to clarify the range of applicability of the equation. The wave attenuation with time can also be calculated from inviscid steady-state solutions under certain assumptions. The amplitude attenuation is found to be exponential for small-amplitude waves and linear for large-amplitude waves.; In addition, numerical experiments on the collapse of an axisymmetric mixed region are presented. The baroclinic vorticity generation and the strain-induced intensification of vorticity result in the formation of a cylindrical solitary wave and a toroidal vortex coupled together for some period of time. The spreading vortex can 'engulf' some fluid from outside and transport it. A theoretical analysis of the vortex decay is performed based on the published results for simpler relevant problems and the resulting estimates are shown to be in a good overall agreement with the present simulations.