Formation of waves, vortices and ligaments in 2D stratified flows around obstacles

Abstract

Wave and vortex fine structure of unsteady stratified flows were studied numerically based on the system of fundamental equations for non-homogeneous incompressible fluid with no-slip and no-flux boundary conditions, and experimentally using high-resolution Schlieren visualization techniques. Different flow regimes, including creeping, wave and vortex ones, which are widespread in the ocean and atmosphere, were investigated in the single problem formulation, starting from the slowest diffusion-induced flows up to the fastest and unsteady ones. A classification of flow components is proposed, which contains waves, vortices, and ligaments, which manifest themselves in the form of extended interfaces with their transverse scales being determined by the dissipative properties of a fluid and the flow dynamics. Due to interrupting the molecular flux of a stratifying agent on a motionless obstacle, fine structural diffusion-induced flows are formed around the obstacle in the form of a multilevel set of vortex cells which are transformed near the edges into horizontally extended streaky structures. A moving body in a stratified fluid produces upstream disturbances, groups of attached internal waves, leading-edge vortices, and a vortex street in the wake, which coexist in the stratified flow as an organic whole and are separated with ligaments. In the unsteady vortex flow regime, the shape of the bluff body essentially affects the flow structure, determining whether it will consist of a quasi-steady chain of vortices with a quite regular vortex shedding structure, or leading-edge vortices and vortex street would evolve into a much more complex and multi-scale vortex evolution. The numerical and experimental visualizations of diffusion-induced flows, internal waves, vortex streets, and fine structural ligaments, are in a qualitative agreement with each other.