Eruption of a boundary layer induced by a 2D vortex patch

Abstract

The boundary-layer eruption phenomenon caused by a 2D patch of vorticity above a wall was investigated. It is shown that the eruption phenomenon depends on the viscosity (or Reynolds number, Re) of the fluid. There exists a threshold value of Re above which the eruption takes place. The initiation of the eruption goes through the creation of a small recirculation zone near the solid wall, the appearance of the saddle point on streamlines inside it and the tearing off process of the recirculation zone. Further increase of the Reynolds number causes a more complex flow. One can observe that eruption is regenerative and that the vortex patch can produce a cascade of secondary vortices. The vortex-in-cell method was employed to investigate the eruption phenomenon.

Codimension three bifurcation of streamline patterns close to a no-slip wall: A topological description of boundary layer eruption

“…It does not erupt but merges with the separation zone which subsequently disappears in a few bifurcations. For higher values of Re these secondary topological changes may lead to eruption [2] and generate more complex streamline patterns which are outside the scope of the present study.…”

“…From numerical computations Kudela & Malecha [1,2] have identified various changes in the topology of the streamlines during the eruption process, when described in a coordinate system fixed to the wall. The configuration is shown in Fig.…”

“…The flow equations are solved by a well-established finite-element code using GLL quadrature and Lagrange polynomials [43,44,45]. Standard domain and resolution studies were performed to ensure the reliability of predictions, and very good agreement with the results by Kudela & Malecha [2] is obtained. For more details on the computational aspects, see [46].…”

“…For a sufficiently high Reynolds number vorticity from the boundary layer is ejected into the surrounding fluid, resulting in secondary vortex structures. This phenomenon has been denoted eruption of the boundary layer [1,2], unsteady separation [3,4] or bursting [5], and it occurs for a wide range of Reynolds numbers [6,7]. The interaction between concentrated vorticity in a fluid and the vorticity created at a no-slip wall occurs in many important settings.…”

“…Our starting point is the analysis by Kudela & Malecha [1,2] who showed numerically how the streamline pattern changes through several stages as a vortex erupts from the boundary layer. We will provide further numerical simulations to understand the process in more detail, and also provide a theoretical framework to establish the possible topological changes in the streamline pattern as time and Reynolds number varies.…”