Topological bifurcations in the evolution of coherent structures in a convection model

Abstract

Blob filaments are coherent structures in a turbulent plasma flow. Understanding the evolution of these structures is important to improve magnetic plasma confinement. Three state variables describe blob filaments in a plasma convection model. A dynamical systems approach analyzes the evolution of these three variables. A critical point of a variable defines a feature point for a region where that variable is significant. For a range of Rayleigh and Prandtl numbers, the bifurcations of the critical points of the three variables are investigated with time as the primary bifurcation parameter. Bifurcation curves separate the parameter planes into regions with different critical point configurations for the state variables. For Prandtl number equal to 1, the number of critical points of each state variable increases with increasing Rayleigh number. For Rayleigh number equal to 10 4 , the number of critical points is the greatest for Prandtl numbers of magnitude 10 0 .

On-wall and interior separation in a two-fluid boundary layer

“…This illustrates a homogeneous fluid flow with a double-vortex appearing on the zero streamline by virtue of a twin saddle-centre bifurcation (see, e.g. [26]). A similar sequence can also be expected in a two-fluid flow illustrated in Fig.…”

Shape curvature effects in viscous streaming

“…Since the two-dimensional streaming flow in our setting is time independent (streamlines ≡ pathlines) and incompressible (i.e. a streamfunction exists), our system can be equivalently represented as an autonomous Hamiltonian system with H ≡ Ψ , where H and Ψ correspond to the Hamiltonian and time-averaged streamfunction, respectively (Dam et al 2017). Due to the H ≡ Ψ equivalence, orbits of streaming fluid particles (iso-contours of Ψ ) can be interpreted as iso-contours of H, enabling us to describe the local flow topology using the scalar function H(x, y) alone (which is conserved along a streamline or fluid orbit).…”

Shape curvature effects in viscous streaming

“…The above characterization allows us to investigate flow topology transitions using bifurcation theory. Since the two dimensional streaming flow in our setting is time-independent (streamlines ≡ pathlines) and incompressible (i.e a streamfunction exists), our system can be equivalently represented as an autonomous Hamiltonian system with H ≡ Ψ, where H and Ψ correspond to the Hamiltonian and time-averaged streamfunction, respectively [44]. Due to the H ≡ Ψ equivalence, orbits of streaming fluid particles (iso-contours of Ψ) can be interpreted as iso-contours of H, enabling us to describe the local flow topology using the scalar function H(x, y) alone (which is conserved along a streamline or fluid orbit).…”