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Modelling the flow in a thin accretion disc like a dynamical system, we analyse the nature of the critical points of the steady solutions of the flow. For the simple inviscid disc there are two critical points, with the outer one being a…
The analysis performed as well as extensive numerical simulations have revealed the possibility of the generation of homoclinic orbits as a result of homoclinic bifurcation in a porous pellet. A method has been proposed for the development…
Combining local bifurcation analysis with numerical continuation and bifurcation methods we study bifurcations from cylindrical vesicles described by the Helfrich equation with volume and area constraints, with a prescribed periodicity…
We analyze stationary accretion of selfgravitating gas onto a compact center within general-relativistic radiation hydrodynamics. Spherical symmetry and thin gas approximation are assumed. Numerical investigation shows that transonic flows…
We examine a model system where attractors may consist of a heteroclinic cycle between chaotic sets; this `cycling chaos' manifests itself as trajectories that spend increasingly long periods lingering near chaotic invariant sets…
The large Reynolds number asymptotic approximation of the neutral curve of Taylor-Couette flow subject to axial uniform magnetic field is analysed. The flow has been extensively studied since early 90's as the magneto-rotational instability…
We consider a test problem for Navier-Stokes solvers based on the flow around a cylinder that exhibits chaotic behavior, to examine the behavior of various numerical methods. We choose a range of Reynolds numbers for which the flow is…
We focus on reducing the computational costs associated with the hydrodynamic stability of solutions of the incompressible Navier-Stokes equations for a Newtonian and viscous fluid in contraction-expansion channels. In particular, we are…
We perform large eddy simulations of flow past a circular cylinder for the Reynolds number ($Re$) range, $2\times 10^3 \leq Re \leq 4\times10^5$, spanning subcritical, critical and supercritical regimes. We investigate the spanwise…
Plasma balls and rings emerge as fluid holographic duals of black holes and black rings in the hydrodynamic/gravity correspondence for the Scherk-Schwarz AdS system. Recently, plasma balls spinning above a critical rotation were found to be…
We analyse numerically the linear stability of a liquid metal flow in a rectangular duct with perfectly electrically conducting walls subject to a uniform transverse magnetic field. A non-standard three dimensional vector stream…
The dynamics of a model, originally proposed for a type of instability in plastic flow, has been investigated in detail. The bifurcation portrait of the system in two physically relevant parameters exhibits a rich variety of dynamical…
A dynamical system description of the transition process in shear flows with no linear instability starts with a knowledge of exact coherent solutions, among them travelling waves (TWs) and relative periodic orbits (RPOs). We describe a…
We present numerical simulations of vortices that appear via primary bifurcations out of the unstructured circular Couette flow in the Taylor-Couette system with counter-rotating as well as with co-rotating cylinders. The full, time…
Cavity flow problems in two dimensions, as well as in the axially symmetric three-dimensional case, have been extensively studied in the literature from a qualitative perspective. While numerous results exist concerning minimizers or stable…
It is well established that the onset of spatially periodic vortex states in the Taylor-Couette flow between rotating cylinders occurs at the value of Reynold's number predicted by local bifurcation theory. However, the symmetry breaking…
Experimental measurements and numerical simulations are made on fluid flow through cross-slot devices with a range of aspect (depth:width) ratios, 0.4 < alpha < 3.87. For low Reynolds numbers Re, the flow is symmetric and a sharp boundary…
A unique pattern selection in the absolutely unstable regime of a driven, nonlinear, open-flow system is analyzed: The spatiotemporal structures of rotationally symmetric vortices that propagate downstream in the annulus of the rotating…
In this paper, we construct growing modes of the linearized Navier-Stokes equations about generic stationary shear flows of the boundary layer type in a regime of sufficiently large Reynolds number: $R \to \infty$. Notably, the shear…
In this study, we numerically investigate hysteretic behaviors of secondary bifurcations in the Taylor-Couette flow of a semidilute, neutrally buoyant, and noncolloidal suspension. We consider a suspension with a bulk particle volume…