The interaction of steady-state and Hopf bifurcations in the presence of O(2) symmetry generically gives a secondary Hopf bifurcation to a family of 2-tori, from the primary rotating wave branch. We present explicit formulas for the coefficients which determine the direction of bifurcation and the stability of the 2-tori. These formulas show that the tori are determined by third-degree terms in...

Various experiments have outlined generic properties of the subcritical transition to turbulence in plane Couette flow. A low order model of a self-sustaining process has been derived by Waleffe [11] from the Navier-Stokes equations for a sinusoidal shear flow. This paper investigates the weakly non-linear properties and the phase space analysis of this model, including the dependence on the mo...

In this paper, the multi-step differential transform method (MDTM), one of the most effective method, is implemented to compute an approximate solution of the system of nonlinear differential equations governing the problem. It has been attempted to show the reliability and performance of the MDTM in comparison with the numerical method (fourth-order Runge–Kutta) and other analytical methods su...

The flow of a magnetic fluid placed inside a small gap between concentric rotating cylinders is investigated for axial, radial and azimuthal magnetic fields. An equation of motion is derived phenomenologically to describe the hydrodynamics of magnetic fluids. Studied are the changes in the critical Taylor number T~ and wave number kc which characterize the instability of primary circular Couett...

We present a finite-volume formulation for the lattice Boltzmann method (FVLBM) based on standard bilinear quadrilateral elements in two dimensions. The accuracy of this scheme is demonstrated by comparing the velocity field with the analytical solution of the Navier-Stokes equations for time dependent rotating Couette flow and Taylor vortex flow. To demonstrate the flexibility of the scheme, w...

Films and molds of nematic polymer materials are notorious for heterogeneity in the orientational distribution of the rigid rod or platelet macromolecules. Predictive tools for structure length scales generated by shear-dominated processing are vitally important: both during processing because of flow feedback phenomena such as shear thinning or thickening, and postprocessing since gradients in...