Weakly nonlinear mode interactions in spherical Rayleigh–Bénard convection

Resonant mode interactions in Rayleigh-Bénard convection

In systems with midplane reflection symmetry the dominant spatial resonance is the 1:3 resonance. Numerical continuation is used to study this and other 1:2k11 resonances in two-dimensional convection between no-slip perfectly conducting horizontal plates. Periodic boundary conditions are imposed in the horizontal. These resonances influence the process of wave number selection at moderate Rayl...

A weakly nonlinear mechanism for mode selection in swirling jets

XXI ICTAM, 15–21 August 2004, Warsaw, Poland NONLINEAR CONVECTIVE PATTERNS IN SPHERICAL RAYLEIGH-BÉNARD SYSTEMS

Nonlinear thermal convection in a spherical fluid layer in the presence of spherically symmetric gravity, spherical RayleighBénard convection, is investigated. At the onset of spherical Rayleigh-Bénard convection, there exists the (2l+1)-fold degeneracy of the linear solution, where l is the degree of a spherical harmonics. Nonlinear convection is studied through fully three-dimensional numeric...

The 1: 2 Mode Interaction in Rayleigh-BéNard convection with Weakly Broken midplane Symmetry

The effects of weak breaking of the midplane reflection symmetry on the 1:2 steady state mode interaction in Rayleigh–Bénard convection are discussed in a PDE setting. Effects of this type arise from the inclusion of non-Boussinesq terms or due to small differences in the boundary conditions at the top and bottom of the convecting layer. The latter provides the simplest realization, and capture...

An Analytical Study of Weakly Nonlinear Convection in a Horizontal Mushy Layer

An Analytical Study of Weakly Nonlinear Convection in a Horizontal Mushy Layer Prof. Dr. P. K. Srimani R & D Director (DSI), Former Chairman, B.U. Bangalore, Karnataka, INDIA Mr. R. Parthasarathi Prof. and HOD, Dept. Mathematics, Jain University – CMS, Bangalore, Karnataka, INDIA _______________________________________________________________________________________ Abstract: The present analyt...