Nonlinear stability analysis of the Bénard problem for fluids with a convex nonincreasing temperature depending viscosity

A nonlinear energy stability analysis of the onset of convection for fluids with viscosity convex nonincreasing function of temperature, is performed. It is shown that condition assuring linear stability, assures nonlinear (conditional) asymptotic stability too.

[1]  G. Schubert,et al.  Numerical simulations of three-dimensional thermal convection in a fluid with strongly temperature-dependent viscosity , 1991, Journal of Fluid Mechanics.

[2]  Brian Straughan,et al.  The Energy Method, Stability, and Nonlinear Convection , 1991 .

[3]  F. Capone,et al.  Nonlinear stability analysis of convection for fluids with exponentially temperature-dependent viscosity , 1994 .

[4]  B. Straughan,et al.  A nonlinear energy stability analysis of convection with temperature dependent viscosity , 1993 .

[5]  Friedrich H. Busse,et al.  The stability of finite amplitude cellular convection and its relation to an extremum principle , 1967, Journal of Fluid Mechanics.

[6]  S. Rosenblat.  Review: Daniel D. Joseph, Stability of fluid motions. I, II , 1978 .

[7]  S. Rionero.  Metodi variazionali per la stabilità asintotica in media in magnetoidrodinamica , 1968 .

[8]  S. Chandrasekhar.  Hydrodynamic and Hydromagnetic Stability , 1961 .

[9]  Dean S. Oliver,et al.  Onset of convection in a variable-viscosity fluid , 1982, Journal of Fluid Mechanics.

[10]  Kenneth E. Torrance,et al.  Thermal convection with large viscosity variations , 1971, Journal of Fluid Mechanics.

[11]  D. White,et al.  The planforms and onset of convection with a temperature-dependent viscosity , 1988, Journal of Fluid Mechanics.

[12]  G. Mulone,et al.  A non-linear stability analysis of the magnetic Bénard problem through the Lyapunov direct method , 1988 .

[13]  F. Richter,et al.  Heat transfer and horizontally averaged temperature of convection with large viscosity variations , 1983, Journal of Fluid Mechanics.

[14]  G. Galdi,et al.  Weighted energy methods in elastostatics on unbounded domains , 1985 .

[15]  Giovanni P. Galdi,et al.  Weighted Energy Methods in Fluid Dynamics and Elasticity , 1985 .

[16]  A. Davaille,et al.  Transient high-Rayleigh-number thermal convection with large viscosity variations , 1993, Journal of Fluid Mechanics.

[17]  D. Jenkins.  Rolls versus squares in thermal convection of fluids with temperature-dependent viscosity , 1987, Journal of Fluid Mechanics.

[18]  E. Palm.  On the tendency towards hexagonal cells in steady convection , 1960, Journal of Fluid Mechanics.

[19]  J. Booker.  Thermal convection with strongly temperature-dependent viscosity , 1976, Journal of Fluid Mechanics.