On the Onset of Rayleigh-Bénard Convection in a Fluid Layer of Slowly Increasing Depth

DOI10.1002/sapm1982673199zbMath0506.76044OpenAlexW2555719866MaRDI QIDQ4743929

I. C. Walton

Publication date: 1982

Published in: Studies in Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1002/sapm1982673199

zbMATH Keywords

weakly nonlinearonset of convectionsecond Painleve transcendentlayer of fluidlocal Rayleigh number close to criticalstronger nonlinear motions

Mathematics Subject Classification ID

Nonlinear effects in hydrodynamic stability (76E30) Boundary-layer theory, separation and reattachment, higher-order effects (76D10) Free convection (76R10) Parallel shear flows in hydrodynamic stability (76E05) Forced convection (76R05)

Related Items

The effect of a shear flow on convection in a layer heated non-uniformly from below, Free convection in an undulating saturated porous layer: resonant wavelength excitation, Rayleigh–Bénard convection with a melting boundary, Wavenumber selection in ramped Rayleigh–Bénard convection, Implicit time splitting for fourth-order parabolic equations, Preferred pattern of convection in a porous layer with a spatially non-uniform boundary temperature, The onset of cellular convection in a shallow two-dimensional container of fluid heated non-uniformly from below, Spanwise pairing of finite-amplitude longitudinal vortex rolls in inclined free-convection boundary layers, Numerical scheme for solving the nonuniformly forced cubic and quintic Swift-Hohenberg equations strictly respecting the Lyapunov functional, Stripe patterns orientation resulting from nonuniform forcings and other competitive effects in the Swift-Hohenberg dynamics, The nonlinear non-parallel wave instability of boundary-layer flow induced by a horizontal heated surface in porous media, Transverse-roll global modes in a Rayleigh-Bénard-Poiseuille system with streamwise variable heating

Cites Work

• A Benard convection problem with a perturbed lower wall
• THE EFFECTS OF SLOW SPATIAL VARIATIONS ON BÉNARD CONVECTION
• The effect of distant sidewalls on the transition to finite amplitude Benard convection
• The smooth transition to a convective régime in a two-dimensional box
• The similarity solution for the Korteweg-de Vries equation and the related Painlevé transcendent
• On the second Painlevé transcendent
• Thermal convection with spatially periodic boundary conditions: resonant wavelength excitation
• Transition Solutions for Axisymmetric Shell Vibrations
• Non-local effects in the stability of flow between eccentric rotating cylinders
• Nonlinear Stability Theory
• Unnamed Item