Transversal convection patterns in horizontal shear flow

Abstract

We investigate the influence of a horizontal plane Poiseuille shear flow transversal to the convective roll chain of the Rayleigh-Benard problem. Using a one-dimensional (1D) amplitude equation and a 2D numerical simulation of the basic field equations, we study how different boundary conditions at the inlet and outlet of the channel affect nonlinear convection. If convection is suppressed near the cell apertures, spatially localized traveling-wave states appear with a uniquely selected bulk wavelength. For convectively unstable parameters this pattern is pushed out of the channel; however, the system becomes very sensitive to perturbations, and noise-driven structures occur. Phase-pinning boundary conditions lead for very small flows to stationary roll patterns with a space-dependent wavelength decreasing downstream. Strengthening the throughflow causes local Eckhaus instabilities, which finally generate a transition to propagating rolls.PACS number(s): 47.20. 8p, 47.20.Ky, 47.60.+i

Pattern selection in the absolutely unstable regime as a nonlinear eigenvalue problem: Taylor vortices in axial flow

“…All coefficients of the GLE have been calculated [27] as functions of Re for several radius ratios η. As a consequence of the system's invariance under the combined symmetry operation {z → −z, Re → −Re} the coefficients τ 0 , ξ 2 0 , γ are even in Re while the group velocity v g and the imaginary parts c 0 , c 1 , c 2 are odd in Re [15,27].…”

“…This multiplicity of solutions of the underlying nonlinear partial differential equations that stably coexist for a fixed configuration of parameters and boundary conditions seems to disappear in an open-flow system: Recent numerical simulations of Rayleigh-Bénard convective rolls traveling downstream in an imposed horizontal Poiseuille flow showed [14][15][16] that their structure is uniquely selected -i. e. it is independent of parameter history, initial conditions, and system size -in the absolutely unstable regime. This is the parameter regime of an open-flow system in which the secondary pattern starting, e. g., from a spatially localized perturbation can grow in upstream as well as in downstream direction [17].…”

Steep nonlinear global modes in spatially developing media

“…The results compare satisfactorily with numerical simulations and experiments for Taylor-Couette flow 12 and Rayleigh-Bénard convection with throughflow. 13,10 Surprisingly, fully nonlinear soft global modes of the CGL equation varying smoothly over a doubly infinite domain have been shown, 14 by application of Wentzel-Kramers-Brillouin-Jeffreys ͑WKBJ͒ theory, to satisfy a nonlinear saddle point criterion which is formally analogous to its linear counterpart. Here we show the existence of a second class of nonlinear spatially extended states in doubly infinite domains: steep global modes with a sharp front.…”

Harmonic mechanical excitations of steady convective instabilities: A means to get more uniform heat transfers in mixed convection flows?

“…In the present DOE, the factor ε is preferred to Ra because it is well known that the main characteristics of the thermoconvective patterns in natural and mixed convection are related to ε (see [1,8,16,29] for instance in mixed convection flows). The Reynolds number range, 100≤Re≤300, was chosen, on the one hand, to avoid to be too close to the critical threshold between the longitudinal and wavy rolls at Re*≈70±30 and, on the other hand, to avoid too long wavy roll growth length, L g , beyond Re>300, since L g increases a lot when Re increases [10].…”

“…Finally the excitation magnitude range, 0.41≤A exc ≤2, corresponds to a maximum spanwise displacement of the inlet agitator that varies between 0.82H and 4H and it covers a part of the range of excitation magnitudes used in the experiments (0.14≤A exc ≤1). In the DOE, the considered factor is not A exc but Log(A exc ) because it was shown in [10,29] that the growth length of the wavy and transversal rolls in the PRB flows linearly decreases as a function of Log(A exc ).…”