Bistability of Slow and Fast Traveling Waves in Fluid Mixtures

Abstract

The appearence of a new type of fast nonlinear traveling wave states in binary fluid convection with increasing Soret effect is elucidated and the parameter range of their bistability with the common slower ones is evaluated numerically. The bifurcation behavior and the significantly different spatiotemporal properties of the different wave states -e.g. frequency, flow structure, and concentration distribution -are determined and related to each other and to a convenient measure of their nonlinearity. This allows to derive a limit for the applicability of small amplitude expansions. Additionally an universal scaling behavior of frequencies and mixing properties is found. 47.10.+g, 47.20.Ky In binary fluid mixtures heated from below there is an interesting feed-back loop between the fields of concentration, velocity, and temperature: The buoyancy force that drives the convective flow is changed by concentration variations. They in turn are produced via the Soret effect [1,2] by temperature gradients, i.e., via thermodiffusion and reduced by dissipative concentration diffusion and by mixing through the convective flow. This coupling chain causes a surprising richness of spatiotemporal pattern formation [3] even close to the onset of convection. In particular there are convective structures [2-15] consisting of coupled traveling waves (TWs) of velocity, temperature, and concentration with significantly different shapes [14,15]. Since nonlinear concentration advection is typically much larger than linear diffusion -the ratio of these two transport rates can easily be above 1000 -it is not surprising that these TW states are typically strongly nonlinear.In this letter we elucidate how with increasing Soret coupling there appear two different bistable TWs -one about twice as fast as the other -which both stably coexist with the stable quiescent conductive state. The convective amplitude of the fast (slow) TW is small (large) while the amplitude of its concentration contrast is large (small). The fast stable TWs have so far remained unnoticed in experiments [4][5][6][7][8][9][10][11][12][13] and numerical simulations [14,15]. They develop with increasing Soret coupling via a saddle node bifurcation out of a dent in the subcritically bifurcating unstable TW branch. They are most easily accessible via a two-loop hysteresis at larger but experimentally realizable Soret effects. Furthermore, we discovered an universal scaling behavior of TW frequencies and mixing properties. And we found that the ratio of flow and phase velocity is a relevant parameter and a convenient measure of their nonlinearity that allows to determine where an amplitude expansion around the onset breaks down.To investigate roll like convection structures in a horizontal layer of, say, ethanol-water with Lewis number L = 0.01 and Prandtl number σ = 10 we determine the convective solutions that bifurcate with a lateral periodicity length λ = 2 out of the quiescent heat conducting state [16]. A finite difference method [17] as well as a many mode Gal...