Pattern Formation in Binary Fluid Convection and in Systems with Throughflow

Lücke, M.; Barten, W.; Büchel, P.; Fütterer, Claus; Hollinger, St.; Jung, Ch.

doi:10.1007/3-540-49537-1_3

Cited by 37 publications

(40 citation statements)

References 158 publications

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“…It should be noted that the solution belonging to the upper part of the TW branch is highly nonlinear and that, even though the temperature and velocity ÿelds are nearly harmonic in the x-direction, the horizontal concentration proÿle has a trapezoidal shape [21,22]. As a consequence, a high spatial resolution is required to resolve the narrow concentration boundary layers of these solutions.…”

Section: Description and Comparison Of The Different Methodsmentioning

confidence: 99%

“…For the parameters chosen in this paper, if we use the Rayleigh number as a bifurcation parameter, the TW branch typically bifurcates subcritically (see Figure 1), acquiring stability at a secondary saddle-node bifurcation. When the Rayleigh number is increased from the saddle-node point, the TW branch disappears in a parity-breaking bifurcation of steady solutions, usually called SOC states (stationary overturning convection), to which stability is transferred [21]. The standing waves are unstable from the onset and usually disappear in a global bifurcation in which the SW solution connects with an unstable SOC state.…”

Section: The Test Problemmentioning

confidence: 99%

“…At R c the phase velocity is c = 2:337 and at R * goes to zero, as corresponds to the parity-breaking bifurcation of the SOC states that takes place there. The structure of the TW, which is shown in Figure 2, and of the SOC states has been discussed extensively in References [21,22].…”

Section: The Test Problemmentioning

confidence: 99%

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Continuation of travelling-wave solutions of the Navier–Stokes equations

Mercader

Batiste

Alonso

2006

Int. J. Numer. Meth. Fluids

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SUMMARYAn e cient way of obtaining travelling waves in a periodic uid system is described and tested. We search for steady states in a reference frame travelling at the wave phase velocity using a ÿrst-order pseudospectral semi-implicit time scheme adapted to carry out the Newton's iterations. The method is compared to a standard Newton-Raphson solver and is shown to be highly e cient in performing this task, even when high-resolution grids are used. This method is well suited to three-dimensional calculations in cylindrical or spherical geometries.

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Section: Description and Comparison Of The Different Methodsmentioning

confidence: 99%

Section: The Test Problemmentioning

confidence: 99%

See 1 more Smart Citation

Continuation of travelling-wave solutions of the Navier–Stokes equations

Mercader

Batiste

Alonso

2006

Int. J. Numer. Meth. Fluids

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“…Eventually, at ψ ≃ −0.07 a regime is reached where stable LTWs coexist near onset with extended TWs [4,7,24,25,26,27,28]. Increasing the Soret coupling strength further to more negative ψ the band (r LT W min , r LT W max ) of Rayleigh numbers in which stable LTWs exist increases monotonically while shifting upwards as a whole -r LT W max (ψ) grows stronger than r LT W min (ψ).…”

Section: Localized Traveling Wavesmentioning

confidence: 99%

“…LTWs consist of slowly drifting, spatially confined convective regions that are embedded in the quiescent fluid. These intriguing structures have been investigated in experiments [4,5,7,10,18,27,28,29,30,31,32,33,34] and numerical simulations [14,24,26,35]. A discussion of various theoretical models aiming at their explanation is contained in Sec.…”

Section: Localized Traveling Wavesmentioning

confidence: 99%

Traveling wave fronts and localized traveling wave convection in binary fluid mixtures

Jung

Lücke

2005

Phys. Rev. E

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Nonlinear fronts between spatially extended traveling wave convection (TW) and quiescent fluid and spatially localized traveling waves (LTWs) are investigated in quantitative detail in the bistable regime of binary fluid mixtures heated from below. A finite-difference method is used to solve the full hydrodynamic field equations in a vertical cross section of the layer perpendicular to the convection roll axes. Results are presented for ethanol-water parameters with several strongly negative separation ratios where TW solutions bifurcate subcritically. Fronts and LTWs are compared with each other and similarities and differences are elucidated. Phase propagation out of the quiescent fluid into the convective structure entails a unique selection of the latter while fronts and interfaces where the phase moves into the quiescent state behave differently. Interpretations of various experimental observations are suggested.

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Convective Patterns in Binary Fluid Mixtures with Positive Separation Ratios

Huke

Lücke

2002

Thermal Nonequilibrium Phenomena in Fluid Mixtures

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Abstract. We summarize our findings about laterally periodic convection structures in binary mixtures in the Rayleigh-Bénard system for positive Soret effect. Stationary roll, square, and crossroll solutions and their stability are determined with a multimode Galerkin expansion. The oscillatory competition of squares and rolls in the form of crossroll oscillations is reviewed. They undergo a subharmonic bifurcation cascade where the oscillation period grows in integer steps as a consequence of an entrainment process.

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Pattern Formation in Binary Fluid Convection and in Systems with Throughflow

Cited by 37 publications

References 158 publications

Continuation of travelling-wave solutions of the Navier–Stokes equations

Continuation of travelling-wave solutions of the Navier–Stokes equations

Traveling wave fronts and localized traveling wave convection in binary fluid mixtures

Convective Patterns in Binary Fluid Mixtures with Positive Separation Ratios

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