New Flow Regimes Generated by Mode Coupling in Buoyant-Thermocapillary Convection

Abstract

We report on a new nonlinear dynamics occurring in a confined cylindrical column filled with fluid (liquid bridge) and heated from above. We demonstrate and analyze the novel oscillatory flow state created by the interaction of two hydrothermal waves of different origins: one propagates vertically from the cold towards the hot side (m ¼ 0) and another is traveling in the azimuthal direction (m ¼ 1). Their interaction leads to an exotic flow structure: during a part of the oscillation period the resulting wave propagates in a given azimuthal direction, whereas during the rest of the period it moves in the opposite direction. A new bimodal flow regime is found to exist over a parameter range where these modes have comparable influence. The phase diagrams, obtained by three-dimensional nonlinear simulations, are reported. They shed light on the instability mechanism and criteria of the existence of novel states. DOI: 10.1103/PhysRevLett.102.134503 PACS numbers: 47.20.Ky, 05.45.Àa, 47.54.Bd, 47.55.nk The investigation of the Rayleigh-Bénard and RayleighMarangoni convection has played a crucial role in the development of the nonlinear stability theory for planar spatially extended systems [1]. Recently, significant progress has been achieved in understanding the nonlinear regimes of buoyant-thermocapillary convection in cylindrical columns [2,3]. The latter problem can be considered as a paradigmatic example of nonlinear dynamics in essentially nonparallel flows. The mechanisms of instability have a universal character. Therefore, it is of a general interest, far beyond its direct applications in engineering. Because of the periodicity of the problem in the azimuthal direction, the spectrum of azimuthal wave numbers is discrete. The hydrothermal waves, which are developed due to the oscillatory instability of a steady axisymmetric flow, are characterized by integer values of the azimuthal wave number m. Typically, above the critical point, a 3D oscillatory flow starts as a finite-amplitude standing or traveling (TW) wave. When the thermal stresses increase, the nonlinear dynamics is determined mostly by the interaction of modes with m ¼ 1 and m ¼ 2, e.g., [2,3].Still, the role of the simplest, axisymmetric oscillatory mode m ¼ 0, is somehow elusive, and there is no agreement on that subject up to now. Xu and Davis However, these measurements were performed above the threshold of the 3D oscillatory regime, where modes with m ! 1 are present. Numerical simulations for aspect ratio close to unity À $ 1 also could not reveal the m ¼ 0 as being critical, e.g., [2,9,10]. In short liquid bridges the rigid walls impose a strong constraint to the appearance and spreading of axial waves.In the present Letter, we clarify the question of the existence of axisymmetric wavy motions, and analyze the consequences of the interaction between the modes with m ¼ 0 and m ¼ 1 that leads to novel, highly nontrivial, flow regimes. Our analysis also explains the enigmatic flow regime with alternating directions of hot or cold spot's moti...

Assessment of the role of axial vorticity in the formation of particle accumulation structures in supercritical Marangoni and hybrid thermocapillary-rotation-driven flows

“…It is the almost two-dimensional nature of the hydrothermal traveling wave (the wave properties depend significantly on the radial and azimuthal coordinates, but, unless very special conditions are established 4 , the component propagating along the axial direction is rather weak, see, e.g, the review of literature in 2,4 ).…”

“…In such a context, much attention has been devoted over recent years to the so-called It is such a line of research which led to identify for supercritical (oscillatory) Marangoni flow two distinct attractors in the phase space, which are today known more or less universally as "pulsating" and "traveling" regimes, the former being featured by the periodic growth and decay of disturbances at fixed positions in space, the latter by the propagation of such disturbances along a preferred direction, see, e.g., Lappa 2 (the reader being also referred to Shevtsova et al 4 for additional exotic attractors due to the combined action of Marangoni and buoyancy forces).…”

On the onset of multi-wave patterns in laterally heated floating zones for slightly supercritical conditions

“…Most surprisingly, although slightly supercritical conditions had been considered, the dominant modal structures was found to be a peculiar combination of disturbances with different azimuthal wavenumbers m = 1, 2, and 3 (a superposition of distinct waves with different spatial modes). In a rather unexpected way, these modal structures were observed to have the characteristics of a standing or a travelling wave, changing from one to another irregularly with the resulting dominant modal structures not depending on the aspect ratio (another important distinguishing feature with respect to earlier studies dealing with the classical liquid-bridge problem [1][2][3][4][5][6]35 ).…”

“…The amount of existing literature on such subjects is really impressive (especially if one considers what has been done for the so-called half-zone liquid bridge, a popular simplified model of the FZ process, Refs [1][2][3][4][5][6] and references therein). Here, due to page limits we limit ourselves to recalling the points still requiring attention, and recent (still unexplained) findings.…”

The Stability of a Thermocapillary-Buoyant Flow in a Liquid Bridge with Heat Transfer Through the Interface

“…Indeed, data obtained for Bi < 0:5 indicate a competition between m ¼ 0 and m ¼ 1 modes near the onset of instability. The interplay of the modes and the related dynamical processes for the adiabatic-interface case were reported in [29,38,39].…”