Convective, absolute, and global instabilities of thermocapillary-buoyancy convection in extended layers (original) (raw)
Related papers
Physics of Fluids, 2001
We report experiments on buoyant-thermocapillary instabilities in differentially heated liquid layers. The results are obtained for a fluid of Prandtl number 10 in a rectangular geometry with different aspect ratios. Depending on the height of liquid and on the aspect ratios, the two-dimensional basic flow destabilizes into oblique traveling waves or longitudinal stationary rolls, respectively, for small and large fluid heights. Temperature measurements and space-time recordings reveal the waves to correspond to the hydrothermal waves predicted by the linear stability analysis of Smith and Davis ͓J. Fluid Mech. 132, 119 ͑1983͔͒. Moreover, the transition between traveling and stationary modes agrees with the work by Mercier and Normand ͓Phys. Fluids 8, 1433 ͑1996͔͒ even if the exact characteristics of longitudinal rolls differ from theoretical predictions. A discussion about the relevant nondimensional parameters is included. In the stability domain of the waves, two types of sources have been evidenced. For larger heights, the source is a line and generally evolves towards one end of the container leaving a single wave whereas for smaller heights, the source looks like a point and emits a circular wave which becomes almost planar farther from the source in both directions.
Journal of Fluid Mechanics, 2006
The oscillatory convection for a real system of fluids under the joint action of buoyancy and thermocapillary effect is investigated. The nonlinear development of the oscillatory instability is studied. Two types of boundary condition are considered. In the case of periodic boundary conditions, regimes of either travelling waves or standing oscillations have been found, depending on the period of the flow. For rigid heat-insulated lateral walls, various types of symmetric and asymmetric standing waves are obtained. Transitions between the motions with different spatial structures are investigated. It is shown that in the case of rigid heat-insulated lateral walls the period of oscillations changes non-monotonically. The nonlinear oscillations exist in a finite interval of the Grashof number values, between the stability regions of a quiescent state and stationary convection.
Instabilities in a laterally heated liquid layer
Physics of Fluids, 2000
We study a convection problem in a free-surface container with lateral walls heated at different temperatures. The effects of buoyancy and thermocapillarity are taken into account. A basic convective state appears as soon as a temperature gradient with nonzero horizontal component is applied. This state bifurcates to new convective solutions for further values on the imposed temperature gradient. Our main contribution is to consider this situation in a container finite not only in the vertical coordinate, but also in the direction of the gradient. The third dimension is kept infinite. We determine the basic state, compare it with the usual one of parallel flow approach, and study its stability. When the lateral heating walls are considered new results are found. The boundary conditions on the top surface are no longer restricted to those that allow analytical solutions for the basic state, and we have considered for the heat interchange with the atmosphere the Newton law with constant ambient temperature. Due to this boundary condition, two control parameters related to the temperature field appear. One is the temperature difference between lateral walls as in previous research, and the new one is the temperature difference between the atmosphere and the cold wall. After a stationary bifurcation a three-dimensional structure which along the infinite direction consists of longitudinal rolls grows. On the vertical plane along the gradient direction this structure is nonhomogeneous but located near the hot side. These features coincide with observations of recent experiments.
Thermocapillary instability of a liquid layer under heat flux modulation
The parametric excitation of the Marangoni instability in a horizontal liquid layer is analyzed in the case of a heat flux periodically varying at the deformable interface. Two response modes of the convective system to an external periodic stimulation, synchronous and subharmonic ones, have been found. The cellular and long-wave instability thresholds are compared. The neutral stability curves are presented for a variety of external conditions. It is shown that contrary to the classical parametric resonance, the synchronous disturbances may become most dangerous for the stability of the base state, and the long-wave mode may cause the instability prior to the cellular mode within a definite range of parameters.
Physics of Fluids, 2011
The nonlinear development of oscillatory instability under the joint action of buoyant and thermocapillary effects in multilayer system is investigated. The nonlinear convective regimes are studied by the finite difference method. The calculations have been performed for two-dimensional flows. The interfaces are assumed to be nondeforming. Rigid heat-insulated lateral walls are considered. Transitions between the flows with different spatial structures are studied. Specific types of nonlinear flows-symmetric and asymmetric oscillations-have been found. It is shown that the oscillatory flow takes place in an interval of Grashof number values bounded both from below by the quiescent mechanical equilibrium, and from above by a convecting steady state. Cavities with different lengths are considered.
Instability of the buoyancy layer on an evenly heated vertical wall
Journal of Fluid Mechanics, 2007
The stability of the buoyancy layer on a uniformly heated vertical wall in a stratified fluid is investigated using both semi-analytical and direct numerical methods. As in the related problem in which the excess temperature of the wall is specified, the basic laminar flow is steady and one-dimensional. Here flows varying in time and with height are considered, the behaviour being determined by the fluid's Prandtl number and a Reynolds number proportional to the ratio of two temperature gradients: the horizontal one imposed at the wall and the vertical one existing in the far field. For low Reynolds numbers, the flow is stable with variation only in the wall-normal direction. For Reynolds numbers greater than a critical value, depending on the Prandtl number, the flow is unstableand supports two-dimensional travelling waves. The critical Reynolds number and other properties have been obtained via linearized stability analysis and are shown to accuratelypredict the behaviour of t...
The origin of instability in enclosed horizontally driven convection
We demonstrate that instability in enclosed horizontally driven convection is due to a convective buoyancy-driven transverse-roll instability resembling the classical Rayleigh–Bénard convection in the thermal forcing boundary layer rather than a shear instability in the corresponding kinematic boundary layer. Instability growth is weakly sensitive to the local velocity profile, with velocity shear acting to select a transverse roll mode in preference to longitudinal rolls. The convectively unstable region grows from the hot end of the forcing boundary with increasing Rayleigh number two orders of magnitude lower than the natural onset of unstable horizontal convection. This analysis highlights the importance of the thermal boundary layer to the instability dynamics of horizontal convection, elucidating the path towards an understanding of turbulence and heat transport scaling in horizontal convection at oceanic Rayleigh numbers
Stability of double-diffusive natural convection in a vertical fluid layer
Physics of Fluids, 2021
The stability of basic buoyant flow in a vertical fluid layer induced by temperature and solute concentration differences between the vertical boundaries is investigated. The linear dynamics of the perturbed flow is formulated as an eigenvalue problem and solved numerically by employing the Chebyshev collocation method. The validity of Squire's theorem is proved, and therefore, two-dimensional motions are considered. The neutral stability curves defining the threshold of linear instability and the critical values of the thermal Grashof number and wave number at the onset of instability are determined for various values of the Prandtl number Pr, the solute Grashof number G S , and the Lewis number Le. The magnitude of the Prandtl number at which the transition from stationary to travelling-wave mode occurs can be either increased or decreased by tuning the values of G S and Le. For certain combinations of the parameters, there exist one or two closed disconnected travelling-wave neutral curves emphasizing the necessity of multiple thermal Grashof numbers to embark upon the stability of fluid flow, a result of contrast to that of the single-diffusive fluid layer. The mechanism of modal instability is deciphered by using the method of energy budget and four different modes of instability are identified, one of which is new and due entirely to the presence of solutal buoyancy.
arXiv (Cornell University), 2022
Effect of interfacial disturbances on instabilities of buoyant/thermocapillary convective flows in rectangular cavities is studied in a series of numerical experiments. The computations are carried out for several two-liquid two-layer systems taking into account properties of liquids used in previously published experiments. Relation between the interface deformations and the Boussinesq approximation is discussed. It is shown that in some systems, including the interface disturbances in the model can alter the critical temperature difference by approximately 10%, producing either destabilizing, or stabilizing effect. The interface oscillations appear as standing or travelling waves whose wavelength can vary from short wave lengths to a single wave occupying all the available space. Rough estimations show that in some liquid-liquid systems the interface oscillations amplitude can reach several tens of microns. Patterns of the most unstable disturbances are presented and discussed. It is argued that instabilities in some two layer systems develop similarly to the Holmboe instabilities in stratified mixing layers.
2022
Effect of interfacial disturbances on instabilities of buoyant/thermocapillary convective flows in rectangular cavities is studied in a series of numerical experiments. The computations are carried out for several two-liquid two-layer systems taking into account properties of liquids used in previously published experiments. Relation between the interface deformations and the Boussinesq approximation is discussed. It is shown that in some systems, including the interface disturbances in the model can alter the critical temperature difference by approximately 10%, producing either destabilizing, or stabilizing effect. The interface oscillations appear as standing or travelling waves whose wavelength can vary from short wave lengths to a single wave occupying all the available space. Rough estimations show that in some liquid-liquid systems the interface oscillations amplitude can reach several tens of microns. Patterns of the most unstable disturbances are presented and discussed. It...