Inertial Benard-Marangoni convection

被引:31
作者
Boeck, T
Thess, A
机构
[1] Center for Physical Fluid Dynamics, Department of Mechanical Engineering, Dresden University of Technology
关键词
D O I
10.1017/S0022112097006782
中图分类号
O3 [力学];
学科分类号
08 ; 0801 ;
摘要
Two-dimensional surface-tension-driven Benard convection in a layer with a free-slip bottom is investigated in the limit of small Prandtl number using accurate numerical simulations with a pseudospectral method complemented by linear stability analysis and a perturbation method. It is found that the system attains a steady state consisting of counter-rotating convection rolls. Upon increasing the Marangoni number Ma the system experiences a transition between two typical convective regimes. The first one is the regime of weak convection characterized by only slight deviations of the isotherms from the linear conductive temperature profile. In contrast, the second regime, called inertial convection, shows significantly deformed isotherms. The transition between the two regimes becomes increasingly sharp as the Prandtl number is reduced. For sufficiently small Prandtl number the transition from weak to inertial convection proceeds via a subcritical bifurcation involving weak hysteresis. In the viscous zero-Prandtl-number limit the transition manifests itself in an unbounded growth of the flow amplitude for Marangoni numbers beyond a critical value Ma(i). For Ma < Ma(i) the zero-Prandtl-number equations provide a reasonable approximation for weak convection at small but finite Prandtl number. The possibility of experimental verification of inertial Benard-Marangoni convection is briefly discussed.
引用
收藏
页码:149 / 175
页数:27
相关论文
共 39 条
[11]   TRANSITION TO TIME-DEPENDENT CONVECTION [J].
CLEVER, RM ;
BUSSE, FH .
JOURNAL OF FLUID MECHANICS, 1974, 65 (OCT2) :625-645
[12]   MAGNETIC DAMPING OF JETS AND VORTICES [J].
DAVIDSON, PA .
JOURNAL OF FLUID MECHANICS, 1995, 299 :153-186
[13]   THERMOCAPILLARY INSTABILITIES [J].
DAVIS, SH .
ANNUAL REVIEW OF FLUID MECHANICS, 1987, 19 :403-435
[14]  
Frisch U., 1995, TURBULENCE, DOI [10.1017/CBO9781139170666, DOI 10.1017/CBO9781139170666]
[15]   AN EXPERIMENTAL-STUDY OF RAYLEIGH-BENARD CONVECTION IN LIQUID-TIN [J].
GINDE, RM ;
GILL, WN ;
VERHOEVEN, JD .
CHEMICAL ENGINEERING COMMUNICATIONS, 1989, 82 :223-228
[16]  
GOTTLIEB D, 1977, CBMS REGIONAL C SERI
[17]   AXISYMMETRIC CONVECTION IN A CYLINDER [J].
JONES, CA ;
MOORE, DR ;
WEISS, NO .
JOURNAL OF FLUID MECHANICS, 1976, 73 (JAN27) :353-388
[18]   OSCILLATIONS IN THERMOCAPILLARY CONVECTION IN A SQUARE CAVITY [J].
KANOUFF, M ;
GREIF, R .
INTERNATIONAL JOURNAL OF HEAT AND MASS TRANSFER, 1994, 37 (06) :885-892
[19]  
Landau L. D., 2013, Fluid Mechanics: Course of Theoretical Physics, V6
[20]   HYDRODYNAMICAL INSTABILITIES OF THERMOCAPILLARY FLOW IN A HALF-ZONE [J].
LEVENSTAM, M ;
AMBERG, G .
JOURNAL OF FLUID MECHANICS, 1995, 297 :357-372