STRONGLY CHAOTIC NON-NEWTONIAN MANTLE CONVECTION

被引:33
作者
MALEVSKY, AV [1 ]
YUEN, DA [1 ]
机构
[1] UNIV MINNESOTA,DEPT GEOL & GEOPHYS,MINNEAPOLIS,MN 55455
关键词
NONLINEAR RHEOLOGY; HARD TURBULENCE; MANTLE CONVECTION;
D O I
10.1080/03091929208225244
中图分类号
P1 [天文学];
学科分类号
0704 ;
摘要
We have studied the problem of strongly time-dependent, two-dimensional, incompressible, infinite Prandtl number thermal convection in an aspect-ratio five box for a non-Newtonian power-law rheology and a heated from below configuration, as applied to mantle dynamics. The convection equations are solved by means of a characteristics-based method with a Lagrangian formulation of the total derivative in the energy equation. Iterations are required al each time step for solving the nonlinear momentum equation. Bicubic splines are used for the spatial discretization. The transition from mildly time-dependent to the strongly chaotic or turbulent regime, in which the plumes become disconnected, occurs at much lower Nusselt numbers (Nu), between 20 and 25, than for Newtonian rheology, The Nu versus Rayleigh number (Ra) relationship displays a kink at this transition. Rising non-Newtonian plumes exhibit much greater curvature in their ascent than Newtonian ones and are strongly attracted by descending currents at the top. The viscosity field becomes strongly mixed and assumes a granular character in the turbulent regime. Horizontal spectral decomposition of the viscosity field outside the boundary layer shows that in the chaotic regime the fluctuations about the mean viscosity do not vary by more than an order of magnitude for one and a half decade in horizontal wavenumber. Vorticity fields produced by non-Newtonian convection are much more intense than Newtonian. Increasing the power law index sharpens the chaotic behavior of the flow with high Ra.
引用
收藏
页码:149 / 171
页数:23
相关论文
共 19 条
[1]  
Ahlberg J. H., 1967, THEORY SPLINES THEIR
[2]  
[Anonymous], 1987, RHEOLOGY EARTH
[3]   POWER SPECTRA IN 2-DIMENSIONAL TURBULENCE [J].
BENZI, R ;
PALADIN, G ;
VULPIANI, A .
PHYSICAL REVIEW A, 1990, 42 (06) :3654-3656
[4]  
Chandrasekhar S., 1961, HYDRODYNAMIC HYDROMA
[5]   CONVECTION WITH PRESSURE-DEPENDENT AND TEMPERATURE-DEPENDENT NON-NEWTONIAN RHEOLOGY [J].
CHRISTENSEN, U .
GEOPHYSICAL JOURNAL OF THE ROYAL ASTRONOMICAL SOCIETY, 1984, 77 (02) :343-384
[6]   TIME-DEPENDENT CONVECTION WITH NON-NEWTONIAN VISCOSITY [J].
CHRISTENSEN, UR ;
YUEN, DA .
JOURNAL OF GEOPHYSICAL RESEARCH-SOLID EARTH AND PLANETS, 1989, 94 (B1) :814-820
[7]   TIME-DEPENDENT CONVECTION IN ELONGATED RAYLEIGH-BENARD CELLS [J].
CHRISTENSEN, UR .
GEOPHYSICAL RESEARCH LETTERS, 1987, 14 (03) :220-223
[8]  
CUVELIER C, 1988, FINITE ELEMENTS NAVI
[9]   LABORATORY STUDY OF DISLOCATION CLIMB AND DIFFUSION IN OLIVINE [J].
GOETZE, C ;
KOHLSTEDT, DL .
JOURNAL OF GEOPHYSICAL RESEARCH, 1973, 78 (26) :5961-5971
[10]   TRANSITION TO HARD TURBULENCE IN THERMAL-CONVECTION AT INFINITE PRANDTL NUMBER [J].
HANSEN, U ;
YUEN, DA ;
KROENING, SE .
PHYSICS OF FLUIDS A-FLUID DYNAMICS, 1990, 2 (12) :2157-2163