TY - JOUR

T1 - Strongly chaotic non-newtonian mantle convection

AU - Malevsky, A. V.

AU - Yuen, David A

PY - 1992/7

Y1 - 1992/7

N2 - We have studied the problem of strongly timedependent, twodimensional, 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 at each time step for solving the nonlinear momentum equation. Bicubic splines are used for the spatial discretization. The transition from mildly timedependent 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.

AB - We have studied the problem of strongly timedependent, twodimensional, 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 at each time step for solving the nonlinear momentum equation. Bicubic splines are used for the spatial discretization. The transition from mildly timedependent 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.

KW - Nonlinear rheology

KW - hard turbulence, mantle convection

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U2 - 10.1080/03091929208225244

DO - 10.1080/03091929208225244

M3 - Article

AN - SCOPUS:84963450642

VL - 65

SP - 149

EP - 171

JO - Geophysical and Astrophysical Fluid Dynamics

JF - Geophysical and Astrophysical Fluid Dynamics

SN - 0309-1929

IS - 1-4

ER -