2:30 PM - 2:45 PM
[MIS12-04] Variation of structures of thermal convection in a fluid with temperature- and stress-dependent viscosity
Keywords:Mantle convection, Convective patterns, Stress hysterisis, Nusselt number, Scaling relations, Plate motion
Thermal convection of highly viscous fluid applying various degree of mantle properties has been investigated in order to understand variety of structures of mantle convection and plate motions in the Earth and planets. Models with temperature-dependent viscosity have been studied as the most fundamental model of mantle convection. Solomatov (1995) derived scaling relations of the Nusselt number with respect to the strength of the temperature-dependence and classified the convective solutions into three regimes. When the temperature-dependence is weak, there emerges almost vertically symmetric convective flow similar to that with constant viscosity (SVC regime). As the temperature-dependence is strengthened, the upper boundary layer becomes thicker and the flow in it becomes weaker due to high viscosity near the top boundary (TR regime). When the temperature-dependence is further strengthened, the upper boundary layer becomes stagnant enough to restrict the convective region beneath it, where convective flow appears similar to that of SVC regime (ST regime).
In recent years, more realistic convection models have been proposed by including weakening effects of viscosity due to large stress, which represent the deformation of broken plates at the subducting area (e.g., Ogawa, 2003; Foley and Bercovici, 2014; Fuchs, 2019). Especially, Ogawa (2003) proposed a stress-history-dependent viscosity model. He classified the numerical solutions with a degree of plate-like motion of the convective solutions estimated by the distribution of the upper surface velocity, and theoretically predicted the parameter space where the solutions with the plate-like motion emerge. However, classification of their solutions into the traditional convective regimes based on the scaling relations of the Nusselt number has not been performed. It is not clear how the convective structures of SVC, TR and ST regimes are modified when the stress-dependent viscosity is introduced.
Therefore, we classify the solutions of the thermal convection model with temperature- and stress-dependent viscosity proposed by Ogawa (2003) with the scaling relations of the Nusselt number. Numerical time integrations of thermal convection in two-dimensional channel domain with the aspect ratio of four are performed for various strength of temperature- and stress-dependence, until a steady solution is obtained for each case. The Rayleigh number is 106 and the Prandtl number is assumed to be infinite. The scaling relations of the Nusselt number for the case without stress dependence are used to specify the convective regimes of the solutions. The results show that some convective solutions of TR regime in the case without stress-dependence are found to become SVC regime solutions when stress-dependent viscosity is applied. Such regime transition from TR to SVC is caused by weakening of viscosity due to the large stress near the upper boundary, resulting in decrease of the effective viscosity contrast of the system. The decrease of viscosity is observed at the large-stress areas of the subducting regions in our numerical solutions.
In recent years, more realistic convection models have been proposed by including weakening effects of viscosity due to large stress, which represent the deformation of broken plates at the subducting area (e.g., Ogawa, 2003; Foley and Bercovici, 2014; Fuchs, 2019). Especially, Ogawa (2003) proposed a stress-history-dependent viscosity model. He classified the numerical solutions with a degree of plate-like motion of the convective solutions estimated by the distribution of the upper surface velocity, and theoretically predicted the parameter space where the solutions with the plate-like motion emerge. However, classification of their solutions into the traditional convective regimes based on the scaling relations of the Nusselt number has not been performed. It is not clear how the convective structures of SVC, TR and ST regimes are modified when the stress-dependent viscosity is introduced.
Therefore, we classify the solutions of the thermal convection model with temperature- and stress-dependent viscosity proposed by Ogawa (2003) with the scaling relations of the Nusselt number. Numerical time integrations of thermal convection in two-dimensional channel domain with the aspect ratio of four are performed for various strength of temperature- and stress-dependence, until a steady solution is obtained for each case. The Rayleigh number is 106 and the Prandtl number is assumed to be infinite. The scaling relations of the Nusselt number for the case without stress dependence are used to specify the convective regimes of the solutions. The results show that some convective solutions of TR regime in the case without stress-dependence are found to become SVC regime solutions when stress-dependent viscosity is applied. Such regime transition from TR to SVC is caused by weakening of viscosity due to the large stress near the upper boundary, resulting in decrease of the effective viscosity contrast of the system. The decrease of viscosity is observed at the large-stress areas of the subducting regions in our numerical solutions.