COMPARISON OF THE DYNAMIC AND PARAMETERIZED MODELS OF MANTLE CONVECTION INCLUDING CORE COOLING
COMPARISON OF THE DYNAMIC AND PARAMETERIZED MODELS OF MANTLE CONVECTION INCLUDING CORE COOLING
复制标题
包括地核冷却在内的地幔对流动态模型和参数化模型的比较
DOI：
10.1016/0012-821x(95)00241-4
复制
发表时间：
1996
影响因子：
5.3
通讯作者：
Y. Iwase
中科院分区：
文献类型：
--
作者：
S. Honda;Y. Iwase
研究了包括地核冷却在内的地幔对流二维冷却模型。假定堆芯温度在空间上是恒定的，但由于热量的对流回收，堆芯温度随时间而变化。粘度在空间中也是恒定的，但它是面积平均（平均）温度的函数，以便检查与温度相关的粘度对冷却的可能影响。冷却速率受三个因素控制：堆芯的温度变化受堆芯热流密度单位变化的影响；粘度定律，由平均温度决定；以及内部加热的贡献。采用几种不同类型的温度场作为初始条件。一些结果表明，时间瑞利数和努塞尔数之间的关系有相当大的波动，这是对上下热边界层都有适当定义的。假设瑞利数和努塞尔数之间的幂律关系，通过对动态计算结果的最小二乘拟合，计算了平均温度和底部温度冷却历史的参数化模型。对于参数化模型，我们进行了时间逆积分。除了冷却速率较大或内部加热衰减较小的情况外，动态计算与参数化计算之间的一致性一般较好。当冷却速率较大时，下热边界层消失。这导致了底部温度的不可预测性。然而，这种情况并不适用于地球。当内部加热衰减较小时，动态模型和参数化模型之间的一致性对参数化模型中假设的内部加热量的变化很敏感。这是因为内部热源直接影响冷却速度。β值为Nu-Ra关系的幂指数，变化范围为0.3 ~ 0.4。当底部热边界层变弱时，由于堆芯的快速冷却，β明显偏离0.3。
The two-dimensional cooling model of mantle convection, including core cooling was studied. The core temperature is assumed to be constant in space, but it changes with time because of the convective retrieval of heat. The viscosity is also constant in space but it is a function of the area-averaged (mean) temperature in order to check the possible effects of temperature-dependent viscosity on the cooling. The rate of cooling is controlled by three factors: the temperature change of the core by a unit change in the core heat flux; the viscosity law, governed by the mean temperature; and the contribution of the internal heating. Several different types of temperature field were used as the initial conditions. Some results showed considerable fluctuations in the relation between the temporal Rayleigh number and the Nusselt numbers, which are appropriately defined for both the upper and lower thermal boundary layers. A parameterized model of the cooling history of the mean and bottom temperatures was calculated assuming the power-law relation between the Rayleigh and the Nusselt numbers, which is determined by the least-square fit of the results of the dynamic calculations. For the parameterized models we integrated backward in time. The agreement between the dynamic and parameterized calculations is generally good, except for the cases when the rate of cooling is large or the decay in internal heating is small. When the rate of the cooling is large the lower thermal boundary layer disappears. This results in unpredictability of the bottom temperature. However, this case is not applicable for the Earth. When the decay in internal heating is small, we find that the agreement between the dynamic and parameterized models is sensitive to the change in the amount of internal heating assumed in parameterized models. This is because the internal heat source directly affects the rate of cooling. The β value, which is the power index of the Nu-Ra relation, varies from 0.3 to 0.4. When the bottom thermal boundary layer becomes weak, because of the fast cooling of the core, β deviates from 0.3 considerably.