Effects of strongly variable viscosity on three‐dimensional compressible convection in planetary mantles
Effects of strongly variable viscosity on three‐dimensional compressible convection in planetary mantles
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强变粘性对行星地幔三维可压缩对流的影响
DOI：
10.1029/95jb03211
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发表时间：
1996
影响因子：
--
通讯作者：
P. Tackley
中科院分区：
文献类型：
--
作者：
P. Tackley
利用有限体积多重网格代码，在笛卡尔几何中进行了数值模拟，系统地研究了温度依赖性黏度对三维可压缩地幔对流的影响，黏度变化系数为1000-2500，瑞利数范围为105-107，上下边界无应力。根据流变学、加热模式、可压缩性和边界条件的细节，发现模型行为存在相当大的差异。参数选择以真实的地球模型为指导。在Boussinesq，粘度完全取决于温度和无应力的基本加热情况，等温边界，非常长的波长流动（~ 25,000 km，假设深度与地幔厚度相对应）与冷羽流和热上升流片形成对比，与在小域中发现的上升流羽流和下升流片形成对比，说明了模拟宽域的重要性。深度依赖性的增加导致了小单元和平台的反转，造成了热羽流和冷板。温度依赖的粘度对流的平台主要是由于温度依赖引起的粘度的垂直变化。可压缩性与相关的深度依赖特性导致上升流羽流较宽，下升流片流较窄，且长径比较大。也许最大的调制效应发生在内部加热的可压缩情况下，在这种情况下，通常在恒定粘度计算中观察到的随时间变化的短波长冷羽流模式完全转变为具有随时间变化的羽流不稳定性的非常长的下沉片（间隔达24000公里）。这些结果特别有趣，因为通常认为地幔的基底热流非常低，例如占总热流的5-20%。粘滞耗散和绝热加热的影响在等粘滞情况下的总热收支中只起很小的作用，这一观察结果受瑞利数的影响不大。然而，当黏度与温度有关时，黏性耗散在刚性上边界层中变得很重要。这种效应是由在这个坚硬的盖子上发生的非常高的应力引起的，通常比这里模拟的粘度对比的区域内部的应力高2个数量级。对流电池内部温度对材料性能高度敏感，与温度相关的粘度和与深度相关的导热系数使内部温度升高，而与深度相关的粘度使内部温度降低。观测到的流动模式对这些不同复杂性的敏感性清楚地说明了进行可压缩、可变粘度的地幔对流计算的重要性，这些计算要尽可能地与地球的流变学和热力学性质相匹配。
A systematic investigation into the effects of temperature dependent viscosity on three-dimensional compressible mantle convection has been performed by means of numerical simulations in Cartesian geometry using a finite volume multigrid code, with a factor of 1000–2500 viscosity variation, Rayleigh numbers ranging from 105–107, and stress-free upper and lower boundaries. Considerable differences in model behavior are found depending on the details of rheology, heating mode, compressibility, and boundary conditions. Parameter choices were guided by realistic Earth models. In Boussinesq, basally heated cases with viscosity solely dependent on temperature and stress-free, isothermal boundaries, very long wavelength flows (∼25,000 km, assuming the depth corresponds to mantle thickness) with cold plumes and hot upwelling sheets result, in contrast to the upwelling plumes and downwelling sheets found in small domains, illustrating the importance of simulating wide domains. The addition of depth dependence results in small cells and reverses the planform, causing hot plumes and cold sheets. The planform of temperature-dependent viscosity convection is due predominantly to vertical variations in viscosity resulting from the temperature dependence. Compressibility, with associated depth-dependent properties, results in a tendency for broad upwelling plumes and narrow downwelling sheets, with large aspect ratio cells. Perhaps the greatest modulation effect occurs in internally heated compressible cases, in which the short-wavelength pattern of time-dependent cold plumes commonly observed in constant-viscosity calculations completely changes into a very long wavelength pattern of downwelling sheets (spaced up to 24,000 km apart) with time-dependent plumelike instabilities. These results are particularly interesting, since the basal heat flow in the Earth's mantle is usually thought to be very low, e.g., 5–20% of total. The effects of viscous dissipation and adiabatic heating play only a minor role in the overall heat budget for constant-viscosity cases, an observation which is not much affected by the Rayleigh number. However, viscous dissipation becomes important in the stiff upper boundary layer when viscosity is temperature dependent. This effect is caused by the very high stresses occurring in this stiff lid, typically 2 orders of magnitude higher than the stresses in the interior of the domain for the viscosity contrast modeled here. The temperature in the interior of convective cells is highly sensitive to the material properties, with temperature-dependent viscosity and depth-dependent thermal conductivity strongly increasing the internal temperature, and depth-dependent viscosity strongly decreasing it. The sensitivity of the observed flow pattern to these various complexities clearly illustrates the importance of performing compressible, variable-viscosity mantle convection calculations with rheological and thermodynamic properties matching as closely as possible those of the Earth.