A nonlinear model for rotationally constrained convection with Ekman pumping
A nonlinear model for rotationally constrained convection with Ekman pumping
复制标题
Ekman 泵浦旋转约束对流的非线性模型
DOI：
10.1017/jfm.2016.225
复制
发表时间：
2016
影响因子：
3.7
通讯作者：
G. Vasil
中科院分区：
文献类型：
--
作者：
K. Julien;J. Aurnou;M. Calkins;E. Knobloch;P. Marti;S. Stellmach;G. Vasil
建立了一种低罗斯比数对流的简化模型，该模型在固定温度下具有上下边界无滑移的平面几何层。完整的动力学描述需要流体层中存在三个不同的区域：一个地转平衡的内部，流体运动主要与旋转轴对齐，紧邻边界板的埃克曼边界层，以及由埃克曼泵驱动的热风层。简化后的模型采用经典的埃克曼抽运参数化，减轻了求解埃克曼边界层的需要。给出了线性稳定性理论和一类由单个水平空间波数描述的特殊非线性解的结果。结果表明，与在无应力边界的模拟中观察到的结果相比，Ekman泵送（与内部对流正相关）可以显著增强热传递。如果没有中间热风层，则由Ekman抽运产生的非线性反馈将会产生在有限瑞利数下发散到无穷大的热输运。这一层阻止了这种爆炸，导致有限的热传输在一个显着提高的值。随着浮力强迫的增加，热输运转变为更有效的状态，这种转变总是在理论的渐近有效性范围内实现，这表明这种行为可能在地球物理和天体物理环境中普遍存在。随着旋转速率的增加，在这一转变之下的热传输曲线的斜率变陡，这一结果与实验室实验和直接数值模拟的观测结果一致。
A reduced model is developed for low-Rossby-number convection in a plane layer geometry with no-slip upper and lower boundaries held at fixed temperatures. A complete description of the dynamics requires the existence of three distinct regions within the fluid layer: a geostrophically balanced interior where fluid motions are predominantly aligned with the axis of rotation, Ekman boundary layers immediately adjacent to the bounding plates, and thermal wind layers driven by Ekman pumping in between. The reduced model uses a classical Ekman pumping parameterization to alleviate the need to resolve the Ekman boundary layers. Results are presented for both linear stability theory and a special class of nonlinear solutions described by a single horizontal spatial wavenumber. It is shown that Ekman pumping (which correlates positively with interior convection) allows for significant enhancement in the heat transport relative to that observed in simulations with stress-free boundaries. Without the intermediate thermal wind layer, the nonlinear feedback from Ekman pumping would be able to generate heat transport that diverges to infinity at finite Rayleigh number. This layer arrests this blowup, resulting in finite heat transport at a significantly enhanced value. With increasing buoyancy forcing, the heat transport transitions to a more efficient regime, a transition that is always achieved within the regime of asymptotic validity of the theory, suggesting that this behaviour may be prevalent in geophysical and astrophysical settings. As the rotation rate increases, the slope of the heat transport curve below this transition steepens, a result that is in agreement with observations from laboratory experiments and direct numerical simulations.