Fixed-flux salt-finger convection in the small diffusivity ratio limit
Fixed-flux salt-finger convection in the small diffusivity ratio limit
复制标题
DOI：
10.1063/5.0031071
复制
发表时间：
2020-12
影响因子：
4.6
通讯作者：
Jin-Han Xie;K. Julien;E. Knobloch
中科院分区：
文献类型：
--
作者：
Jin-Han Xie;K. Julien;E. Knobloch
盐指对流提供了地球物理和天体物理流体流动的关键混合过程。由于其特征空间尺度小，扩散时间尺度慢，这一过程必须在地球物理和天体物理模型中参数化，其中需要将背景梯度与通量联系起来。为了得到这样的关系，大多数作者研究了温度和盐度通量对固定背景梯度的依赖性。使用Xie et al. [“A reduced model for salt-finger convection in the small diffusivity ratio limit，”Fluids 2（1），6（2017）]导出的简化模型，用于小扩散率和大密度比限制下的盐指对流，本文考虑了通量固定但允许调整平均梯度的共轭问题。在小区域，固定通量条件导致稳定的单模解，这是固定梯度条件下无法实现的。在具有统计稳定饱和状态的大区域中，平均通量和平均梯度之间的关系对于两组条件是相同的。固定通量条件提供了一个新的视角，通过确定两个不同的制度具有相同的耗散率来理解所产生的统计稳态。我们发现，统计稳定的动力学选择的状态与较小的瑞利比Ra受约束Ra > 1，确保背景状态是线性不稳定的。固定通量配方的结果在一个更有力的恢复机制，统计稳定状态，具有更小的方差，偏度，和特征时间尺度比在固定梯度设置。这种独特的功能可以被用来作为一个诊断，以确定是否在原位盐指对流是通量驱动或梯度驱动。
Salt-finger convection provides a key mixing process in geophysical and astrophysical fluid flows. Because of its small characteristic spatial scale and slow diffusive time scale, this process must be parameterized in geophysical and astrophysical models, where relations linking background gradients to fluxes are required. To obtain such relations, most authors study the dependence of temperature and salinity fluxes on fixed background gradients. Using the reduced model derived by Xie et al. [“A reduced model for salt-finger convection in the small diffusivity ratio limit,” Fluids 2(1), 6 (2017)] for salt-finger convection in the limit of small diffusivity and large density ratios, this paper considers the conjugate problem where the fluxes are fixed, but the mean gradients are permitted to adjust in response. In small domains, the fixed-flux condition leads to stable single-mode solutions, which are not achievable with fixed-gradient conditions. In large domains, with statistically steady saturated states, the relations between mean fluxes and mean gradients are identical for both sets of conditions. The fixed-flux condition provides a new perspective for understanding the resulting statistically steady states by identifying two distinct regimes with the same dissipation rate. We find that the statistically steady dynamics select the state with the smaller Rayleigh ratio Ra subject to the constraint Ra > 1, ensuring that the background state is linearly unstable. The fixed-flux formulation results in a more potent restoring mechanism toward the statistically steady state, with a smaller variance, skewness, and characteristic time scale than in the fixed-gradient setup. This distinctive feature can be used as a diagnostic to determine whether in situ salt-finger convection is flux-driven or gradient-driven.