温盐双扩散系统的多平衡稳定性

STABILITY OF MULTIPLE EQUILIBRIA IN THERMOHALINE DOUBLE-DIFFUSIVE SYSTEM

采用数值试验的方法研究了温盐双扩散系统中的多平衡稳定性在系统中引入非线性状态方程、温通量边界条件和变强迫因子在数值模拟中引入边界拟会坐标系，并按照温盐浮力比λ大于1，等于1和小于1将流场分为温度控制场、温盐均势场和盐度控制场得到了四种稳定平衡状态，特别是，大强迫因子和强非线性影响下的四胞环流对称状态．在对称的定常强迫边条件作用下的流场、温度场和盐度场均为对称分布引入温通量边条件后，对称流场在小干扰下失去对称性，发展为非对称分布，并因为干扰位置的不同而造成不同的非对称性，出现了从对称状态到非对称状态的音叉分叉，得到了a-Ras的稳定曲线及分叉图。

Stability of multiple equilibria in the thermohaline double-diffusive system is studied here with numerical method in a body-fitted curvilinear coordinate system by introducing nonlinear equation of state, temperature-flux boundary condition and variable limit of forced boundary condition into this system. With heat-to-salt buoyancy ratio A larger than, equal to and smaller than 1, the flow is divided into temperature-dominated regime, temperature-salinity equilibrant regime and salinity-dominated regime. Four symmetric equilibria solutions are given, especially,four symmetric cell flows at large parameter of forced boundary condition or high coefficient of nonlinear state equation are found. When such a fluid is forced with a specified distribution of temparture and salinity at the surface-symmetry about a vertical axis-it attains a stable two-cell circulation, with the same symmetry. On the other hand, replacement of the specified temperature surface condition with an appropriate symmetric temperature-flux condition leads to loss of stability of the symmetric circulation and gives rise to a new, symmetric state. The transfer of stability from a single equilbrium to a pair of equilbria with mirror symmetry, because of different position of small perturbation, suggests the presence of a pitchfork bifurcation in the system. The physical mechanism of the pitchfork bifurcation from symmetric to asymmetric state is outlined.