Linear and nonlinear baroclinic instability with rigid sidewalls
Linear and nonlinear baroclinic instability with rigid sidewalls
复制标题
刚性侧壁的线性和非线性斜压不稳定性
作者：
M. Mundt;N. Brummell;J. Hart
描述了斜压波在具有刚性（无滑移）侧壁的两层通道流动中从不稳定中生长的行为，并与更传统的自由滑移边界条件进行了对比。小振幅扰动开始的线性理论表明，横向边界条件的变化对典型的实验室参数值只有适度的影响，尽管无滑移情况在非常小的底部摩擦值下稍微不稳定。另一方面，无滑移模态的非线性演化是完全不同的。自由滑移情况只有在较大的超临界(F-Fc)/Fc值时才会是非周期性的，而刚性壁面情况可能是亚临界混沌的。对于设置在参数空间线性稳定区域的外部控制值，非周期的、高度非线性的波动是可能的。弱非线性分析表明，对于中等小的底部摩擦，无滑移情况具有负的朗道常数，并且正是在这种情况下，高分辨率数值模拟表现出亚临界混沌。在较大的底部摩擦值下，刚性壁面模拟在适度的一阶超临界下经历超临界准周期过渡到混沌，这比自由滑移情况下混沌所需的时间要小得多。
The behaviour of baroclinic waves growing from instability in a two-layer channel flow with rigid (no-slip) sidewalls is described and contrasted with that for the more traditional free-slip boundary conditions. The linear theory for the onset of small-amplitude disturbances shows that the change in lateral boundary conditions has only a modest effect for typical laboratory parameter values, although the no-slip case is slightly more unstable at very small values of bottom friction. On the other hand, the nonlinear evolution of no-slip modes is completely different. While the free-slip case becomes aperiodic only at large values of the supercriticality (F–Fc)/Fc, the rigid wall case can be subcritically chaotic. Aperiodic, highly nonlinear wave motions are possible for external control values set in the linearly stable region of parameter space. Weakly nonlinear analysis shows that the no-slip case has a negative Landau constant for moderately small values of bottom friction, and it is in this regime that high-resolution numerical simulations exhibit subcritical chaos. At larger values of bottom friction, the rigid-wall simulations undergo a supercritical quasi-periodic transition to chaos at modest, order one, supercriticality, which is substantially smaller than that required for chaos in the free-slip case.