Ageostrophic instability in rotating, stratified interior vertical shear flows
Ageostrophic instability in rotating, stratified interior vertical shear flows
复制标题
旋转分层内部垂直剪切流中的地转不稳定性
DOI：
10.1017/jfm.2014.426
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发表时间：
2014
影响因子：
3.7
通讯作者：
C. Ménesguen
中科院分区：
文献类型：
--
作者：
Peng Wang;J. McWilliams;C. Ménesguen
用Boussinesq方程计算了几种旋转的、稳定分层的、内部垂直剪切流$\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}\overline{U}(z)$的线性不稳定性。在中间罗斯比数（$\mathit{Ro}$）的奇对称$\overline{U}(z)$中发现了两种斜压类型，即地转不稳定性AI1和AI2。AI1频率为零；它表现为经典斜压不稳定性（BCI）与离心不稳定性（CI）之间不稳定模态性质的连续转换。它开始发生在中间$\mathit{Ro}$值和水平波数（$k,l$），远离$l= 0$或$k = 0$，在那里BCI或CI的增长速度是最强的。AI1通过从平均流中吸取动能生长，微扰将动能转化为势能。不稳定性AI2具有惯性临界层（ICL）；因此，它与惯性重力波联系在一起。对于不稳定的AI2模式，耦合要么发生在内部平衡剪切波和惯性重力波（BG）之间，要么发生在两个惯性重力波（GG）之间。不稳定BG模态的主要能量来源是平均动能，而不稳定GG模态的主要能量来源是平均有效势能。AI1和BG型AI2发生在$A-S= 0$附近(这是绝对垂直涡度和水平应变率在等熵坐标下的差值变化的标志；见McWilliams et al., Phys.；流体，vol. 10, 1998, pp. 3178-3184)，而GG型AI2出现在此条件之外。AI1和AI2都是不平衡不稳定性；它们可以作为三维内部流动失去平衡的可能局部路线的起始点，从而导致小尺度的有效能量转移。
Abstract The linear instability of several rotating, stably stratified, interior vertical shear flows $\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}\overline{U}(z)$ is calculated in Boussinesq equations. Two types of baroclinic, ageostrophic instability, AI1 and AI2, are found in odd-symmetric $\overline{U}(z)$ for intermediate Rossby number ( $\mathit{Ro}$ ). AI1 has zero frequency; it appears in a continuous transformation of the unstable mode properties between classic baroclinic instability (BCI) and centrifugal instability (CI). It begins to occur at intermediate $\mathit{Ro}$ values and horizontal wavenumbers ( $k,l$ ) that are far from $l= 0$ or $k = 0$ , where the growth rate of BCI or CI is the strongest. AI1 grows by drawing kinetic energy from the mean flow, and the perturbation converts kinetic energy to potential energy. The instability AI2 has inertia critical layers (ICL); hence it is associated with inertia-gravity waves. For an unstable AI2 mode, the coupling is either between an interior balanced shear wave and an inertia-gravity wave (BG), or between two inertia-gravity waves (GG). The main energy source for an unstable BG mode is the mean kinetic energy, while the main energy source for an unstable GG mode is the mean available potential energy. AI1 and BG type AI2 occur in the neighbourhood of $A-S= 0$ (a sign change in the difference between absolute vertical vorticity and horizontal strain rate in isentropic coordinates; see McWilliams et al., Phys. Fluids, vol. 10, 1998, pp. 3178–3184), while GG type AI2 arises beyond this condition. Both AI1 and AI2 are unbalanced instabilities; they serve as an initiation of a possible local route for the loss of balance in 3D interior flows, leading to an efficient energy transfer to small scales.