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首页> 外文期刊>Journal of Physical Oceanography >Baroclinic Instability with a Simple Model for Vertical Mixing
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Baroclinic Instability with a Simple Model for Vertical Mixing

机译：具有垂直混合的简单模型的斜压不稳定性

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Here, we examine baroclinic instability in the presence of vertical mixing in an idealized setting. Specifically, we use a simple model for vertical mixing of momentum and buoyancy and expand the buoyancy and vorticity in a series for small Rossby numbers. A flow in subinertial mixed layer (SML) balance (see the study by Young in 1994) exhibits a normal mode linear instability, which is studied here using linear stability analysis and numerical simulations. The most unstable modes grow by converting potential energy associated with the basic state into kinetic energy of the growing perturbations. However, unlike the inviscid Eady problem, the dominant energy balance is between the buoyancy flux and the energy dissipated by vertical mixing. Vertical mixing reduces the growth rate and changes the orientation of the most unstable modes with respect to the front. By comparing with numerical simulations, we find that the predicted scale of the most unstable mode matches the simulations for small Rossby numbers while the growth rate and orientation agree for a broader range of parameters. A stability analysis of a basic state in SML balance using the inviscid QG equations shows that the angle of the unstable modes is controlled by the orientation of the SML flow, while stratification associated with an advection/diffusion balance controls the size of growing perturbations for small Ekman numbers and/or large Rossby numbers. These results imply that baroclinic instability can be inhibited by small-scale turbulence when the Ekman number is sufficiently large and might explain the lack of submesoscale eddies in observations and numerical models of the ocean surface mixed layer during summer.
机译：在这里，我们研究在理想设置下垂直混合存在下的斜压不稳定性。具体来说，我们使用一个简单的模型对动量和浮力进行垂直混合，并针对小Rossby数系列扩展浮力和涡度。非惯性混合层（SML）平衡中的流动（请参阅Young在1994年的研究）显示出一种正常模式的线性不稳定性，这里使用线性稳定性分析和数值模拟对其进行研究。最不稳定的模式通过将与基本状态相关的势能转换为不断增长的扰动的动能而增长。但是，与无粘性的Eady问题不同，主要的能量平衡是在浮力通量和垂直混合耗散的能量之间。垂直混合会降低生长速度，并改变最不稳定模式相对于正面的方向。通过与数值模拟进行比较，我们发现最不稳定模式的预测尺度与小Rossby数值的模拟匹配，而增长率和方向适合更广泛的参数范围。使用无粘性QG方程对SML平衡中的基本状态进行稳定性分析表明，不稳定模态的角度由SML流动的方向控制，而与对流/扩散平衡相关的分层控制了小分子生长扰动的大小艾克曼数和/或大罗斯比数。这些结果表明，当埃克曼数足够大时，小规模湍流可以抑制斜压不稳定，这可能解释了夏季海洋表层混合层的观测和数值模型缺乏亚中尺度涡旋。

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