A specific instability of vortices is found in rotating shallow water equations with horizontal density/temperature gradients, which is used for modelling atmospheric and oceanic mixed layers. The model is re-interpreted as dynamics of rotating non-isentropic two-dimensional gas. The instability, which was not reported previously, develops in a way suggesting its convective character. It appears when anomaly of buoyancy at the center of the vortex and the vorticity have opposite signs (for positive Coriolis parameters), and coexists with the standard barotropic instability, having higher growth rates in a wide range of parameters and leading to efficient mixing at a nonlinear stage.

中文翻译：

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具有水平温度/密度梯度的旋转浅水中的热不稳定性

在具有水平密度/温度梯度的旋转浅水方程中发现了涡流的特定不稳定性，该方程用于模拟大气和海洋混合层。该模型被重新解释为旋转非等熵二维气体的动力学。以前没有报道过的不稳定性以一种表明其对流特征的方式发展。当涡流中心的浮力异常和涡流具有相反的符号（对于正科里奥利参数）时出现，并与标准的正压不稳定性共存，在广泛的参数范围内具有更高的增长率并导致在非线性阶段。