Exact steady eastward-moving vortex-dipole solutions, the equatorial modons, are constructed in the asymptotic limit of low divergence and small temperature variations in the thermal rotating shallow water (TRSW) model on the equatorial beta-plane. This regime is known to be relevant for the tropical atmosphere. The model itself is a generalization, allowing for horizontal temperature gradients, of the classical rotating shallow water model. The asymptotic modons can carry a temperature anomaly and exist also on the inhomogeneous temperature background. The modon configurations are then used to initialize numerical simulations, in order to check whether such coherent structures can exist in the full TRSW model. The results show that this is, indeed, the case. The parameter regimes and limitations on the structure of the temperature anomaly inside, in order for the modons to persist, are established. It is also shown that the modons keep their coherence even while evolving on the background of meridionally inhomogeneous temperature fields, or while interacting with sharp temperature fronts. A general scenario of disaggregation of the modons, if they are out of the stability domain, is exhibited and analysed.

中文翻译：

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热旋转浅水模型中的赤道模

在赤道β平面上的热旋转浅水（TRSW）模型中，在低发散和小温度变化的渐近极限下构造了精确稳定的东移涡旋偶极子解，即赤道模子。众所周知，这种制度与热带大气有关。该模型本身是经典旋转浅水模型的概括，允许水平温度梯度。渐近模子可以携带温度异常并且也存在于非均匀温度背景中。然后使用模子配置来初始化数值模拟，以检查这种相干结构是否可以存在于完整的 TRSW 模型中。结果表明，情况确实如此。为了使模子持续存在，建立了内部温度异常结构的参数制度和限制。研究还表明，即使在经向不均匀温度场的背景下演化，或与尖锐的温度锋相互作用时，模子仍保持其相干性。如果模子超出稳定域，则会展示并分析模子分解的一般情况。