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Analysis of one-dimensional models for exchange flows under strong stratification

机译：强分层下的一维交换流量模型分析

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One-dimensional models of exchange flows driven by horizontal density gradients are well known for performing poorly in situations with weak turbulent mixing. The main issue with these models is that the horizontal density gradient is usually imposed as a constant, leading to non-physically high stratification known as runaway stratification. Here, we propose two new parametrizations of the horizontal density gradient leading to one-dimensional models able to tackle strongly stratified exchange flows at high and low Schmidt number values. The models are extensively tested against results from laminar two-dimensional simulations and are shown to outperform the models using the classical constant parametrization for the horizontal density gradients. Four different flow regimes are found by exploring the parameter space defined by the gravitational Reynolds number Re-g, the Schmidt number Sc, and the aspect ratio of the channel Gamma. For small values of Re-g Gamma, when diffusion dominates, all models perform well. However, as Re-g Gamma increases, two clearly distinct regimes emerge depending on the Sc value, with an equally clear distinction of the performance of the one-dimensional models.
机译：由水平密度梯度驱动的交换流的一维模型在湍流混合较弱的情况下表现较差，这是众所周知的。这些模型的主要问题是水平密度梯度通常被强加为常数，从而导致非物理性高分层，即失控分层。在这里，我们提出了水平密度梯度的两个新参数化方法，从而形成了一维模型，该模型能够处理高和低施密特数值下的强分层交换流。针对层流二维模拟的结果对模型进行了广泛测试，结果表明，对于水平密度梯度，使用经典的恒定参数化方法，该模型优于模型。通过探索由引力雷诺数Re-g，施密特数Sc和通道Gamma的纵横比定义的参数空间，可以找到四种不同的流态。对于较小的Re-g Gamma值，当扩散占主导地位时，所有模型均表现良好。但是，随着Re-g Gamma的增加，取决于Sc值，出现了两个明显不同的状态，一维模型的性能也有明显的区别。

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