Abstract

The investigation of dynamics of mixed fluid spots in a stratified environment is of interest both for the study of the ocean fine structure and for the study of wake dynamics behind moving underwater objects. The paper is devoted to the construction of a physical and mathematical model for this problem. Salinity is used as the stratifying component. This model is described by the Navier–Stokes equations in the Boussinesq approximation. The problem is solved using a recent version of the splitting method by physical factors the finite difference scheme of which has a high approximation order, minimum scheme viscosity and dispersion, and, which is especially important for problems with large gradients of hydrophysical parameters, problems with a free surface and internal waves, the monotonicity property. Numerous test computations for the study of the influence of grid parameters on the results are performed. The results of comparison with analytical estimates, experimental data, and computations of other researchers are presented. By way of example, the dynamics of the salinity perturbation is discussed, which corresponds to the isophase lines describing the behavior of internal waves during the collapse of spots.

中文翻译：

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分层介质中点动力学的数学建模

摘要

分层环境中混合流体点动力学的研究，不仅对海洋精细结构的研究，而且对水下运动物体后的尾流动力学的研究都有兴趣。本文致力于解决该问题的物理和数学模型。盐度用作分层成分。该模型由Boussinesq近似中的Navier–Stokes方程描述。使用最新版本的分裂方法，可以通过物理因子解决问题，该物理因子的有限差分方案具有较高的近似阶数，最小的方案粘度和色散，并且对于水物理参数梯度较大的问题特别重要。自由表面和内部波，具有单调性。为了研究网格参数对结果的影响，进行了大量的测试计算。介绍了与分析估计值，实验数据和其他研究人员的计算结果进行比较的结果。通过示例的方式，讨论了盐度微扰的动力学，其对应于描述点崩塌期间内部波的行为的等相线。