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**Numerical simulation of wind-driven circulation in a thermally stratified flow.**
*(English)*
Zbl 1433.76038

Summary: The closed water bodies, such as reservoirs and lakes, can be polluted by an inflow of pollutants in the upstream as well as a stratification caused by seasonal natural phenomena. The vertical circulation particularly plays an important role in reducing environmental pollutants. The factors of the vertical circulation are the temperature, wind, thermal diffusivity, sunlight, and so on. The wind is the most significant factor among all possible factors causing the vertical circulation. Thus, it is necessary to describe the validation and application of a three-dimensional numerical model of wind-driven circulation in a thermally stratified flow.

In this study, the numerical model is conducted in three steps to calculate the velocity components from the momentum equations in \(x\)- and \(y\)-directions, the elevations from the free surface equation, and the temperature from the scalar transport equation. The present model was applied to two tests for verification of the numerical accuracy. Numerical results are compared with analytical solutions of the sloshing free surface movement in a rectangular basin and the model is applied to the circulation for the wind-driven flow in a thermal stratification. Consequently, the developed model is validated by two verifications and phenomena of the internal flow.

In this study, the numerical model is conducted in three steps to calculate the velocity components from the momentum equations in \(x\)- and \(y\)-directions, the elevations from the free surface equation, and the temperature from the scalar transport equation. The present model was applied to two tests for verification of the numerical accuracy. Numerical results are compared with analytical solutions of the sloshing free surface movement in a rectangular basin and the model is applied to the circulation for the wind-driven flow in a thermal stratification. Consequently, the developed model is validated by two verifications and phenomena of the internal flow.

### MSC:

76D05 | Navier-Stokes equations for incompressible viscous fluids |

65M06 | Finite difference methods for initial value and initial-boundary value problems involving PDEs |

86A10 | Meteorology and atmospheric physics |

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