Integration of Advection and Mixing Using Fluid Mass-Momentum-Covering Relationships

Abstract

Zhiren Wang

Classical discretization of discrete fluids and parameterization of mixing bring modeling uncertainties for momentumuneven fluids by setting the grid spacing as the distance for fluids to move within one time step, using low resolutions, and introducing dozens of parameters dependent of scales and modeling processes. Low resolutions have linearized, in a rather extent, nonlinear motions and failed to forecast accelerations that can cause climate adjustments, especially during solving tide-associated dynamics. Here, I wrote Newton Law directly for discrete fluids under conservations of momentum and mass using “mass and momentum-covering relationships (MMCR)”, and combined advection and mixing terms. Mixing became a higher-order advection terms induced from speed gradients times coefficients that are functions of density, grid spacing, and the gradients of speed, density and momentum. Parameterization can be avoided and no uncertain parameters are involved in modeling. Preliminary modeling experiments showed skill for simulation of sea surface temperatures over tropical oceans where momentum was more uneven than as compared with higher latitudes.

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