General Solution to 2D Steady Navier-Stokes Equation for Incompressible Flow without vorticity diffusion

Peng Shi

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arXiv · 2206.06073

General Solution to 2D Steady Navier-Stokes Equation for Incompressible Flow without vorticity diffusion

Peng Shi

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Abstract

The study solves the general solution to 2D steady Navier-Stokes equation for incompressible flow without vorticity diffusion, which is more general than Stokes flow. In order to obtain the general solution, two potential functions are introduced to express the velocity: a vector potential describing the rotational incompressible flow and a scalar potential describing the irrotational incompressible flow. The results show that the vorticity equation expressed with potential functions is a biharmonic function, which means that the potential functions describing the flow field are polynomials of no more than fourth degree. For a steady unidirectional shear flow, the velocity and pressure fields can be described with the vector potential expressed by a polynomial of third degree. For non unidirectional two-dimensional steady shear flow, there may be four independent parameters in the two potential functions.

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Peng Shi. 2022-06-13. General Solution to 2D Steady Navier-Stokes Equation for Incompressible Flow without vorticity diffusion. https://arxiv.org/abs/2206.06073

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