Physics > Fluid Dynamics
[Submitted on 26 Apr 2025
]
Title: A Lie Scale Invariance in Fluids with Applications
Title: 流体中的李比例不变性及其应用
Abstract: Lie scale invariance is used to reduce the incompressible Navier-Stokes equations to non-linear ordinary equations. This yields a formulation in terms of logarithmic spirals as independent variables. We give the equations when the spirals lie on cones as well as in planes. The theory gives a locus in cylindrical coordinates of singularities as they arise in the reduced Navier-Stokes equations. We give two formal examples aimed at discovering singularities in the flow; another example is related to a Hele-Shaw cell, and finally we explore the flow through propellers comprised of blades made from congruent logarithmic spirals.
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