A Lie Scale Invariance in Fluids with Applications
Fuente:
arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866910920268054528 |
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| author | Henriksen, Richard |
| author_facet | Henriksen, Richard |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_18946 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A Lie Scale Invariance in Fluids with Applications Henriksen, Richard Fluid Dynamics 34 (primary) 76 (ssecondary) 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. |
| title | A Lie Scale Invariance in Fluids with Applications |
| topic | Fluid Dynamics 34 (primary) 76 (ssecondary) |
| url | https://arxiv.org/abs/2504.18946 |