Explicit Unsteady Navier-Stokes Solutions and their Analysis via Local Vortex Criteria

Tiemo Pedergnana; David Oettinger; Gabriel Provencher-Langlois; George Haller

doi:10.1063/5.0003245

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arXiv · 1908.04657

Explicit Unsteady Navier-Stokes Solutions and their Analysis via Local Vortex Criteria

Tiemo Pedergnana·David Oettinger·Gabriel Provencher-Langlois·George Haller

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Abstract

We construct a class of spatially polynomial velocity fields that are exact solutions of the planar unsteady Navier-Stokes equation. These solutions can be used as simple benchmarks for testing numerical methods or verifying the feasibility of flow-feature identification principles. We use examples from the constructed solution family to illustrate deficiencies of streamlines-based feature detection and of the Okubo-Weiss criterion, which is the common two-dimensional version of the broadly used Q-, Delta-, Lambda-2- and Lambda-Ci-criteria for vortex-detection. Our planar polynomial solutions also extend directly to explicit, three-dimensional unsteady Navier-Stokes solutions with a symmetry.

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Tiemo Pedergnana, David Oettinger, Gabriel Provencher-Langlois, George Haller. 2019-08-13. Explicit Unsteady Navier-Stokes Solutions and their Analysis via Local Vortex Criteria. https://doi.org/10.1063/5.0003245

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