Flows between orthogonally stretching parallel plates
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hdl:2117/355551
Tipus de documentArticle
Data publicació2021-02-01
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Abstract
Navier–Stokes equilibrium solutions of a viscous fluid confined between two infinite parallel plates that can independently stretch or shrink in orthogonal directions are studied. It is assumed that the admissible solutions satisfy spatial self-similarity in the stretching or shrinking perpendicular coordinates. The nonlinear steady boundary-value problem is discretized using a spectral Legendre method, and equilibrium solutions are found and tracked in the two-dimensional parameter space by means of pseudo-arclength continuation Newton–Krylov schemes. Different families of solutions have been identified, some of which are two-dimensional and correspond to the classical Wang and Wu self-similar flows arising in a plane channel with one stretching–shrinking wall [Wang, C.-A. and Wu, T.-C., “Similarity solutions of steady flows in a channel with accelerating walls,” Comput. Math. Appl. 30, 1–16 (1995)]. However, a large variety of three-dimensional solutions have also been found, even for low stretching or shrinking rates. When slightly increasing those rates, some of these solutions disappear at saddle-node bifurcations. By contrast, when both plates are simultaneously stretching or shrinking at higher rates, a wide variety of new families of equilibria are created and annihilated in the neighborhood of cuspidal codimension-2 bifurcation points. This behavior has similarities with the one observed in other planar and cylindrical self-similar flows.
CitacióAyats, R. [et al.]. Flows between orthogonally stretching parallel plates. "Physics of fluids", 1 Febrer 2021, vol. 33, núm. 2, p. 024103:1-024103:14.
ISSN1070-6631
Versió de l'editorhttps://aip.scitation.org/doi/10.1063/5.0037097
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