×

zbMATH — the first resource for mathematics

Patterns in wall-bounded shear flows. (English) Zbl 1439.76032
Davis, Stephen H. (ed.) et al., Annual review of fluid mechanics. Vol. 52. Palo Alto, CA: Annual Reviews. Annu. Rev. Fluid Mech. 52, 343-367 (2020).
Summary: Experiments and numerical simulations have shown that turbulence in transitional wall-bounded shear flows frequently takes the form of long oblique bands if the domains are sufficiently large to accommodate them. These turbulent bands have been observed in plane Couette flow, plane Poiseuille flow, counter-rotating Taylor-Couette flow, torsional Couette flow, and annular pipe flow. At their upper Reynolds number threshold, laminar regions carve out gaps in otherwise uniform turbulence, ultimately forming regular turbulent-laminar patterns with a large spatial wavelength. At the lower threshold, isolated turbulent bands sparsely populate otherwise laminar domains, and complete laminarization takes place via their disappearance. We review results for plane Couette flow, plane Poiseuille flow, and free-slip Waleffe flow, focusing on thresholds, wavelengths, and mean flows, with many of the results coming from numerical simulations in tilted rectangular domains that form the minimal flow unit for the turbulent-laminar bands.
For the entire collection see [Zbl 1446.76006].

MSC:
76F06 Transition to turbulence
76E05 Parallel shear flows in hydrodynamic stability
76-02 Research exposition (monographs, survey articles) pertaining to fluid mechanics
PDF BibTeX XML Cite
Full Text: DOI