A multi-parameter criterion for layer formation in a stratified shear flow using sorted buoyancy coordinates

• Published in: Journal of fluid mechanics Vol. 823
• Main Authors: Taylor, J. R., Zhou, Q.
• Format: Journal Article
• Language: English
• Published: Cambridge, UK Cambridge University Press 25.07.2017
• Subjects: Abstracts; Buoyancy; Computational fluid dynamics; Computer simulation; Deep sea; Deep sea environments; Density stratification; Experiments; Fluid flow; Fluids; Frameworks; Gravitational waves; Laboratories; Parameterization; Prandtl number; Rapids; Reynolds number; Richardson number; Shear flow; Stratification; Stratified shear flow; turbulent flows; stratified turbulence
• ISSN: 0022-1120; 1469-7645
• DOI: 10.1017/jfm.2017.375

Here, we examine the conditions for layer formation in a stratified shear flow. We reformulate the conditions for amplification of small perturbations to a uniform stratification first proposed by Phillips (Deep Sea Research and Oceanographic Abstracts, vol. 19, 1972, pp. 79–81, Elsevier) and Posmentier (J. Phys. Oceanogr., vol. 7 (2), 1977, pp. 298–300) using the sorted buoyancy coordinates introduced by Nakamura (J. Atmos. Sci., vol. 53 (11), 1996, pp. 1524–1537) and Winters & D’Asaro (J. Fluid Mech., vol. 317, 1996, pp. 179–193). We consider the possible dependence of the effective diffusivity on three non-dimensional parameters, the gradient Richardson number, the buoyancy Reynolds number and the Prandtl number, and obtain a simple expression for conditions favourable for layer formation. The new framework is applied to direct numerical simulations of stratified shear flow. We then apply a recent multi-parameter parameterization developed by Salehipour et al. (Geophys. Res. Lett., vol. 43 (7), 2016, pp. 3370–3379), which suggests that layer formation is favoured for large Prandtl numbers and moderate to large values of the gradient Richardson and buoyancy Reynolds numbers.