Scaling analysis and simulation of strongly stratified turbulent flows

Abstract

International audienceDirect numerical simulations of stably and strongly stratified turbulent flows with Reynolds number Re " 1 and horizontal Froude number Fh Gt; 1 are presented. The results are interpreted on the basis of a scaling analysis of the governing equations. The analysis suggests that there are two different strongly stratified regimes according to the parameter R = ReFh2. When R " 1, viscous forces are nimportant and lv scales as lv ~ U/N (U is a characteristic horizontal velocity and N is the Brunt - Väis¨alä frequency) so that the dynamics of the flow is inherently three-dimensional but strongly anisotropic. When R " 1, vertical viscous shearing is important so that lv ~ lh/Re1/2 (lh is a characteristic horizontal length scale). The parameter R is further shown to be related to the buoyancy Reynolds number and proportional to (lO/?) 4/3, where lO is the Ozmidov length scale and ? the Kolmogorov length scale. This implies that there are simultaneously two distinct ranges in strongly stratified turbulence when R " 1: the scales larger than lO are strongly influenced by the stratification while those between lO and ? are weakly affected by stratification. The direct numerical simulations with forced large-scale horizontal two-dimensional motions and uniform stratification cover a wide Re and Fh range and support the main parameter controlling strongly stratified turbulence being R. The numerical results are in good agreement with the scaling laws for the vertical length scale. Thin horizontal layers are observed independently of the value of R but they tend to be smooth for R > 1, while for R > 1 small-scale three-dimensional turbulent disturbances are increasingly superimposed. The dissipation of kinetic energy is mostly due to vertical shearing for R > 1 but tends to isotropy as R increases above unity. When R > 1, the horizontal and vertical energy spectra are very steep while, when R > 1, the horizontal spectra of kinetic and potential energy exhibit an pproximate kh-5/3-power-law range and a clear forward energy cascade is observed. © 2007 Cambridge University Press

Robust identification of dynamically distinct regions in stratified turbulence

“…Billant & Chomaz 2001;Lindborg 2006;Brethouwer et al 2007;Riley & Lindborg 2008). Although this asymptotic regime is sometimes referred to as '(strongly) stratified turbulence' in the fluid dynamical literature, this nomenclature can lead to confusion as 'stratified turbulence' is typically used in a much broader sense in the geophysical literature.…”

“…The significance of this issue can be understood by considering figure 1, which follows from figure 18 of Brethouwer et al (2007). In the figure, Re t and Fr t are the turbulent Reynolds and Froude numbers with the generic horizontal length scale L h of (1.1) equated to the turbulence length scale…”

“…The threshold for the LAST regime, as defined by Brethouwer et al (2007) assuming A = 1, is Fr t ≈ 0.02 as indicated by a dashed line on the figure. The grey band indicates the uncertainty in this threshold taking into account that A in isotropic homogeneous turbulence ranges between 0.4 and 1.81 (Sreenivasan 1998), and that A is observed to be as low as 0.3 in stratified turbulence (Maffioli & Davidson 2016).…”

“…Their parameters are listed in table 1, and we mark their location on the regime diagram. We believe that the value of Re t chosen for these simulations is sufficiently large for turbulent flow, and we vary Fr t so that these simulations straddle the transition from the 'weakly' stratified turbulence regime (using the nomenclature of Brethouwer et al (2007)) to the 'strongly' stratified or LAST regime.…”

Caracterización experimental del campo lejano de los vertidos de salmuera al mar

“…ej., una pluma del campo lejano de un vertido de salmuera). En este caso, de sencilla geometría, la similitud geométrica es directa, mientras que la similitud dinámica se consigue garantizando la igualdad del número adimensional de Froude (Frd 0 = 1/ 2 Ri 0 ) por ser un flujo totalmente desarrollado (se ha de tener en cuenta que la viscosidad no es un parámetros escalable; véase la referencia [29] sobre flujos turbulentos a escalas de laboratorio).…”