Turbulence energetics in stably stratified geophysical flows: Strong and weak mixing regimes

Abstract

ABSTRACT:Traditionally, turbulence energetics is characterised by turbulent kinetic energy (TKE) and modelled using solely the TKE budget equation. In stable stratification, TKE is generated by the velocity shear and expended through viscous dissipation and work against buoyancy forces. The effect of stratification is characterised by the ratio of the buoyancy gradient to squared shear, called the Richardson number, Ri. It is widely believed that at Ri exceeding a critical value, Ri c , local shear cannot maintain turbulence, and the flow becomes laminar. We revise this concept by extending the energy analysis to turbulent potential and total energies (TPE, and TTE = TKE + TPE), consider their budget equations, and conclude that TTE is a conservative parameter maintained by shear in any stratification. Hence there is no 'energetics Ri c ', in contrast to the hydrodynamic-instability threshold, Ri c−instability , whose typical values vary from 0.25 to 1. We demonstrate that this interval, 0.25 < Ri < 1, separates two different turbulent regimes: strong mixing and weak mixing rather than the turbulent and the laminar regimes, as the classical concept states. This explains persistent occurrence of turbulence in the free atmosphere and deep ocean at Ri 1, clarifies the principal difference between turbulent boundary layers and free flows, and provides the basis for improving operational turbulence closure models.

On the Velocity Gradient in Stably Stratified Sheared Flows. Part 1: Asymptotic Analysis and Applications

“…Lo et al (2005) derived a quite similar relationship between k and (τ/E K ) Ri=0 for stationary and homogenous sheared flows: k = C 3/2 2 (τ/E K ) Ri=0 and determined the constant C 2 ≈ 2 (that appears in the second-order velocity structure function) from a large number of laboratory and numerical experiments. Relying on this estimate, we obtain Zilitinkevich et al 2008) and k ≈ 0.4, Eq. 14 yields a reasonably close value of C K ≈ 2.4.…”

“…Garratt 1992), whereas the free atmosphere is characterised by Ri of order 10. Furthermore, it seems reasonable to define the upper boundary of the stable PBL just as the height at which Ri passes the above threshold (Zilitinkevich et al 2008). From this point of view, the stable PBL flow should be considered as weakly stable, so that Eqs.…”

“…The maximum value of the flux Richardson number: R ∞ ≈ 0.2 has been determined from various experimental, large-eddy simulation (LES) and direct numerical simulation (DNS) data for extremely strong static stabilities, namely, for the values of Ri between 1 and 10 2 , at which Ri f definitely levels off (e.g., Yamada 1975;Stroscio 1982;Zilitinkevich et al , 2008Zilitinkevich et al , 2009Stretch et al 2009;Venayagamoorthy and Stretch 2010). It is remarkable that the coefficient 1/R ∞ ≈ 5 in Eq.…”

“…The stability dependence of E K /|τ | has been examined theoretically and empirically by Zilitinkevich et al ( , 2008Zilitinkevich et al ( , 2009), and . With increasing stability, E K /|τ | increases starting from 3 to 5 in neutral stratification (Mann 1994;Lo et al 2005) and approaches 10-15 in very strong static stability at Ri > 10.…”

Bulk Mixing and Decoupling of the Nocturnal Stable Boundary Layer Characterized Using a Ubiquitous Natural Tracer

“…Progress has been made in recent years in classifying mixing/scaling regimes incorporating the vSBL (Holtslag and Nieuwstadt 1986;Ohya et al 1997;Mahrt et al 1998;Mahrt 1998Mahrt , 1999; Van de Wiel et al 2002a,b, 2003Zilitinkevich et al 2008;Sorbjan and Grachev 2010), developing similarity formulations applicable over a wider range of stabilities (e.g. Sorbjan 2006aSorbjan , 2008Sorbjan and Grachev 2010) and dealing with data analysis problems associated with submeso motions, non-stationarity and self-correlation Mahrt 2003, 2006;Klipp and Mahrt 2004;Sorbjan 2006b;Mahrt 2011).…”