ALBERT

Description: 〈div data-abstract-type="normal"〉〈p〉We consider the asymmetry of the buoyancy field in the vertical direction in stratified turbulence. While this asymmetry is known, its causes are not well understood, and it has not been systematically quantified previously. Using theoretical arguments, it is shown that both stratified turbulence and isotropic turbulence in the presence of a mean scalar gradient will become positively skewed, as a direct consequence of the presence of stratification and mean scalar gradient, respectively. Assuming a rapid adjustment of isotropic turbulence to a stable stratification on a time scale 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190506170913752-0434:S0022112019002404:S0022112019002404_inline1.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉, where 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190506170913752-0434:S0022112019002404:S0022112019002404_inline2.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉 is the Brunt–Väisälä frequency, a scaling for the skewness of the vertical buoyancy gradient is obtained. Direct numerical simulations of stratified turbulence with forcing are performed and the positive skewness of 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190506170913752-0434:S0022112019002404:S0022112019002404_inline3.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉 is confirmed (〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190506170913752-0434:S0022112019002404:S0022112019002404_inline4.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉 is the buoyancy). Both the volume-averaged dimensional skewness, 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190506170913752-0434:S0022112019002404:S0022112019002404_inline5.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉, and the non-dimensional skewness, 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190506170913752-0434:S0022112019002404:S0022112019002404_inline6.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉, are computed and compared against the theoretical predictions. There is a good agreement for 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190506170913752-0434:S0022112019002404:S0022112019002404_inline7.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉, while there is a discrepancy in the behaviour of 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190506170913752-0434:S0022112019002404:S0022112019002404_inline8.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉. The theory predicts 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190506170913752-0434:S0022112019002404:S0022112019002404_inline9.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉 and a constant skewness, while the direct numerical simulations confirm that the skewness is 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190506170913752-0434:S0022112019002404:S0022112019002404_inline10.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉 but with a remaining dependence on the Froude number. The results are interpreted as being due to the concurrent action of linear and nonlinear processes in stratified turbulence leading to 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190506170913752-0434:S0022112019002404:S0022112019002404_inline11.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉 and to the formation of layers and interfaces in vertical profiles of buoyancy.〈/p〉〈/div〉

Description: We consider mixing of the density field in stratified turbulence and argue that, at sufficiently high Reynolds numbers, stationary turbulence will have a mixing efficiency and closely related mixing coefficient described solely by the turbulent Froude number Fr = ϵk=(Nu2), where ϵk is the kinetic energy dissipation, u is a turbulent horizontal velocity scale and N is the Brunt-Väisälä frequency. For Fr≥1, in the limit of weakly stratified turbulence, we show through a simple scaling analysis that the mixing coefficient scales as Λ σ Fr-2, where Λ =ϵp=ϵk and ϵp is the potential energy dissipation. In the opposite limit of strongly stratified turbulence with Fr≤1, we argue that Λ should reach a constant value of order unity. We carry out direct numerical simulations of forced stratified turbulence across a range of Fr and confirm that at high Fr, Λ σ Fr-2, while at low Fr it approaches a constant value close to Λ = 0:33. The parametrization of Λ based on Reb due to Shih et al. (J. Fluid Mech., vol. 525, 2005, pp. 193-214) can be reinterpreted in this light because the observed variation of Λ in their study as well as in datasets from recent oceanic and atmospheric measurements occurs at a Froude number of order unity, close to the transition value Fr =0:3 found in our simulations. © 2016 Cambridge University Press.

Description: Localized regions of turbulence, or turbulent clouds, in a stratified fluid are the subject of this study, which focuses on the edge dynamics occurring between the turbulence and the surrounding quiescent region. Through laboratory experiments and numerical simulations of stratified turbulent clouds, we confirm that the edge dynamics can be subdivided into materially driven intrusions and horizontally travelling internal wave-packets. Three-dimensional visualizations show that the internal gravity wave-packets are in fact large-scale pancake structures that grow out of the turbulent cloud into the adjacent quiescent region. The wave-packets were tracked in time, and it is found that their speed obeys the group speed relation for linear internal gravity waves. The energetics of the propagating waves, which include waveforms that are inclined with respect to the horizontal, are also considered and it is found that, after a period of two eddy turnover times, the internal gravity waves carry up to 16 % of the cloud kinetic energy into the initially quiescent region. Turbulent events in nature are often in the form of decaying turbulent clouds, and it is therefore suggested that internal gravity waves radiated from an initial cloud could play a significant role in the reorganization of energy and momentum in the atmosphere and oceans.©2013 Cambridge University Press.

Description: We consider the asymmetry of the buoyancy field in the vertical direction in stratified turbulence. While this asymmetry is known, its causes are not well understood, and it has not been systematically quantified previously. Using theoretical arguments, it is shown that both stratified turbulence and isotropic turbulence in the presence of a mean scalar gradient will become positively skewed, as a direct consequence of the presence of stratification and mean scalar gradient, respectively. Assuming a rapid adjustment of isotropic turbulence to a stable stratification on a time scale , where is the Brunt-Väisälä frequency, a scaling for the skewness of the vertical buoyancy gradient is obtained. Direct numerical simulations of stratified turbulence with forcing are performed and the positive skewness of is confirmed ( is the buoyancy). Both the volume-averaged dimensional skewness, , and the non-dimensional skewness, , are computed and compared against the theoretical predictions. There is a good agreement for , while there is a discrepancy in the behaviour of . The theory predicts and a constant skewness, while the direct numerical simulations confirm that the skewness is but with a remaining dependence on the Froude number. The results are interpreted as being due to the concurrent action of linear and nonlinear processes in stratified turbulence leading to 0]]〉 and to the formation of layers and interfaces in vertical profiles of buoyancy. © 2019 Cambridge University PressA.

Description: We present direct numerical simulations (DNS) of unforced stratified turbulence with the objective of testing the strongly stratified turbulence theory. According to this theory the characteristic vertical scale of the turbulence is given by , where is the horizontal velocity scale and the Brunt-Väisälä frequency. Combined with the hypothesis of the energy dissipation rate scaling as , this theory predicts inertial range scalings for the horizontal spectrum of horizontal kinetic energy and of potential energy, according to . We begin by presenting a scaling analysis of the horizontal vorticity equation from which we recover the result regarding the vertical scale, , highlighting in the process the important dynamical role of large-scale vertical shear of horizontal velocity. We then present the results from decaying DNS, which show a good agreement with aspects of the theory. In particular, the vertical Froude number is found to reach a constant plateau in time, of the form with in all the runs. The derivation of the dissipation scaling at low Reynolds number in the context of decaying stratified turbulence highlights that the same scaling holds at high as well as at low , which is known (see Brethouwer et al., J. Fluid Mech., vol. 585, 2007, pp. 343-368) but not sufficiently emphasized in recent literature. We find evidence in our DNS of the dissipation scaling holding at , which we interpret as being in the viscous regime. We also find and (with ), in our high-resolution run at earlier times corresponding to , which is in the transition between the strongly stratified and the viscous regimes. The horizontal spectrum of horizontal kinetic energy collapses in time using the scaling and the horizontal potential energy spectrum is well described by . The presence of an inertial range in the horizontal direction is confirmed by the constancy of the energy flux spectrum over narrow ranges of . However, the vertical energy spectrum is found to differ significantly from the expected scaling, showing that is not of order unity on a scale-by-scale basis, thus providing motivation for further investigation of the vertical structure of stratified turbulence. © © 2015 Cambridge University Press.