Correction to: Variations of characteristic time scales in rotating stratified turbulence using a large parametric numerical study

Rosenberg, Duane; Marino, Raffaele; Herbert, Corentin; Pouquet, A.

doi:10.1140/epje/i2017-11577-5

Cited by 3 publications

(4 citation statements)

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“…Together with the multitude of vortex tubes that are visible in the flow, this indicates that the generation of fully developed turbulence by the strong stirring linked with large-scale vertical shear can be studied in this simplified set up. The ratio of dissipation of kinetic to potential energy is roughly 3 for the high-resolution run A8; thus, r ≈ 1/4, comparable to what was found in [43,86,87] for an ensemble of rotating stratified flows in the absence of forcing. Similarly, when measuring the so-called mixing efficiency, Γ = B V / V , with B V = N wθ the properly dimensionalised vertical heat flux, we find Γ ≈ 0.4 for run A8, again comparable with previous studies and observations.…”

Section: Discussionsupporting

confidence: 78%

Generation of turbulence through frontogenesis in sheared stratified flows

2018

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The large-scale structures in the ocean and the atmosphere are in geostrophic balance, and a conduit must be found to channel the energy to the small scales where it can be dissipated. In turbulence this takes the form of an energy cascade, whereas one possible mechanism in a balanced flow at large scales is through the formation of fronts, a common occurrence in geophysical dynamics. We show in this paper that an iconic configuration in laboratory and numerical experiments for the study of turbulence, that of the Taylor-Green or von Kármán swirling flow, can be suitably adapted to the case of fluids with large aspect ratios, leading to the creation of an imposed large-scale vertical shear. To this effect we use direct numerical simulations of the Boussinesq equations without net rotation and with no small-scale modeling, and with this idealized Taylor-Green set-up. Various grid spacings are used, up to 2048 2 × 256 spatial points. The grids are always isotropic, with box aspect ratios of either 1 : 4 or 1 : 8. We find that when shear and stratification are comparable, the imposed shear layer resulting from the forcing leads to the formation of multiple fronts and filaments which destabilize and further evolve into a turbulent flow in the bulk, with a sizable amount of dissipation and mixing, and with a cycle of front creation, instability, and development of turbulence. The results depend on the vertical length scales for shear and for stratification, with stronger large-scale gradients being generated when the two length scales are comparable.

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Section: Discussionsupporting

confidence: 78%

Generation of turbulence through frontogenesis in sheared stratified flows

2018

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“…Runs with an emphasis on realistic parameters for the mesosphere and lower thermosphere, and that overlap with the present data base, were investigated for the energy partition between waves and slow modes and the link with kinetic-potential energy exchanges in Marino et al (2015b), as well as for parametric characteristic time-scale variations in Rosenberg et al (2016) (see also Rosenberg et al (2017)). Here, the runs on grids of 1024 3 points, cover the following parameter ranges (see Table 1): 0.11 Ro 41, 1985 Re 18590, 0.001 F r 5.5, 0.02 < R B < 1.2 × 10 5 and 2.47 N/f 312.…”

Section: Overview Of the Runsmentioning

confidence: 99%

Scaling laws for mixing and dissipation in unforced rotating stratified turbulence

Pouquet

Rosenberg²,

Marino

et al. 2018

J. Fluid Mech.

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We present a model for the scaling of mixing in weakly rotating stratified flows characterized by their Rossby, Froude and Reynolds numbers Ro, F r, Re. It is based on quasiequipartition between kinetic and potential modes, sub-dominant vertical velocity w, and lessening of the energy transfer to small scales as measured by a dissipation efficiency β = V / D , with V the kinetic energy dissipation and D = u 3 rms /L int its dimensional expression, w, u rms the vertical and rms velocities, and L int the integral scale. We determine the domains of validity of such laws for a large numerical study of the unforced Boussinesq equations mostly on grids of 1024 3 points, with Ro/F r 2.5, and with 1600 Re ≈ 5.4 × 10 4 ; the Prandtl number is one, initial conditions are either isotropic and at large scale for the velocity, and zero for the temperature θ, or in geostrophic balance. Three regimes in Froude number, as for stratified flows, are observed: dominant waves, eddy-wave interactions and strong turbulence. A wave-turbulence balance for the transfer time τ tr = N τ 2 N L , with τ N L = L int /u rms the turn-over time and N the Brunt-Väisälä frequency, leads to β growing linearly with F r in the intermediate regime, with a saturation at β ≈ 0.3 or more, depending on initial conditions for larger Froude numbers. The Ellison scale is also found to scale linearly with F r. The flux Richardson number, with B f = N wθ the buoyancy flux, transitions for roughly the same parameter values as for β. These regimes for the present study are delimited bythe mixing efficiency, putting together the three relationships of the model allows for the prediction of the scaling Γ f ∼ F r −2 ∼ R −1 B in the low and intermediate regimes for high Re, whereas for higher Froude numbers, Γ f ∼ R −1/2 B, a scaling already found in observations: as turbulence strengthens, β ∼ 1, w ≈ u rms , and smaller buoyancy fluxes altogether correspond to a decoupling of velocity and temperature fluctuations, the latter becoming passive.

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“…It is less clear what the impact this rotation has on small scale turbulent mixing, especially in a role that is coupled with stratification [31]. The inclusion of rotation has led to increased study of inertial gravity waves and what is classified as rotating stratified turbulence (RST) [22,23,29,37,38]. An important question that has not been clearly answered is whether or not the inclusion of rotation will impact the existing parameterizations for the irreversible mixing e ciency in stably stratified flows that mostly do not account for the rotation.…”

Section: Introductionmentioning

confidence: 99%

“…Direct numerical simulations (DNS) have been an important avenue for understanding stratified turbulence both with and without the influence of rotation [4,14,18,20,21,29,30,32,35,37,38,44]. Recent work using DNS has led to some insights and parameterizations of small-scale mixing [9,17,19,25] by trying to answer questions about turbulent mixing in geophysical flows and demonstrating how DNS can be useful and informative to the broader study of geophysical flows.…”

Section: Introductionmentioning

confidence: 99%

Effect of rotation on mixing efficiency in homogeneous stratified turbulence using unforced direct numerical simulations

et al. 2022

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Diapycnal (irreversible) mixing is analyzed using thirty high resolution direct numerical simulations of homogeneous rotating stratified turbulence (RST) in the absence of imposed shear or forcing. Influence of varied rotation and stratification on the energetics (in particular the dissipation rates of kinetic and potential energies) is presented. Data is also presented in new a parametric framework using the turbulent Froude and Rossby numbers F r t = ✏/N k, Ro t = ✏/f k, where k is the turbulent kinetic energy, ✏ its rate of dissipation, N the buoyancy frequency and f the Coriolis parameter. This framework is used to illustrate relative Irreversible mixing in rotating, stratified turbulence magnitudes of the stratification and rotation in geophysical flows and provide a useful tool for explicating the relationship between F r t and Ro t . Results indicate that rotation does not impact the magnitude of the irreversible mixing coe cient ( = ✏ P /✏) when compared to results without rotation, where ✏ P is the rate of potential energy dissipation. Moreover, it is shown that the recent scaling laws for mixing e ciency in stably stratified in the absence of rotation, as exemplified in Garanaik & Venayagamoorthy (J. Fluid Mech. 867, 2019, pp. 323-333), are applicable as well for homogeneous and decaying RST. Results also highlight the ambiguity of the ratio N/f as a control parameter for the classification of small-scale RST, and thus for evaluating diapycnal mixing.

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Correction to: Variations of characteristic time scales in rotating stratified turbulence using a large parametric numerical study

Cited by 3 publications

References 2 publications

Generation of turbulence through frontogenesis in sheared stratified flows

Generation of turbulence through frontogenesis in sheared stratified flows

Scaling laws for mixing and dissipation in unforced rotating stratified turbulence

Effect of rotation on mixing efficiency in homogeneous stratified turbulence using unforced direct numerical simulations

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