Isotropization at small scales of rotating helically driven turbulence

Mininni, Pablo D.; Rosenberg, Duane; Pouquet, A.

doi:10.1017/jfm.2012.99

Cited by 76 publications

(130 citation statements)

References 53 publications

Supporting

Mentioning

111

Contrasting

Order By: Relevance

“…Fourier spectra will be built-up from their axisymmetric counterparts defined from the two-point one-time velocity covariance U (k) (see, e.g., [2])…”

Section: A Equationsmentioning

confidence: 99%

“…Similarly, in a purely rotating flow, isotropy recovers beyond the Zeman scale for R Ω ≥ 1 [2]. The partition of energy between kinetic and potential modes can be measured by their ratio, E V /E P , which is one possible definition of the Richardson number.…”

Section: Other Dimensionless Parametersmentioning

confidence: 99%

“…For R B >> 1, a Kolmogorov range, typical of isotropic and homogeneous turbulence, develops before dissipation can become effective. One can similarly define the Zeman scale, Ω = 2π ε V /f 3 , for recovery of isotropy in a purely rotating flow, as shown in [2]. According to the relative values of these parameters, several ranges can co-exist, with one effect overcoming others in each range (say, nonlinearities over wave motions or vice-versa).…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Evidence for Bolgiano-Obukhov scaling in rotating stratified turbulence using high-resolution direct numerical simulations

et al. 2015

Self Cite

View full text Add to dashboard Cite

We report results on rotating stratified turbulence in the absence of forcing, with large-scale isotropic initial conditions, using direct numerical simulations computed on grids of up to 4096 3 points. The Reynolds and Froude numbers are respectively equal to Re = 5.4×10 4 and F r = 0.0242. The ratio of the Brunt-Väisälä to the inertial wave frequency, N/f , is taken to be equal to 4.95, a choice appropriate to model the dynamics of the southern abyssal ocean at mid latitudes. This gives a global buoyancy Reynolds number RB = ReF r 2 = 32, a value sufficient for some isotropy to be recovered in the small scales beyond the Ozmidov scale, but still moderate enough that the intermediate scales where waves are prevalent are well resolved. We concentrate on the largescale dynamics, for which we find a spectrum compatible with the Bolgiano-Obukhov scaling, and confirm that the Froude number based on a typical vertical length scale is of order unity, with strong gradients in the vertical. Two characteristic scales emerge from this computation, and are identified from sharp variations in the spectral distribution of either total energy or helicity. A spectral break is also observed at a scale at which the partition of energy between the kinetic and potential modes changes abruptly, and beyond which a Kolmogorov-like spectrum recovers. Large slanted layers are ubiquitous in the flow in the velocity and temperature fields, with local overturning events indicated by small Richardson numbers, and a small large-scale enhancement of energy directly attributable to the effect of rotation is also observed.

show abstract

“…Fourier spectra will be built-up from their axisymmetric counterparts defined from the two-point one-time velocity covariance U (k) (see, e.g., [2])…”

Section: A Equationsmentioning

confidence: 99%

Section: Other Dimensionless Parametersmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Evidence for Bolgiano-Obukhov scaling in rotating stratified turbulence using high-resolution direct numerical simulations

et al. 2015

Self Cite

View full text Add to dashboard Cite

show abstract

“…In order to characterize the anisotropy that develops in the flow, we use different definitions for the energy spectrum, as well as for anisotropic fluxes. We start from the axisymmetric kinetic energy spectrum defined as [62,63]:…”

Section: Simulations Of Rotating and Stratified Flowsmentioning

confidence: 99%

Large-scale anisotropy in stably stratified rotating flows

et al. 2014

Self Cite

View full text Add to dashboard Cite

We present results from direct numerical simulations of the Boussinesq equations in the presence of rotation and/or stratification, both in the vertical direction. The runs are forced isotropically and randomly at small scales and have spatial resolutions of up to 1024 3 grid points and Reynolds numbers of ≈ 1000. We first show that solutions with negative energy flux and inverse cascades develop in rotating turbulence, whether or not stratification is present. However, the purely stratified case is characterized instead by an early-time, highly anisotropic transfer to large scales with almost zero net isotropic energy flux. This is consistent with previous studies that observed the development of vertically sheared horizontal winds, although only at substantially later times. However, and unlike previous works, when sufficient scale separation is allowed between the forcing scale and the domain size, the total energy displays a perpendicular (horizontal) spectrum with power law behavior compatible with ∼ k −5/3 ⊥ , including in the absence of rotation. In this latter purely stratified case, such a spectrum is the result of a direct cascade of the energy contained in the large-scale horizontal wind, as is evidenced by a strong positive flux of energy in the parallel direction at all scales including the largest resolved scales.

show abstract

“…In rotating turbulent flows, quadratic quantities in the fields, such as the energy, the helicity, and the enstrophy, are often characterized with isotropic and anisotropic spectra [5,8,9] (or, equivalently, with second-order structure functions [10,11]) following power laws in the inertial range. However, turbulent flows tend also to be intermittent [12,13].…”

Section: Introductionmentioning

confidence: 99%

Sign cancellation and scaling in the vertical component of velocity and vorticity in rotating turbulence

Horne

Mininni

2013

Phys. Rev. E

Self Cite

View full text Add to dashboard Cite

We study sign changes and scaling laws in the Cartesian components of the velocity and vorticity of rotating turbulence, in the helicity, and in the components of vertically averaged fields. Data for the analysis are provided by high-resolution direct numerical simulations of rotating turbulence with different forcing functions, with up to 1536 3 grid points, with Reynolds numbers between ≈1100 and ≈5100, and with moderate Rossby numbers between ≈0.06 and ≈8. When rotation is negligible, all Cartesian components of the velocity show similar scaling, in agreement with the expected isotropy of the flow. However, in the presence of rotation, only the vertical components of the fields show clear scaling laws, with evidence of possible sign singularity in the limit of an infinite Reynolds number. Horizontal components of the velocity are smooth and do not display rapid fluctuations for arbitrarily small scales. The vertical velocity and vorticity, as well as the vertically averaged vertical velocity and vorticity, show the same scaling within error bars, in agreement with theories that predict that these quantities have the same dynamical equation for very strong rotation.

show abstract

Isotropization at small scales of rotating helically driven turbulence

Cited by 76 publications

References 53 publications

Evidence for Bolgiano-Obukhov scaling in rotating stratified turbulence using high-resolution direct numerical simulations

Evidence for Bolgiano-Obukhov scaling in rotating stratified turbulence using high-resolution direct numerical simulations

Large-scale anisotropy in stably stratified rotating flows

Sign cancellation and scaling in the vertical component of velocity and vorticity in rotating turbulence

Contact Info

Product

Resources

About