Vertical drafts and mixing in stratified turbulence: Sharp transition with Froude number

Feraco, Fabio; Marino, Raffaele; Pumir, Alain; Primavera, Leonardo; Mininni, Pablo D.; Pouquet, A.; Rosenberg, Duane

doi:10.1209/0295-5075/123/44002

Cited by 59 publications

(116 citation statements)

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“…[23]). Such a marginal state close to a threshold almost everywhere can be modeled through simplified dynamical systems following field gradients [17,18,22,24], in line with classical approaches in turbulence, as reviewed e.g. in [25].…”

Section: Introductionmentioning

confidence: 91%

“…In fact, strong vertical winds, as well as vertically sheared horizontal winds, can be viewed as common features of stably stratified turbulence [17], in the presence or not of rotation. Even though such a behavior takes place in a narrow range of the control parameter [18], it affects measurably the overall dynamics of the flow, with a slow return to isotropy at small scale [2,19,20], together with strong localized mixing, dissipation and intermittency for Richardson numbers close to the threshold of linear or convective instabilities [20][21][22]. Furthermore, the trajectories of Lagrangian particles are also measurably modified in the vicinity of shear layers (see, e.g.…”

Section: Introductionmentioning

confidence: 99%

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Coupling Large Eddies and Waves in Turbulence: Case Study of Magnetic Helicity at the Ion Inertial Scale

2020

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In turbulence, for neutral or conducting fluids, a large ratio of scales is excited because of the possible occurrence of inverse cascades to large, global scales together with direct cascades to small, dissipative scales, as observed in the atmosphere and oceans, or in the solar environment. In this context, using direct numerical simulations with forcing, we analyze scale dynamics in the presence of magnetic fields with a generalized Ohm's law including a Hall current. The ion inertial length H serves as the control parameter at fixed Reynolds number. Both the magnetic and generalized helicity -invariants in the ideal case -grow linearly with time, as expected from classical arguments. The cross-correlation between the velocity and magnetic field grows as well, more so in relative terms for a stronger Hall current. We find that the helical growth rates vary exponentially with H , provided the ion inertial scale resides within the inverse cascade range. These exponential variations are recovered phenomenologically using simple scaling arguments. They are directly linked to the wavenumber power-law dependence of generalized and magnetic helicity, ∼ k −2 , in their inverse ranges. This illustrates and confirms the important role of the interplay between large and small scales in the dynamics of turbulent flows. arXiv:2001.11625v1 [physics.flu-dyn] 31 Jan 2020 and large scales play an essential role in estimating the efficiency of mixing in such flows [28][29][30], and it is found to vary linearly with the control parameter, namely the Froude number [31,32]. B. The case of space plasmasSimilar phenomena are observed as well for turbulent flows in the presence of magnetic fields. Such fields, together with charged particles, are abundant in the cosmos. At large scales, the magnetohydrodynamic (MHD) approximation, in which the displacement current is neglected in Maxwell's equations, is adequate, and observations of the Solar Wind, dating back to the Voyager spacecraft, confirmed the physical description of a medium governed by the interactions of turbulent, nonlinear eddies and Alfvén waves (see, e.g., for recent reviews, [33-36] and references therein). Turbulence is also found to play a central role in shaping these media [37][38][39].However, as the direct turbulent cascade of energy approaches smaller scales, plasma effects and dispersive waves come into effect, appearing for example through a generalized Ohm's law whose expression depends on the degree of ionization of the medium, which itself can differ greatly from the solar wind to the interstellar gas. Current spacecraft technologies allow for the resolution of much smaller temporal and spatial scales than what was available previously, and one can now reach the ion inertial length, H , and perhaps the electron inertial length (see for definitions the next section, and e.g. [40]). Other types of waves, kinetic Alfvén waves or whistler waves for example, come into play between the ion and electron scales, and the distribution of energy among modes is altered...

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Section: Introductionmentioning

confidence: 91%

Section: Introductionmentioning

confidence: 99%

Coupling Large Eddies and Waves in Turbulence: Case Study of Magnetic Helicity at the Ion Inertial Scale

2020

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“…The presence of waves affects directly turbulent flows in lessening the rate at which energy is dissipated. It has been observed in several instances (Alexakis, 2013;Campagne et al, 2016;Feraco et al, 2018;Maffioli et al, 2016;Pouquet et al, 2017), within the case of rotating stratified flows, a clear linear dependence of the measured dissipation on the control parameter, the Froude number in an intermediate regime of eddy-wave interactions Pouquet et al, 2018). On the other hand, the Rossby number controls the amount of energy going to the large scales in a simultaneous inverse cascade, whereas for MHD the control parameter is the magnitude of the large-scale imposed magnetic field.…”

Section: 1029/2018ea000432mentioning

confidence: 97%

“…Similarly, the non‐Gaussian wings observed, for example, in four‐wave interactions for Langmuir waves are associated with wave breaking, and intermittency is stronger when the linear and nonlinear characteristic times become comparable (Choi et al, ). A simple case of such a strong intermittency, when linear and nonlinear characteristic times are comparable, is that of the vertical velocity of rotating stratified flows; a model for it can be developed for a Philipps saturation spectrum (Dewan, ), as shown, for example, in recent direct numerical simulations (DNS; Feraco et al, ; Rorai et al, ), or when the shorter time scale of the problem is that associated with random sweeping (Clark di Leoni et al, ).…”

Section: Introductionmentioning

confidence: 99%

Helicity Dynamics, Inverse, and Bidirectional Cascades in Fluid and Magnetohydrodynamic Turbulence: A Brief Review

Pouquet

Rosenberg

Stawarz

et al. 2019

Earth and Space Science

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We briefly review helicity dynamics, inverse and bidirectional cascades in fluid and magnetohydrodynamic (MHD) turbulence, with an emphasis on the latter. The energy of a turbulent system, an invariant in the nondissipative case, is transferred to small scales through nonlinear mode coupling. Fifty years ago, it was realized that, for a two‐dimensional fluid, energy cascades instead to larger scales and so does magnetic excitation in MHD. However, evidence obtained recently indicates that, in fact, for a range of governing parameters, there are systems for which their ideal invariants can be transferred, with constant fluxes, to both the large scales and the small scales, as for MHD or rotating stratified flows, in the latter case including quasi‐geostrophic forcing. Such bidirectional, split, cascades directly affect the rate at which mixing and dissipation occur in these flows in which nonlinear eddies interact with fast waves with anisotropic dispersion laws, due, for example, to imposed rotation, stratification, or uniform magnetic fields. The directions of cascades can be obtained in some cases through the use of phenomenological arguments, one of which we derive here following classical lines in the case of the inverse magnetic helicity cascade in electron MHD. With more highly resolved data sets stemming from large laboratory experiments, high‐performance computing, and in situ satellite observations, machine learning tools are bringing novel perspectives to turbulence research. Such algorithms help devise new explicit subgrid‐scale parameterizations, which in turn may lead to enhanced physical insight, including in the future in the case of these new bidirectional cascades.

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“…But this is not the only way in which finite dimensional dynamical systems can help us unveil the dynamics of complex flows. Extreme events, associated to intermittency, are important in the atmosphere and the ocean, where turbulence is also ubiquitous [7][8][9]. In homogeneous and isotropic turbulence (HIT) intermittency has been captured by two dimensional restricted Euler models [10].…”

Section: Introductionmentioning

confidence: 99%

Invariant manifolds in stratified turbulence

2019

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We present a reduced system of 7 ordinary differential equations that captures the time evolution of spatial gradients of the velocity and the temperature in fluid elements of stratified turbulent flows. We show the existence of invariant manifolds (further reducing the system dimensionality), and compare the results with data stemming from direct numerical simulations of the full incompressible Boussinesq equations in the stably stratified case. Numerical results accumulate over the invariant manifolds of the reduced system, indicating the system lives at the brink of an instability. Finally, we study the stability of the reduced system, and show that it is compatible with recent observations in stratified turbulence of non-monotonic dependence of intermittency with stratification.

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Vertical drafts and mixing in stratified turbulence: Sharp transition with Froude number

Cited by 59 publications

References 37 publications

Coupling Large Eddies and Waves in Turbulence: Case Study of Magnetic Helicity at the Ion Inertial Scale

Coupling Large Eddies and Waves in Turbulence: Case Study of Magnetic Helicity at the Ion Inertial Scale

Helicity Dynamics, Inverse, and Bidirectional Cascades in Fluid and Magnetohydrodynamic Turbulence: A Brief Review

Invariant manifolds in stratified turbulence

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