Resolving the paradox of oceanic large-scale balance and small-scale mixing

Evidence of dual energy transfer driven by magnetic reconnection at subion scales

The properties of energy transfer in the kinetic range of plasma turbulence have fundamental implications on the turbulent heating of space and astrophysical plasmas. It was suggested that magnetic reconnection may be responsible for driving the subion scale cascade, and that this process would be characterized by a direct energy transfer toward even smaller scales (until dissipation), and a simultaneous inverse transfer of energy toward larger scales, until the ion break. Here we employ the space-filter technique on high-resolution 2D3V hybrid-Vlasov simulations of continuously driven turbulence providing quantitative evidence that magnetic reconnection is indeed able to trigger a dual energy transfer originating at subion scales.

Lagrangian Irreversibility and Energy Exchanges in Rotating-Stratified Turbulent Flows

Turbulence in stratified and rotating turbulent flows is characterized by an interplay between waves and eddies, resulting in continuous exchanges between potential and kinetic energy. Here, we study how these processes affect the turbulent energy cascade from large to small scales, which manifests itself by an irreversible evolution of the relative kinetic energy between two tracer particles. We find that when r_{0}, the separation between particles, is below a characteristic length ℓ_{t}, potential energy is on average transferred to kinetic energy, reducing time irreversibility, and conversely when r_{0}>ℓ_{t}. Our Letter reveals that the scale ℓ_{t} coincides with the buoyancy length scale L_{B} over a broad range of configurations until a transition to a wave-dominated regime is reached.

Large-scale self-organization in dry turbulent atmospheres

How turbulent convective fluctuations organize to form larger-scale structures in planetary atmospheres remains a question that eludes quantitative answers. The assumption that this process is the result of an inverse cascade was suggested half a century ago in two-dimensional fluids, but its applicability to atmospheric and oceanic flows remains heavily debated, hampering our understanding of the energy balance in planetary systems. We show using direct numerical simulations with spatial resolutions of 122882 × 384 points that rotating and stratified flows can support a bidirectional cascade of energy, in three dimensions, with a ratio of Rossby to Froude numbers comparable to that of Earth's atmosphere. Our results establish that, in dry atmospheres, spontaneous order can arise through an inverse cascade to the largest spatial scales.

Direct observational evidence of an oceanic dual kinetic energy cascade and its seasonality

The ocean's turbulent energy cycle has a paradox; large-scale eddies under the control of Earth's rotation transfer kinetic energy (KE) to larger scales via an inverse cascade, while a transfer to smaller scales is needed for dissipation. It has been hypothesized, using simulations, that fronts, waves, and other turbulent structures can produce a forward cascade of KE toward dissipation scales. However, this forward cascade and its coexistence with the inverse cascade have never been observed. Here, we present the first evidence of a dual KE cascade in the ocean by analyzing in situ velocity measurements from surface drifters. Our results show that KE is injected at two dominant scales and transferred to both large and small scales, with the downscale flux dominating at scales smaller than ∼1 to 10 km. The cascade rates are modulated seasonally, with stronger KE injection and downscale transfer during winter.

Helical fluid and (Hall)-MHD turbulence: a brief review

Helicity, a measure of the breakage of reflectional symmetry representing the topology of turbulent flows, contributes in a crucial way to their dynamics and to their fundamental statistical properties. We review several of their main features, both new and old, such as the discovery of bi-directional cascades or the role of helical vortices in the enhancement of large-scale magnetic fields in the dynamo problem. The dynamical contribution in magnetohydrodynamic of the cross-correlation between velocity and induction is discussed as well. We consider next how turbulent transport is affected by helical constraints, in particular in the context of magnetic reconnection and fusion plasmas under one- and two-fluid approximations. Central issues on how to construct turbulence models for non-reflectionally symmetric helical flows are reviewed, including in the presence of shear, and we finally briefly mention the possible role of helicity in the development of strongly localized quasi-singular structures at small scale. This article is part of the theme issue 'Scaling the turbulence edifice (part 2)'.

Destabilizing resonances of precessing inertia-gravity waves

Instabilities in stratified precessing fluid are investigated. We extend the study by Mahalov [Phys. Fluids A 5, 891 (1993)0899-821310.1063/1.858635] in the stably stratified Boussinesq framework, with an external Coriolis force (with rate Ω_{p}) altering the base flow through the distortion of the circular streamlines of the unperturbed axially stratified rotating columns (with constant vorticity 2Ω.) It is shown that the inviscid part of the modified velocity flow (0,Ωr,-2ɛΩrsinφ) and buoyancy with gradient N^{2}(-2ɛcosφ,2ɛsinφ,1) are an exact solution of Boussinesq-Euler equations. Here (r,φ,z) is a cylindrical coordinate system, with ɛ=Ω_{p}/Ω being the Poincaré number and N the Brunt-Väisälä frequency. The base flow is transformed into a Cartesian coordinate system, and the stability of a superimposed perturbation is studied in terms of Fourier (or Kelvin) modes. The resulting Floquet system for the Fourier modes has three parameters: ɛ, N=N/Ω, and μ, which is the angle between the wave vector k and the solid-body rotation axis in the limit ɛ=0. In this limit, there are inertia-gravity waves propagating with frequency ±ω and the resonant cases are those for which 2ω=nΩ, n being an integer. We perform an asymptotic analysis to leading order in ɛ and characterize the destabilizing resonant case of order n=1 (i.e., the subharmonic instability) which exists and for 0≤N<Ω/2. In this range, the subharmonic instability remains the strongest with a maximal growth rate σ_{m}=[ɛ(5sqrt[15]/8)sqrt[1-4N^{2}]/(4-N^{2})]. Stable stratification acts in such a way as to make the subharmonic instability less efficient, so as it disappears for N≥0.5Ω. The destabilizing resonant cases of order n=2,3,4,5 are investigated in detail by numerical computations. The effect of viscosity on these instabilities is briefly addressed assuming the diffusive coefficients (kinematic and thermal) are equal. Likewise, we briefly investigate the case where N^{2}<0 and show that the instability associated to the mode with k_{3}=0 is the strongest.

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

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 ϵ 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 ϵ 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.

The hammam effect or how a warm ocean enhances large scale atmospheric predictability

The atmosphere's chaotic nature limits its short-term predictability. Furthermore, there is little knowledge on how the difficulty of forecasting weather may be affected by anthropogenic climate change. Here, we address this question by employing metrics issued from dynamical systems theory to describe the atmospheric circulation and infer the dynamical properties of the climate system. Specifically, we evaluate the changes in the sub-seasonal predictability of the large-scale atmospheric circulation over the North Atlantic for the historical period and under anthropogenic forcing, using centennial reanalyses and CMIP5 simulations. For the future period, most datasets point to an increase in the atmosphere's predictability. AMIP simulations with 4K warmer oceans and 4 × atmospheric CO2 concentrations highlight the prominent role of a warmer ocean in driving this increase. We term this the hammam effect. Such effect is linked to enhanced zonal atmospheric patterns, which are more predictable than meridional configurations.

Turbulence-Driven Ion Beams in the Magnetospheric Kelvin-Helmholtz Instability

The description of the local turbulent energy transfer and the high-resolution ion distributions measured by the Magnetospheric Multiscale mission together provide a formidable tool to explore the cross-scale connection between the fluid-scale energy cascade and plasma processes at subion scales. When the small-scale energy transfer is dominated by Alfvénic, correlated velocity, and magnetic field fluctuations, beams of accelerated particles are more likely observed. Here, for the first time, we report observations suggesting the nonlinear wave-particle interaction as one possible mechanism for the energy dissipation in space plasmas.

Log-Normal Turbulence Dissipation in Global Ocean Models

Data from turbulent numerical simulations of the global ocean demonstrate that the dissipation of kinetic energy obeys a nearly log-normal distribution even at large horizontal scales O(10  km). As the horizontal scales of resolved turbulence are larger than the ocean is deep, the Kolmogorov-Yaglom theory for intermittency in 3D homogeneous, isotropic turbulence cannot apply; instead, the down-scale potential enstrophy cascade of quasigeostrophic turbulence should. Yet, energy dissipation obeys approximate log-normality-robustly across depths, seasons, regions, and subgrid schemes. The distribution parameters, skewness and kurtosis, show small systematic departures from log-normality with depth and subgrid friction schemes. Log-normality suggests that a few high-dissipation locations dominate the integrated energy and enstrophy budgets, which should be taken into account when making inferences from simplified models and inferring global energy budgets from sparse observations.

Submesoscale currents in the ocean

This article is a perspective on the recently discovered realm of submesoscale currents in the ocean. They are intermediate-scale flow structures in the form of density fronts and filaments, topographic wakes and persistent coherent vortices at the surface and throughout the interior. They are created from mesoscale eddies and strong currents, and they provide a dynamical conduit for energy transfer towards microscale dissipation and diapycnal mixing. Consideration is given to their generation mechanisms, instabilities, life cycles, disruption of approximately diagnostic force balance (e.g. geostrophy), turbulent cascades, internal-wave interactions, and transport and dispersion of materials. At a fundamental level, more questions remain than answers, implicating a programme for further research.

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

We study rotating stratified turbulence (RST) making use of numerical data stemming from a large parametric study varying the Reynolds, Froude and Rossby numbers, Re, Fr and Ro in a broad range of values. The computations are performed using periodic boundary conditions on grids of 1024(3) points, with no modeling of the small scales, no forcing and with large-scale random initial conditions for the velocity field only, and there are altogether 65 runs analyzed in this paper. The buoyancy Reynolds number defined as R(B) = ReFr2 varies from negligible values to ≈ 10(5), approaching atmospheric or oceanic regimes. This preliminary analysis deals with the variation of characteristic time scales of RST with dimensionless parameters, focusing on the role played by the partition of energy between the kinetic and potential modes, as a key ingredient for modeling the dynamics of such flows. We find that neither rotation nor the ratio of the Brunt-Väisälä frequency to the inertial frequency seem to play a major role in the absence of forcing in the global dynamics of the small-scale kinetic and potential modes. Specifically, in these computations, mostly in regimes of wave turbulence, characteristic times based on the ratio of energy to dissipation of the velocity and temperature fluctuations, T(V) and T(P), vary substantially with parameters. Their ratio γ=T(V)/T(P) follows roughly a bell-shaped curve in terms of Richardson number Ri. It reaches a plateau - on which time scales become comparable, γ≈0.6 - when the turbulence has significantly strengthened, leading to numerous destabilization events together with a tendency towards an isotropization of the flow.

Stably stratified turbulence in the presence of large-scale forcing

We perform two high-resolution direct numerical simulations of stratified turbulence for Reynolds number equal to Re≈25000 and Froude number, respectively, of Fr≈0.1 and Fr≈0.03. The flows are forced at large scale and discretized on an isotropic grid of 2048(3) points. Stratification makes the flow anisotropic and introduces two extra characteristic scales with respect to homogeneous isotropic turbulence: the buoyancy scale, L(B), and the Ozmidov scale, ℓ(oz). The former is related to the number of layers that the flow develops in the direction of gravity, and the latter is regarded as the scale at which isotropy is recovered. The values of L(B) and ℓ(oz) depend on the Froude number, and their absolute and relative amplitudes affect the repartition of energy among Fourier modes in ways that are not easy to predict. By contrasting the behavior of the two simulated flows we identify some surprising similarities: After an initial transient the two flows evolve towards comparable values of the kinetic and potential enstrophy and energy dissipation rate. This is the result of the Reynolds number being large enough in both flows for the Ozmidov scale to be resolved. When properly dimensionalized, the energy dissipation rate is compatible with atmospheric observations. Further similarities emerge at large scales: The same ratio between potential and total energy (≈0.1) is spontaneously selected by the flows, and slow modes grow monotonically in both regimes, causing a slow increase of the total energy in time. The axisymmetric total energy spectrum shows a wide variety of spectral slopes as a function of the angle between the imposed stratification and the wave vector. One-dimensional energy spectra computed in the direction parallel to gravity are flat from the forcing up to buoyancy scale. At intermediate scales a ∼k(-3) parallel spectrum develops for the Fr≈0.03 run, whereas for weaker stratification, the saturation spectrum does not have enough scales to develop and instead one observes a power law compatible with Kolmogorov scaling. Finally, the spectrum of helicity is flat until L(B), as observed in the nocturnal planetary boundary layer.