In the presence of stratification, turbulent flows exhibit intermittency not only at small scales but also at large scales, comparable to the mean flow, as observed in the atmosphere and oceans. We study such flows through a large parametric exploration using direct numerical simulations of the Boussinesq equations with different forcing types. We examine two Prandtl numbers (1 and 6) and vary the Froude number (Fr) over a range of geophysical interest values, 0.01≤ Fr ≤ 1, corresponding to a variation in terms of the buoyancy Reynolds number (R_IB) of 0.06≤ R_IB≤ 2300. We analyze the dependence on R_IB of the buoyancy flux (B_f), the mixing efficiency, the shear parameters, and the vertical momentum flux. Strongly non-Gaussian tails in the spatio-temporal distribution of the B_f are observed, with kurtosis reaching ≈ 10^2, indicating the potential for stratified geophysical flows to be characterized by highly variable transport properties along the direction of gravity even under stable stratification. This is associated with long-time intermittent behavior of vertical velocity and temperature at large scale, which produces local turbulence and enhances dissipation and transport. We present evidence that the skewness of B_f increases with R_IB as a power-law and saturates in the passive-scalar limit. We also show that the domain-averaged B_f exhibits two distinct trends: logarithmic growth with R_IB and approach to a small offset as stratification strengthens. A simple model for the temporal evolution of energy and B_f indicates that the defect between vertical and potential energy drives strong B_f events. This trend directly leads to convective instabilities, the formation of two-dimensional and three-dimensional eddies, and rapid dissipation on a turnover timescale, allowing the energetic cycle to restart-also occurring in bursts.

The transport of matter by turbulent flows plays an important role, in particular in a geophysical context. Here, we study the relative movement of groups of two (pairs) and four (tetrahedra) Lagrangian particles using direct numerical simulations of the stably-stratified Boussinsesq equations, with Brunt-Väisälä frequency N and Coriolis parameter f. We cover regimes close to homogeneous isotropic turbulence, to flows dominated by stratification and rotation, keeping fixed the ratio N/f = 5. The flows studied are anisotropic, so the relative motion between two particles depends not only on the initial separation between the particles, but also on their orientation with respect to the vertical axis. In all cases considered, we demonstrate that the relative particle motion differs depending on whether dispersion is considered forward or backwards in time, although the asymmetry becomes less pronounced when stratification and rotation increase. On the other hand, the strong fluctuations in the dispersion between two particles become more extreme when N and f increase. We also find evidence for the formation of shear layers, which become more pronounced as N and f become larger. Finally, we show that the irreversibility on the dispersion of a set of particles forming initially a regular tetrahedron becomes weaker when the influence of stratification and rotation increase, a property that we relate to that of the perceived rate-of-strain tensor.

AbstractThe mesosphere and lower thermosphere (MLT) is a fluid framework whose multiscale dynamics is determined by a superposition of non‐linear processes and by the interplay of gravity waves and turbulent motions. A thorough comprehension of this atmospheric region requires substantial observational infrastructure, needed to resolve and disentangle its complex dynamics. State‐of‐the‐art observational methods struggle to accurately capture mesoscale dynamics due to the inherent difficulty to perform observations at MLT altitudes. A majority of the observational methods rely on assumptions such as homogeneity, smoothness of the prognostic fields, or zero vertical wind velocities, which may not hold in the upper atmosphere at the mesoscales. In this study, we introduce a novel machine learning‐based approach HYPER (HYdrodynamic Point‐wise Environment Reconstructor), designed to characterize MLT dynamics. HYPER utilizes a physics‐informed neural network to project sparse Doppler meteor detections into four‐dimensional time‐series arrays containing the Cartesian components of the velocity field. This method combines meteor radar observations with the physics prescribed by the Navier‐Stokes equations. The validation of HYPER was conducted through a series of benchmarks on numerical data and the application of our algorithm on actual meteor radar observations, all of which yielded realistic approximations of the reconstructed physical fields. This innovative approach represents a significant step toward an accurate characterization of the MLT dynamics, overcoming the limitations of existing methods, and providing valuable insights into the behavior of this poorly accessible region of the atmosphere.

In this study we consider a freely decaying, stably stratified homogeneous magnetohydrodynamic turbulent plasma with a weak vertical background magnetic field (B-0 = B0z<^>), aligned with the density gradient of strength NN (i.e. Brunt-Vaisala frequency). Both linear theory and direct numerical simulations (DNS) are used to analyse the flow dynamics for a Boussinesq fluid with unitary magnetic and thermal Prandtl numbers. We implemented a normal mode decomposition emphasizing different types of motions depending on whether both the Froude F-r and Alfven-Mach MM numbers are small or only F-r is small but MM is finite. In the former case, there is a non-propagating (NP) mode and fast modes: Alfven waves with frequency omega a omega a and magnetogravity waves with frequency omega(.)(ag) In the latter case, there are fast gravity waves with frequency omega(g) and slow modes: NP mode and slow Alfven waves. The numerical simulations carried out are started from initial isotropic conditions with zero initial magnetic and density fluctuations, so that the initial energy of the NP mode is strictly zero, for 0 < B-0/(LiN) <= 0.12 and a weak mean magnetic field (B-0 = 0.2 or B-0= 0.4), where L-i denotes the isotropic integral length scale. The DNS results indicate a weak turbulence regime for which F-r is small and MM is finite. It is found that the vertical magnetic energy as well as the energy of the NP mode are drastically reduced as NN increases, while there is instead a forward cascade even for the magnetic field. The contribution coming from the energy of fast (gravity) waves does not exceed 50%,50%, while that coming from the energy of the NP mode does not exceed 10%.10%. Vertical motions are more affected by the effect of stratification than by the effect of the mean magnetic field, while it is the opposite for horizontal motions. We show that the spectrum of slow (Alfven) waves and fast (gravity) waves tends to follow the power law k(perpendicular to)(-3) for a wide range of time, 3 < t < 20. At high vertical (or horizontal) wave numbers, the main contribution to total energy comes from the energy of slow Alfven waves. At large and intermediate horizontal (or vertical) scales, the spectra of the energy of NP mode exhibit a flat shape.

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.

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 study reveals that the scale ℓ_t coincides with the buoyancy length scale L_B over a broad range of configurations until a transitional wave-dominated regime is reached.

Simulating plasmas in the Hall-magnetohydrodynamics (Hall-MHD) regime represents a valuable approach for the investigation of complex nonlinear dynamics developing in astrophysical frameworks and fusion machines. The Hall electric field is computationally very challenging as it involves the integration of an additional term, proportional to $\boldsymbol {\nabla } \times ((\boldsymbol {\nabla }\times \boldsymbol {B})\times \boldsymbol {B})$, in Faraday's induction law. The latter feeds back on the magnetic field $B$ at small scales (between the ion and electron inertial scales), requiring very high resolutions in both space and time to properly describe its dynamics. The computational advantage provided by the kinetic lattice Boltzmann (LB) approach is exploited here to develop a new code, the fast lattice-Boltzmann algorithm for MHD experiments (flame). The flame code integrates the plasma dynamics in lattice units coupling two kinetic schemes, one for the fluid protons (including the Lorentz force), the other to solve the induction equation describing the evolution of the magnetic field. Here, the newly developed algorithm is tested against an analytical wave-solution of the dissipative Hall-MHD equations, pointing out its stability and second-order convergence, over a wide range of the control parameters. Spectral properties of the simulated plasma are finally compared with those obtained from numerical solutions from the well-established pseudo-spectral code ghost. Furthermore, the LB simulations we present, varying the Hall parameter, highlight the transition from the MHD to the Hall-MHD regime, in excellent agreement with the magnetic field spectra measured in the solar wind.

Ocean turbulence causes flows to split into smaller whirls or merge to make larger whirls, cascading energy to small or large scales respectively. Conventional ocean dynamics dictates that the kinetic energy in the ocean will cascade primarily to larger scales, via the inverse energy cascade, and has raised the question of how the kinetic energy in the ocean dissipates, which would necessarily require the transfer towards the molecular scales. However, so far no clear observational quantification of the energy cascade at the scales where these mechanisms are potentially active has been made. By using forcing-scale resolving third-order structure-function theory, which captures bidirectional energy fluxes and is applicable beyond inertial ranges, we analyse data from surface drifters, released in dense arrays in the Gulf of Mexico, to obtain the kinetic energy flux magnitude and directions along with the energy injection scales. We provide the first direct observational verification that the surface kinetic energy cascades to both small and large scales, with the forward cascade dominating at scales smaller than approximately 1-10km. Our results also show that there is a seasonality in these cascades, with winter months having a stronger injection of energy into the surface flows and a more energetic cascade to smaller scales. This work provides exciting new opportunities for further probing the energetics of ocean turbulence using non-gridded sparse observations, such as from drifters, gliders, or satellites.

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.

We observe the emergence of strong vertical drafts in direct numerical simulations of the Boussinesq equations in a range of parameters of geophysical interest. These structures, which appear intermittently in space and time, generate turbulence and enhance kinetic and potential energy dissipation, providing a possible explanation for the observed variability of the local energy dissipation in the bulk of oceanic flows and the modulation of its probability distribution function. We show how, due to the extreme drafts, in runs with Froude numbers observable in geophysical scenarios, roughly 10% of the domain flow can account for up to 50% of the global volume dissipation, reminiscent of estimates based on oceanic models.

Investigating energy injection mechanisms in stratified turbulent flows is critical to understand the multi-scale dynamics of the atmosphere and the oceans. Geophysical fluids are characterized by anisotropy, supporting the propagation of gravity waves. Classical paradigms of homogeneous isotropic turbulence may therefore not apply, the energy transfer in these frameworks being determined by the interplay of waves and turbulence as well as by the presence of structures emerging intermittently in space and time. In particular, it has been observed that stably stratified fluids can develop large-scale intermittent events in the form of extreme vertical velocity drafts, in a specific range of Froude numbers ([1]). These events were found to be associated with the enhancement of small-scale intermittency ([2]) and local dissipation ([3]). Here we verify the possibility that such extreme vertical drafts may release energy to the flow, affecting its overall dynamics and energetics. The analysis presented consists in the implementation of a space-filtering technique ([4]) applied to three-dimensional direct numerical simulations of the Boussinesq equations. The strength of this approach relies on dealing with quantities (referred to as “sub-grid terms”) which are a reliable proxies of the classical Fourier flux terms but defined locally in the physical space, allowing for a scale analysis of the energy transfer at specific location of the domain flow. By investigating the correlation between values of the sub-grid terms and the presence of the extreme values of the vertical velocity, we found an increase in the energy transfer at intermediate scales that is likely to be associated with the development of vertical drafts in the flow. In the range of the governing parameters (namely the Froude and the Reynolds numbers) in which the extreme vertical drafts are detected in stratified turbulent flows, enhancement of the coupling between kinetic and potential energy modes is also observed, feeding in turn the scale-to-scale potential energy transfer. [1] Feraco et al., EPL, 2018 [2] Feraco et al., EPL, 2021 [3] Marino et al., PRF, in review [4] Camporeale et al., PRL, 2018

The polar summer mesosphere is the Earth's coldest region, allowing the formation of mesospheric ice clouds. These ice clouds produce strong polar mesospheric summer echoes (PMSE) that are used as tracers of mesospheric dynamics. Here, we report the first observations of extreme vertical drafts (+/- 50 ms-1) in the mesosphere obtained from PMSE, characterized by velocities more than five standard deviations larger than the observed vertical wind variability. Using aperture synthesis radar imaging, the observed PMSE morphology resembles a solitary wave in a varicose mode, narrow along propagation (3-4 km) and elongated (>10 km) transverse to propagation direction, with a relatively large vertical extent (similar to 13 km). These spatial features are similar to previously observed mesospheric bores, but we observe only one crest with much larger vertical extent and higher vertical velocities.

The polar summer mesosphere is the Earth’s coldest region, allowing the formation of mesospheric ice clouds, potentially linked to climate change. These clouds produce strong radar echoes that are used as tracers of mesospheric dynamics. Here we report the first observations of extreme vertical drafts in the mesosphere, characterized by velocities larger than 40 m/s, i.e., more than five standard deviations larger than the observed wind variability. The morphology seems to resemble mesospheric bores, however the scales observed are much larger. Powerful vertical drafts, intermittent in space and time, emerge also in direct numerical simulations of stratified flows, predicting non-Gaussian statistics of vertical velocities. This evidence suggests that mesospheric bores might result from the interplay of gravity waves and turbulent motions. Our extreme event is interpreted as a mesospheric "super-bore", impacting mesospheric mixing and ice-formation, and would potentially impact planning of sub-orbital flights, and the investigation of biological material in the near space.

We investigate the dynamics of turbulent dispersion by means of direct numerical simulations of a passive tracer released in a homogeneous isotropic turbulent flow. We focus on the link between the probability density function (PDF) of the passive scalar concentration and its mixing properties. In particular, we show how the gamma distribution can be used as a suitable model for the PDF, as has been previously verified in wind tunnel experiments in wall-bounded turbulent flows. Finally, we develop a simple mixing model to estimate the time scale that regulates the decay rate of the intensity of concentration fluctuations.

Non-Gaussian statistics of large-scale fields are routinely observed in data from atmospheric and oceanic campaigns and global models. Recent direct numerical simulations (DNSs) showed that large-scale intermittency in stably stratified flows is due to the emergence of sporadic, extreme events in the form of bursts in the vertical velocity and the temperature. This phenomenon results from the interplay between waves and turbulent motions, affecting mixing. We provide evidence of the enhancement of the classical small-scale (or internal) intermittency due to the emergence of large-scale drafts, connecting large- and small-scale bursts. To this aim we analyze a large set of DNSs of the stably stratified Boussinesq equations over a wide range of values of the Froude number ($Fr\approx 0.01-1$). The variation of the buoyancy field kurtosis with $Fr$ is similar to (though with smaller values than) the kurtosis of the vertical velocity, both showing a non-monotonic trend. We present a mechanism for the generation of extreme vertical drafts and vorticity enhancements which follows from the exact equations for field gradients.

Geophysical fluid flows are predominantly turbulent and often strongly affected by the Earth's rotation, as well as by stable density stratification. Using direct numerical simulations of forced Boussinesq equations, we study the influence of these effects on the motion of fluid particles. We perform a detailed study of Lagrangian statistics of acceleration, velocity, and related quantities, focusing on cases where the frequencies associated with rotation and stratification (RaS), f and N, respectively, are held at a fixed ratio N/f = 5. The simulations are performed in a periodic domain, at Reynolds number Re approximate to 4000, and Froude number Fr in the range 0.03 less than or similar to Fr less than or similar to 0.2 (with Rossby number Ro = 5Fr). As the intensity of RaS increases, a sharp transition is observed between a regime dominated by eddies to a regime dominated by waves, which corresponds to Fr less than or similar to 0.07. For the given runs, this transition to a wave-dominated regime can also be seemingly described by simply comparing the timescales 1/N and tau(eta), the latter being the Kolmogorov timescale based on the mean kinetic energy dissipation. Due to the known anisotropy induced by RaS, we consider separately the motion in the horizontal and vertical directions. In the regime N tau(eta) < 1, acceleration statistics exhibit well known characteristics of isotropic turbulence in both directions, such as probability density functions with wide tails and acceleration variance approximately scaling as per Kolmogorov's theory. In contrast for N tau(eta )> 1, they behave very differently, experiencing the direct influence of the imposed rotation and stratification. On the other hand, the Lagrangian velocity statistics exhibit visible anisotropy for all runs; nevertheless the degree of anisotropy becomes very strong in the regime N tau(eta) > 1. We observe that in the regime N tau(eta )< 1, rotation enhances the mean-square displacements in horizontal planes in the ballistic regime at short times but suppresses them in the diffusive regime at longer times. This suppression of the horizontal displacements becomes stronger in the regime N tau(eta) > 1, with no clear diffusive behavior. In contrast, the displacements in the vertical direction are always reduced. This inhibition is extremely strong in the N tau(eta )> 1 regime, leading to a scenario where particles almost appear to be trapped in horizontal planes.

The opportunity of using a kinetic Lattice Boltzmann (LB) approach for the numerical simulation of three-dimensional magneto-hydrodynamic (MHD) turbulence is examined. A significant advantage of dealing with a kinetic representation of the plasma (even in simulating the MHD scales) is that the derivatives of the magnetic field are directly encompassed in the solution, thus allowing for an intrinsically accurate description of the small-scale current density structures. A novel LB framework is proposed here to address the three-dimensional Orszag-Tang vortex problem at increasing Reynolds numbers. Our analysis shows that both small-scale dynamics and spectral properties of LB runs are compatible with the outcome of analogous pseudo-spectral simulations (Mininni et al. 2006) generated with a well-established pseudo-spectral code (Mininni et al. 2011; Pou-quet et al. 2019). This study shows how phenomenology of MHD turbulence is suitably captured by our LB simulations, which reproduced it with accuracy and computational efficiency. The newly developed algorithm couples two LB schemes for fluid dynamics including the Lorentz force and the magnetic induction equation respectively. The fluid incompressibility is achieved in the low-Mach-number limit, whereas the divergence-free condition for the magnetic field is preserved within machine precision. It is also emphasized how such novel scheme is amenable to a high level of parallelism and can exploit the computational power of many-core accelerators such as Graphic Processing Units (GPUs) thus leading to very advantageous turnaround times. This is supported by a preliminary benchmark that shows the high scalability of our model implementation.