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Quantifying kinetic energy (KE) and enstrophy transfer, mixing, and dissipation in the Arctic Ocean is key to understanding polar ocean dynamics, which are critical components of the global climate system. However, in ice‐covered regions, limited eddy‐resolving observations make characterizing KE and enstrophy transfer across scales challenging. Here, we use satellite‐derived sea ice floe rotation rates to infer the surface ocean enstrophy spectra in the marginal ice zone. Employing a coarse‐graining approach, we treat each floe as a local spatial filter. The method is validated with idealized sea ice–ocean simulations and applied to floe observations in the Beaufort Gyre. Our results reveal steepened spectral slopes at low sea ice concentrations, indicating enhanced mesoscale activity during the spring‐to‐summer transition. High‐resolution simulations support these findings but overestimate enstrophy, highlighting the need for eddy‐resolving observations. Our two‐dimensional spectral estimates are the first of their kind, providing a scalable approach for mapping under‐ice ocean eddy characteristics.

The submesoscale energy budget is complex and remains understood only in region-by-region analyses. Based on a series of nested numerical simulations, this study investigated the submesoscale energy budget and flux in the upper ocean of the Kuroshio Extension, including some innovations for examining submesoscale energy budgets in general. The highest-resolution simulation on a ~500 m grid resolves a variety of submesoscale instabilities allowing an energetic analysis in the submesoscale range. The frequency–wavenumber spectra of vertical vorticity variance (i.e., enstrophy) and horizontal divergence variance were used to identify the scales of submesoscale flows as distinct from those of inertia-gravity waves but dominating horizontal divergence variance. Next, the energy transfers between the background scales and the submesoscale were examined. The submesoscale kinetic and potential energy (SMKE and SMPE) were mainly contained in the mixed layer and energized through both barotropic (shear production) and baroclinic (buoyancy production) routes. Averaged over the upper 50 m of ROMS2, the baroclinic transfers amounted to approximately 75% of the sources for the SMKE (3.42 × 10 −9 W/kg) versus the remaining 25% (1.12 × 10 −9 W/kg) via barotropic downscale KE transfers. The KE field was greatly strengthened by energy sources through the boundary—this flux is larger than the mesoscale-to-submesoscale transfers in this region. Spectral energy production, importantly, reveals upscale KE transfers at larger submesoscales and downscale KE transfers at smaller submesoscales (i.e., a transition from inverse to forward KE cascade). This study seeks to extend our understanding of the energy cycle to the submesoscale and highlight the forward KE cascade induced by upper-ocean submesoscale activities in the research domain.

We perform direct numerical simulations (DNS) of emulsions in homogeneous isotropic turbulence using a pseudopotential lattice-Boltzmann (PP-LB) method. Improving on previous literature by minimizing droplet dissolution and spurious currents, we show that the PP-LB technique is capable of long stable simulations in certain parameter regions. Varying the dispersed-phase volume fraction$\\unicode[STIX]{x1D719}$, we demonstrate that droplet breakup extracts kinetic energy from the larger scales while injecting energy into the smaller scales, increasingly with higher$\\unicode[STIX]{x1D719}$, with approximately the Hinze scale (Hinze, AIChE J. , vol. 1 (3), 1955, pp. 289–295) separating the two effects. A generalization of the Hinze scale is proposed, which applies both to dense and dilute suspensions, including cases where there is a deviation from the$k^{-5/3}$inertial range scaling and where coalescence becomes dominant. This is done using the Weber number spectrum$We(k)$, constructed from the multiphase kinetic energy spectrum$E(k)$, which indicates the critical droplet scale at which$We\\approx 1$. This scale roughly separates coalescence and breakup dynamics as it closely corresponds to the transition of the droplet size ($d$) distribution into a$d^{-10/3}$scaling (Garrett et al. , J. Phys. Oceanogr. , vol. 30 (9), 2000, pp. 2163–2171; Deane & Stokes, Nature , vol. 418 (6900), 2002, p. 839). We show the need to maintain a separation of the turbulence forcing scale and domain size to prevent the formation of large connected regions of the dispersed phase. For the first time, we show that turbulent emulsions evolve into a quasi-equilibrium cycle of alternating coalescence and breakup dominated processes. Studying the system in its state-space comprising kinetic energy$E_{k}$, enstrophy$\\unicode[STIX]{x1D714}^{2}$and the droplet number density$N_{d}$, we find that their dynamics resemble limit cycles with a time delay. Extreme values in the evolution of$E_{k}$are manifested in the evolution of$\\unicode[STIX]{x1D714}^{2}$and$N_{d}$with a delay of${\\sim}0.3{\\mathcal{T}}$and${\\sim}0.9{\\mathcal{T}}$respectively (with${\\mathcal{T}}$the large eddy timescale). Lastly, we also show that flow topology of turbulence in an emulsion is significantly more different from single-phase turbulence than previously thought. In particular, vortex compression and axial straining mechanisms increase in the droplet phase.

The incompressible two-dimensional Euler equations on a sphere constitute a fundamental model in hydrodynamics. The long-time behaviour of solutions is largely unknown; statistical mechanics predicts a steady vorticity configuration, but detailed numerical results in the literature contradict this theory, yielding instead persistent unsteadiness. Such numerical results were obtained using artificial hyperviscosity to account for the cascade of enstrophy into smaller scales. Hyperviscosity, however, destroys the underlying geometry of the phase flow (such as conservation of Casimir functions), and therefore might affect the qualitative long-time behaviour. Here, we develop an efficient numerical method for long-time simulations that preserve the geometric features of the exact flow, in particular conservation of Casimirs. Long-time simulations on a non-rotating sphere then reveal three possible outcomes for generic initial conditions: the formation of either 2, 3 or 4 coherent vortex structures. These numerical results contradict the statistical mechanics theory and show that previous numerical results, suggesting 4 coherent vortex structures as the generic behaviour, display only a special case. Through integrability theory for point vortex dynamics on the sphere we present a theoretical model which describes the mechanism by which the three observed regimes appear. We show that there is a correlation between a first integral$\\unicode[STIX]{x1D6FE}$(the ratio of total angular momentum and the square root of enstrophy) and the long-time behaviour:$\\unicode[STIX]{x1D6FE}$small, intermediate and large yields most likely 4, 3 or 2 coherent vortex formations. Our findings thus suggest that the likely long-time behaviour can be predicted from the first integral $\\unicode[STIX]{x1D6FE}$.

In this article we detail the use of machine learning for spatio-temporally dynamic turbulence model classification and hybridization for large eddy simulations (LES) of turbulence. Our predictive framework is devised around the determination of local conditional probabilities for turbulence models that have varying underlying hypotheses. As a first deployment of this learning, we classify a point on our computational grid as that which requires the functional hypothesis, the structural hypothesis or no modelling at all. This ensures that the appropriate model is specified from a priori knowledge and an efficient balance of model characteristics is obtained in a particular flow computation. In addition, we also utilize the conditional-probability predictions of the same machine learning to blend turbulence models for another hybrid closure. Our test case for the demonstration of this concept is given by Kraichnan turbulence, which exhibits a strong interplay of enstrophy and energy cascades in the wavenumber domain. Our results indicate that the proposed methods lead to robust and stable closure and may potentially be used to combine the strengths of various models for complex flow phenomena prediction.

The effects of background turbulence on the entrainment process, as well as the nature of the interfacial region between two bodies of turbulent fluid, were examined through an investigation of the far wake of a circular cylinder that is subjected to free-stream turbulence. Simultaneous particle image velocimetry and planar laser induced fluorescence measurements were conducted 40 diameters downstream of the cylinder. Despite the availability of turbulent, rotational fluid in the background, the outer interface between the wake and the ambient fluid exhibits an enstrophy jump akin to the classical result of a turbulent/non-turbulent interface. This jump at the wake boundary persists even when the intensity of the background turbulence is greater than the turbulence intensity of the wake itself. Analysis on the structure of the wake boundary reveals that an increase in background turbulence intensity results in an increased interfacial surface area relative to the non-turbulent case. However, instead of the intuitive result of increased entrainment as a result of increased surface area, a reduction in mean entrainment mass flux is observed with increased background turbulence intensity. Through the analysis of the flux probability density functions, the reduction in mean entrainment can be attributed to a tip in balance of extreme entrainment and detrainment events to the detrainment side in the presence of background turbulence. Lastly, a scale by scale analysis of entrainment behaviour revealed that free-stream turbulence affects entrainment behaviour across all length scales and is not just limited to the energy containing scales.

Viscous anti-parallel vortex reconnection is studied by means of direct numerical simulation for vortex Reynolds numbers$Re$($\\equiv \\unicode[STIX]{x1D6E4}/\\unicode[STIX]{x1D708}$, circulation/viscosity) up to 40 000. To suppress the inherent symmetry breaking due to the Kelvin–Helmholtz (planar jet) instability, as prevalent in prior studies, and to better explore the progression of the mechanism details, the simulation is performed by imposing symmetry and using double-precision arithmetic. We show, for the first time, the evidence of vortex reconnection cascade scenario initially proposed by Melander and Hussain (CTR Report, 1988), who suggested that the remnant threads, following the first reconnection, undergo successive reconnections in a cascade. Secondary reconnection (the details distinctly captured and visualized at a lower$Re=9000$) leads to the successive generation of numerous small-scale structures, including vortex rings, hairpin-like vortex packets and vortex tangles. As$Re$increases, the third and higher generations of reconnection form a turbulent cloud avalanche consisting of a tangle of fine vortices. The energy is rapidly transferred to finer scales during reconnection, and a distinct - 5/3 inertial range is observed for the kinetic energy spectrum, associated with numerous resulting fine-scale bridgelets and thread filaments. In addition, we also discover an inverse cascade at large scales through the accumulation of bridgelets. The separation distance$\\unicode[STIX]{x1D6FF}(t)$before the first reconnection is found to scale as$t^{3/4}$, which is different from the typical 1/2 scaling for classical and quantum vortex filament reconnections. Both peak enstrophy and its production rate grow with$Re$faster than the power law suggested by Hussain and Duraisamy ( Phys. Fluids , vol. 23, 2011, 021701). Our simulations not only reveal the detailed mechanisms of high-$Re$reconnection, but also shed light on the physics of turbulence cascade and present the reconnection avalanche as a realistic physical model for turbulence cascade.

The rules that govern a two-dimensional inviscid incompressible fluid are simple. Yet, to characterise the long-time behaviour is a knotty problem. The fluid fulfils Euler's equations: a nonlinear Hamiltonian system with an infinite number of conservation laws. In both experiments and numerical simulations, coherent vortex structures emerge after an initial stage. These formations dominate the large-scale dynamics, but small scales also emerge and persist. The resulting scale separation resembles Kraichnan's theory of forward and backward cascades of enstrophy and energy. Previous attempts to model the double cascade use filtering techniques that enforce separation from the outset. Here, we show that Euler's equations possess an intrinsic, canonical splitting of the vorticity function. The splitting is remarkable in four ways: (i) it is defined solely by the Poisson bracket and the Hamiltonian; (ii) it characterises steady flows; (iii) it innately separates scales, enabling the dynamics behind Kraichnan's qualitative description; and (iv) it accounts for ‘broken line’ energy spectra observed in both experiments and numerical simulations. The splitting originates from Zeitlin's truncated model of Euler's equations in combination with a standard quantum tool: the spectral decomposition of Hermitian matrices. In addition to theoretical insight, the scale separation dynamics enables stochastic model reduction, where multiplicative noise models small scales.

The two-phase mixing layer formed between parallel gas and liquid streams is an important fundamental problem in turbulent multiphase flows. The problem is relevant to many industrial applications and natural phenomena, such as air-blast atomizers in fuel injection systems and breaking waves in the ocean. The velocity difference between the gas and liquid streams triggers an interfacial instability which can be convective or absolute depending on the stream properties and injection parameters. In the present study, a direct numerical simulation of a two-phase gas–liquid mixing layer that lie in the absolute instability regime is conducted. A dominant frequency is observed in the simulation and the numerical result agrees well with the prediction from viscous stability theory. As the interfacial wave plays a critical role in turbulence transition and development, the temporal evolution of turbulent fluctuations (such as the enstrophy) also exhibits a similar frequency. To investigate the statistical response of the multiphase turbulence flow, the simulation has been run for a long physical time so that time-averaging can be performed to yield the statistically converged results for Reynolds stresses and the turbulent kinetic energy (TKE) budget. An extensive mesh refinement study using from 8 million to about 4 billions cells has been performed. The turbulent dissipation is shown to be highly demanding on mesh resolution compared with other terms in TKE budget. The results obtained with the finest mesh are shown to be close to converged results of turbulent dissipation which allow us to obtain estimations of the Kolmogorov and Hinze scales. The estimated Kolmogorov scale is found to be similar to the cell size of the finest mesh used here. The computed Hinze scale is significantly larger than the size of droplets observed and does not seem to be a relevant length scale to describe the smallest size of droplets formed in atomization.

Oceanic mixing, mostly driven by the breaking of internal waves at small scales in the ocean interior, is of major importance for ocean circulation and the ocean response to future climate scenarios. Understanding how internal waves transfer their energy to smaller scales from their generation to their dissipation is therefore an important step for improving the representation of ocean mixing in climate models. In this study, the processes leading to cross-scale energy fluxes in the internal wave field are quantified using an original decomposition approach in a realistic numerical simulation of the California Current. We quantify the relative contribution of eddy–internal wave interactions and wave–wave interactions to these fluxes and show that eddy–internal wave interactions are more efficient than wave–wave interactions in the formation of the internal wave continuum spectrum. Carrying out twin numerical simulations, where we successively activate or deactivate one of the main internal wave forcing, we also show that eddy–near-inertial internal wave interactions are more efficient in the cross-scale energy transfer than eddy–tidal internal wave interactions. This results in the dissipation being dominated by the near-inertial internal waves over tidal internal waves. A companion study focuses on the role of stimulated cascade on the energy and enstrophy fluxes.