Kinetic Energy Cascade Research Articles

Order out of Chaos: Shifting Paradigm of Convective Turbulence

AbstractTurbulence is ever produced in the low-viscosity/large-scale fluid flows by velocity shears and, in unstable stratification, by buoyancy forces. It is commonly believed that both mechanisms produce the same type of chaotic motions, namely, the eddies breaking down into smaller ones and producing direct cascade of turbulent kinetic energy and other properties from large to small scales toward viscous dissipation. The conventional theory based on this vision yields a plausible picture of vertical mixing and has remained in use since the middle of the twentieth century in spite of increasing evidence of the fallacy of almost all other predictions. This paper reveals that in fact buoyancy produces chaotic vertical plumes, merging into larger ones and producing an inverse cascade toward their conversion into the self-organized regular motions. Herein, the velocity shears produce usual eddies spreading in all directions and making the direct cascade. This new paradigm is demonstrated and proved empirically; so, the paper launches a comprehensive revision of the theory of unstably stratified turbulence and its numerous geophysical or astrophysical applications.

Seasonal Modulation of Submesoscale Kinetic Energy in the Upper Ocean of the Northeastern South China Sea

AbstractAlthough submesoscale processes are revealed to have a strong seasonality in many regions of global ocean, their seasonal modulation in the northeastern South China Sea (NESCS) remains unexplored by observations. In this study, approaches to diagnose submesoscale kinetic energy (KE) and its conversion terms using data from a single mooring are proposed and validated. Based on these approaches, seasonal modulation of submesoscale KE in the NESCS is for the first time investigated using 8.7‐year‐long moored velocity and temperature data between August 2010 and April 2019. It is found that the monthly climatology of submesoscale KE shows an asymmetric annual cycle with a steep peak between December and February but a flat trough between April and October. The maximum and minimum of this annual cycle occur in January and May, respectively. Although the submesoscale KE rapidly decreases with depth, its seasonality is still evident at 300 m, which is far beneath the mixed layer. Statistical analysis suggests that the overall seasonality of submesoscale KE is shaped by mixed‐layer depth while its steep peak in winter is modulated by mesoscale strain rate. It therefore suggests that the combination of mixed‐layer instability and strain‐induced frontogenesis determines the detailed annual cycle of submesoscale KE. Energetics analysis demonstrates that submesoscales obtain their KE from the release of available potential energy but lose a small portion of its KE through inverse cascade. This submesoscale inverse KE cascade may play an important role in modulating the temporal variation of mesoscale KE in winter.

Damping and dissipation in a fuzzy structure

Damping describes processes that lead systems to reach equilibrium during which energy either escapes from the system or is redistributed within it. In both cases, the kinetic energy cascades to shorter spatial and temporal dimensions, eventually reaching a state of thermalization. Radiative damping due to energy escape from a system is generally studied using the system-environment paradigm. This approach also explains how a structural fuzzy that refers to ancillary substructures attached to a primary structure leads to apparent damping. It is known that an infinite number of lossless harmonic oscillators with continuously distributed frequencies yield a perfect loss mechanism, since energy has infinitely many paths to travel within the complex structure. For a more realistic structure with a finite number of oscillators, however, energy may return to the primary, unless its frequencies follow a certain distribution (Carcaterra and Akay, JASA). This presentation will focus on the loss mechanism of a fuzzy structure and compare it with dissipation mechanisms at the molecular level.

On the inverse kinetic energy cascade in premixed isotropic turbulent flames

The understanding of energy transfer in fluids is important for the accurate modeling of turbulent reacting flows. In this study, we investigate interscale kinetic energy transfer and subgrid-scale (SGS) backscatter using data from direct numerical simulations (DNSs) of premixed isotropic turbulent flames. Results reveal that in the examined premixed flames, the pressure transfer term appearing in the transport equation of turbulent kinetic energy dominates the nonlinear advection and the dissipation at large scales, and noticeably contributes to the inverse kinetic energy cascade. Filtered DNS data show that SGS backscatter is correlated with the appearance of positive pressure-dilatation work, i.e. thermal expansion. A priori test results of three SGS stress models reveal that the Smagorinsky stress model is unable to capture SGS backscatter, but that two nonlinear structural stress models are able to predict SGS backscatter.

Kinetic energy cascade in stably stratified open-channel flows

In this paper, the kinetic energy cascade in stably stratified open-channel flows is investigated. A mathematical framework to incorporate vertical scales into the conventional kinetic energy spectrum and its budget is introduced. This framework defines kinetic energy density in horizontal spectral and vertical scale space. The energy cascade is studied by analysing the evolution of kinetic energy density. It is shown that energetic streamwise scales ($\lambda _x$) become larger with increasing vertical scale. For the strongest stratification, for which the turbulence becomes intermittent, the energetic streamwise scales are suppressed, and energy density resides in $\lambda _x$ of the size of the domain. It is shown that, in an unstratified case, vertical scales of the size comparable to the height of the logarithmic layer connect viscous regions to the outer layer. By contrast, in stratified cases, such a connection is not observed. Moreover, it is shown that nonlinear transfer for streamwise scales is dominated by in-plane triad interactions and inter-plane transfer is more active in transferring energy density among small vertical scales of the size comparable to the height of viscous sublayer. The vertical scales of size comparable to the height of the viscous sublayer and buffer layer are the most active scales in the viscous term and the production term in the energy density budget, respectively.

Rotating thermal convection: surface turbulence observed with altimetry and thermal radiometry

The surface dynamics of the rotating thermal convection are examined in finely resolved laboratory flows. Deep rotating convection creates geostrophic turbulent flow at the surface, the regime of convection relevant to flows observed in deep convection sites in the ocean or in the atmospheres of the gas giants Jupiter and Saturn. Spectral analyses reveal a dual energy cascade of the surface kinetic energy and a downscale cascade of surface buoyancy. The spectral slopes of these quantities are found to be very similar to each other. This property is further confirmed theoretically; it was showed in particular that buoyancy is proportional to velocity in the subsurface thermal boundary layer.

Scaling of Turbulent Viscosity and Resistivity: Extracting a Scale-dependent Turbulent Magnetic Prandtl Number

Abstract Turbulent viscosity ν t and resistivity η t are perhaps the simplest models for turbulent transport of angular momentum and magnetic fields, respectively. The associated turbulent magnetic Prandtl number Pr t ≡ ν t /η t has been well recognized to determine the final magnetic configuration of accretion disks. Here, we present an approach to determining these “effective transport” coefficients acting at different length scales using coarse-graining and recent results on decoupled kinetic and magnetic energy cascades. By analyzing the kinetic and magnetic energy cascades from a suite of high-resolution simulations, we show that our definitions of ν t , η t , and Pr t have power-law scalings in the “decoupled range.” We observe that Pr t ≈ 1–2 at the smallest inertial-inductive scales, increasing to ≈5 at the largest scales. However, based on physical considerations, our analysis suggests that Pr t has to become scale independent and of order unity in the decoupled range at sufficiently high Reynolds numbers (or grid resolution) and that the power-law scaling exponents of velocity and magnetic spectra become equal. In addition to implications for astrophysical systems, the scale-dependent turbulent transport coefficients offer a guide for large-eddy simulation modeling.

Characteristics of oceanic mesoscale variabilities associated with the inverse kinetic energy cascade

Characteristics of oceanic mesoscale variabilities associated with the inverse kinetic energy cascade

Supersonic turbulence in giant HII regions: clues from 30 Doradus

The tight correlation between turbulence and luminosity in giant HII regions (GHRs) is not well understood. While the luminosity is due to the UV radiation from the massive stars in the ionizing clusters, it is not clear what powers the turbulence. Observations of the two prototypical GHRs in the local Universe, 30 Doradus and NGC 604, show that part of the kinetic energy of the nebular gas comes from the combined stellar winds of the most massive stars, the cluster winds, but not all. We present a study of the kinematics of 30 Doradus based on archival VLT FLAMES/GIRAFFE data and new high-resolution observations with HARPS. We find that the nebular structure and kinematics are shaped by a hot cluster wind and not by the stellar winds of individual stars. The cluster wind powers most of the turbulence of the nebular gas, with a small contribution from the combined gravitational potential of stars and gas. We estimate the total mass of 30 Doradus and we argue that the region does not contain significant amounts of neutral (HI) gas, and that the giant molecular cloud 30 Dor-10, which is close to the center of the nebula in projection, is in fact an inflating cloud tens of parsecs away from R136, the core of the ionizing cluster. We rule out a Kolmogorov-like turbulent kinetic energy cascade as the source of supersonic turbulence in GHRs.

Magnetized decaying turbulence in the weakly compressible Taylor-Green vortex

Magnetohydrodynamic (MHD) turbulence affects both terrestrial and astrophysical plasmas. The properties of magnetized turbulence must be better understood to more accurately characterize these systems. This work presents ideal MHD simulations of the compressible Taylor-Green vortex under a range of initial subsonic Mach numbers and magnetic field strengths. We find that regardless of the initial field strength, the magnetic energy becomes dominant over the kinetic energy on all scales after at most several dynamical times. The spectral indices of the kinetic and magnetic energy spectra become shallower than k^{-5/3} over time and generally fluctuate. Using a shell-to-shell energy transfer analysis framework, we find that the magnetic fields facilitate a significant amount of the energy flux and that the kinetic energy cascade is suppressed. Moreover, we observe nonlocal energy transfer from the large-scale kinetic energy to intermediate and small-scale magnetic energy via magnetic tension. We conclude that even in intermittently or singularly driven weakly magnetized systems, the dynamical effects of magnetic fields cannot be neglected.

Scale dependence and cross-scale transfer of kinetic energy in compressible hydrodynamic turbulence at moderate Reynolds numbers

We investigate properties of the scale dependence and cross-scale transfer of kinetic energy in compressible three-dimensional hydrodynamic turbulence, by means of two direct numerical simulations of decaying turbulence with initial Mach numbers M = 1/3 and M = 1, and with moderate Reynolds numbers, R_lambda ~ 100. The turbulent dynamics is analyzed using compressible and incompressible versions of the dynamic spectral transfer (ST) and the Karman-Howarth-Monin (KHM) equations. We find that the nonlinear coupling leads to a flux of the kinetic energy to small scales where it is dissipated; at the same time, the reversible pressure-dilatation mechanism causes oscillatory exchanges between the kinetic and internal energies with an average zero net energy transfer. While the incompressible KHM and ST equations are not generally valid in the simulations, their compressible counterparts are well satisfied and describe, in a quantitatively similar way, the decay of the kinetic energy on large scales, the cross-scale energy transfer/cascade, the pressure dilatation, and the dissipation. There exists a simple relationship between the KHM and ST results through the inverse proportionality between the wave vector k and the spatial separation length l as k l ~ 3^1/2. For a given time the dissipation and pressure-dilatation terms are strong on large scales in the KHM approach whereas the ST terms become dominant on small scales; this is owing to the complementary cumulative behavior of the two methods. The effect of pressure dilatation is weak when averaged over a period of its oscillations and may lead to a transfer of the kinetic energy from large to small scales without a net exchange between the kinetic and internal energies. Our results suggest that for large-enough systems there exists an inertial range for the kinetic energy cascade ...

Mesoscale helicity distinguishes Vinen from Kolmogorov turbulence in helium-II

Experiments and numerical simulations show that quantum turbulence exists in two distinct limiting regimes: Kolmogorov turbulence (which shares with classical turbulence the important property of a cascade of kinetic energy from large eddies to small eddies) and Vinen turbulence (which is more similar to a random flow). In this work, we define a mesoscale helicity for the superfluid, which, tested in numerical experiments, distinguishes the two turbulent regimes, quantifying the amount of nonlocal vortex interactions and the orientation of the vortex lines.

Barotropic and Baroclinic Inverse Kinetic Energy Cascade in the Antarctic Circumpolar Current

AbstractStratified geostrophic turbulence theory predicts an inverse energy cascade for the barotropic (BT) mode. Satellite altimetry has revealed a net inverse cascade in the baroclinic (BC) mode. Here the spatial variabilities of BT and BC kinetic energy fluxes in the Antarctic Circumpolar Current (ACC) were investigated using ECCO2 data, which synthesize satellite data and in situ measurements with an eddy-permitting general circulation model containing realistic bathymetry and wind forcing. The BT and BC inverse kinetic energy cascades both reveal complex spatial variations that could not be explained fully by classical arguments. For example, the BC injection scales match better with most unstable scales than with the first-mode deformation scales, but the opposite is true for the BT mode. In addition, the BT and BC arrest scales do not follow the Rhines scale well in terms of spatial variation, but show better consistency with their own energy-containing scales. The reverse cascade of the BT and BC modes was found related to their EKE, and better correlation was found between the BT inverse cascade and barotropization. Speculations of the findings were proposed; however, further observations and modeling experiments are needed to test these interpretations. Spectral flux anisotropy exhibits a feature associated with oceanic jets that is consistent with classical expectations. Specifically, the spectral flux along the along-stream direction remains negative at scales up to that of the studied domain (~2000 km), while that in the perpendicular direction becomes positive close to the scale of the width of a typical jet.

As a Matter of Tension: Kinetic Energy Spectra in MHD Turbulence

Abstract While magnetized turbulence is ubiquitous in many astrophysical and terrestrial systems, our understanding of even the simplest physical description of this phenomena, ideal magnetohydrodynamic (MHD) turbulence, remains substantially incomplete. In this work, we highlight the shortcomings of existing theoretical and phenomenological descriptions of MHD turbulence that focus on the joint (kinetic and magnetic) energy fluxes and spectra by demonstrating that treating these quantities separately enables fundamental insights into the dynamics of MHD turbulence. This is accomplished through the analysis of the scale-wise energy transfer over time within an implicit large eddy simulation of subsonic, super-Alfvénic MHD turbulence. Our key finding is that the kinetic energy spectrum develops a scaling of approximately k −4/3 in the stationary regime as magnetic tension mediates large-scale kinetic to magnetic energy conversion and significantly suppresses the kinetic energy cascade. This motivates a reevaluation of existing MHD turbulence theories with respect to a more differentiated modeling of the energy fluxes.

Spatial and Temporal Characteristics of the Submesoscale Energetics in the Gulf of Mexico

AbstractThe submesoscale energetics of the eastern Gulf of Mexico (GoM) are diagnosed using outputs from a 1/48° MITgcm simulation. Employed is a recently developed, localized multiscale energetics formalism with three temporal-scale ranges (or scale windows), namely, a background flow window, a mesoscale window, and a submesoscale window. It is found that the energy cascades are highly inhomogeneous in space. Over the eastern continental slope of the Campeche Bank, the submesoscale eddies are generated via barotropic instability, with forward cascades of kinetic energy (KE) following a weak seasonal variation. In the deep basin of the eastern GoM, the submesoscale KE exhibits a seasonal cycle, peaking in winter, maintained via baroclinic instability, with forward available potential energy (APE) cascades in the mixed layer, followed by a strong buoyancy conversion. A spatially coherent pool of inverse KE cascade is found to extract energy from the submesoscale KE reservoir in this region to replenish the background flow. The northern GoM features the strongest submesoscale signals with a similar seasonality as seen in the deep basin. The dominant source for the submesoscale KE during winter is from buoyancy conversion and also from the forward KE cascades from mesoscale processes. To maintain the balance, the excess submesoscale KE must be dissipated by smaller-scale processes via a forward cascade, implying a direct route to finescale dissipation. Our results highlight that the role of submesoscale turbulence in the ocean energy cycle is region and time dependent.

Numerical study on the energy cascade of pulsatile Newtonian and power-law flow models in an ICA bifurcation

The complex physics and biology underlying intracranial hemodynamics are yet to be fully revealed. A fully resolved direct numerical simulation (DNS) study has been performed to identify the intrinsic flow dynamics in an idealized carotid bifurcation model. To shed the light on the significance of considering blood shear-thinning properties, the power-law model is compared to the commonly used Newtonian viscosity hypothesis. We scrutinize the kinetic energy cascade (KEC) rates in the Fourier domain and the vortex structure of both fluid models and examine the impact of the power-law viscosity model. The flow intrinsically contains coherent structures which has frequencies corresponding to the boundary frequency, which could be associated with the regulation of endothelial cells. From the proposed comparative study, it is found that KEC rates and the vortex-identification are significantly influenced by the shear-thinning blood properties. Conclusively, from the obtained results, it is found that neglecting the non-Newtonian behavior could lead to underestimation of the hemodynamic parameters at low Reynolds number and overestimation of the hemodynamic parameters by increasing the Reynolds number. In addition, we provide physical insight and discussion onto the hemodynamics associated with endothelial dysfunction which plays significant role in the pathogenesis of intracranial aneurysms.

Submesoscale Fronts and Their Dynamical Processes Associated with Symmetric Instability in the Northwest Pacific Subtropical Ocean

AbstractSubmesoscale density fronts and the associated processes of frontogenesis and symmetric instability (SI) are investigated in the northwest Pacific subtropical countercurrent (STCC) system by a high-resolution simulation and diagnostic analysis. Both satellite observations and realistic simulation show active surface fronts with a horizontal scale of ~20 km in the STCC upper ocean. Frontogenesis-induced buoyancy advection is detected to rapidly sharpen these density fronts. The direct straining effect of larger-scale geostrophic flows is a primary influence on the buoyancy-gradient frontogenetic tendency and frontal baroclinic potential vorticity (PV) enhancement. The enhanced lateral buoyancy gradients in conjunction with atmospheric forced surface buoyancy loss can produce a negative Ertel PV and trigger frontal SI in the STCC region. Up to 30% of the mixed layer (ML) inside a typical eddy has negative PV in the high-resolution simulation. As a result, the cross-front ageostrophic secondary circulations tend to restratify the surface boundary layer and induce a large vertical velocity reaching ~100 m day−1, substantially facilitating the vertical communication of the STCC system. At the same time, the SI is identified to be responsible for a forward cascade of geostrophic kinetic energy in the STCC region, despite the coexistence of ML eddies and SI in the deep winter ML. Therefore, these active density fronts and their SI-associated submesoscale processes play important roles in the enhanced vertical exchanges (e.g., heat, nutrients, and carbon) and energy transfer to smaller scales in the eddy-active STCC upper ocean, as well as triggering phytoplankton blooms at the periphery of eddies.

Physiologic blood flow is turbulent

Contemporary paradigm of peripheral and intracranial vascular hemodynamics considers physiologic blood flow to be laminar. Transition to turbulence is considered as a driving factor for numerous diseases such as atherosclerosis, stenosis and aneurysm. Recently, turbulent flow patterns were detected in intracranial aneurysm at Reynolds number below 400 both in vitro and in silico. Blood flow is multiharmonic with considerable frequency spectra and its transition to turbulence cannot be characterized by the current transition theory of monoharmonic pulsatile flow. Thus, we decided to explore the origins of such long-standing assumption of physiologic blood flow laminarity. Here, we hypothesize that the inherited dynamics of blood flow in main arteries dictate the existence of turbulence in physiologic conditions. To illustrate our hypothesis, we have used methods and tools from chaos theory, hydrodynamic stability theory and fluid dynamics to explore the existence of turbulence in physiologic blood flow. Our investigation shows that blood flow, both as described by the Navier–Stokes equation and in vivo, exhibits three major characteristics of turbulence. Womersley’s exact solution of the Navier–Stokes equation has been used with the flow waveforms from HaeMod database, to offer reproducible evidence for our findings, as well as evidence from Doppler ultrasound measurements from healthy volunteers who are some of the authors. We evidently show that physiologic blood flow is: (1) sensitive to initial conditions, (2) in global hydrodynamic instability and (3) undergoes kinetic energy cascade of non-Kolmogorov type. We propose a novel modification of the theory of vascular hemodynamics that calls for rethinking the hemodynamic–biologic links that govern physiologic and pathologic processes.

The Submesoscale Kinetic Energy Cascade: Mesoscale Absorption of Submesoscale Mixed Layer Eddies and Frontal Downscale Fluxes

AbstractMesoscale eddies can be strengthened by the absorption of submesoscale eddies resulting from mixed layer baroclinic instabilities. This is shown for mesoscale eddies in the Agulhas Current system by investigating the kinetic energy cascade with a spectral and a coarse-graining approach in two model simulations of the Agulhas region. One simulation resolves mixed layer baroclinic instabilities and one does not. When mixed layer baroclinic instabilities are included, the largest submesoscale near-surface fluxes occur in wintertime in regions of strong mesoscale activity for upscale as well as downscale directions. The forward cascade at the smallest resolved scales occurs mainly in frontogenetic regions in the upper 30 m of the water column. In the Agulhas ring path, the forward cascade changes to an inverse cascade at a typical scale of mixed layer eddies (15 km). At the same scale, the largest sources of the upscale flux occur. After the winter, the maximum of the upscale flux shifts to larger scales. Depending on the region, the kinetic energy reaches the mesoscales in spring or early summer aligned with the maximum of mesoscale kinetic energy. This indicates the importance of submesoscale flows for the mesoscale seasonal cycle. A case study shows that the underlying process is the mesoscale absorption of mixed layer eddies. When mixed layer baroclinic instabilities are not included in the simulation, the open-ocean upscale cascade in the Agulhas ring path is almost absent. This contributes to a 20% reduction of surface kinetic energy at mesoscales larger than 100 km when submesoscale dynamics are not resolved by the model.

Interannual to Decadal Variations of Submesoscale Motions around the North Pacific Subtropical Countercurrent

The outputs from a submesoscale permitting hindcast simulation from 1990 to 2016 are used to investigate the interannual to decadal variations of submesoscale motions. The region we focus on is the subtropical Northwestern Pacific including the subtropical countercurrent. The submesoscale kinetic energy (KE) is characterized by strong interannual and decadal variability, displaying larger magnitudes in 1996, 2003, and 2015, and smaller magnitudes in 1999, 2009, 2010, and 2016. These variations are partially explained by those of the available potential energy (APE) release at submesoscale driven by mixed layer instability in winter. Indeed, this APE release depends on the mixed layer depth and horizontal buoyancy gradient, both of them modulated with the Pacific Decadal Oscillation (PDO). As a result of the inverse KE cascade, the submesoscale KE variability possibly leads to interannual to decadal variations of the mesoscale KE (eddy KE (EKE)). These results show that submesoscale motions are a possible pathway to explain the impact associated with the PDO on the decadal EKE variability. The winter APE release estimated from the Argo float observations varies synchronously with that in the simulation on the interannual time scales, which suggests the observation capability to diagnose the submesoscale KE variability.