Non-local Energy Transfer Research Articles

Mind the gap: non-local cascades and preferential heating in high-β Alfvénic turbulence

ABSTRACT Characterizing the thermodynamics of turbulent plasmas is key to decoding observable signatures from astrophysical systems. In magnetohydrodynamic (MHD) turbulence, non-linear interactions between counter-propagating Alfvén waves cascade energy to smaller spatial scales where dissipation heats the protons and electrons. When the thermal pressure far exceeds the magnetic pressure, linear theory predicts a spectral gap at perpendicular scales near the proton gyroradius where Alfvén waves become non-propagating. For simple models of an MHD turbulent cascade that assume only local non-linear interactions, the cascade halts at this gap, preventing energy from reaching smaller scales where electron dissipation dominates, leading to an overestimate of the proton heating rate. In this work, we demonstrate that non-local contributions to the cascade, specifically large-scale shearing and small-scale diffusion, can bridge the non-propagating gap, allowing the cascade to continue to smaller scales. We provide an updated functional form for the proton-to-electron heating ratio accounting for this non-local energy transfer by evaluating a non-local weakened cascade model over a range of temperature and pressure ratios. In plasmas where the thermal pressure dominates the magnetic pressure, we observe that the proton heating is moderated compared to the significant enhancement predicted by local models.

Effect of non-local near-resonant interactions of Rossby waves on formation of large-scale zonal flows in unforced two-dimensional turbulence on rotating sphere

This study investigates the effect of nonlinear interactions of Rossby waves on large-scale zonal flow formation in two-dimensional turbulence on a rotating sphere. The coefficients of nonlinear interactions are first calculated. Then, the non-local, near-resonant, and non-local near-resonant interactions are investigated in detail. The results show that the formation of large-scale westward circumpolar zonal flows is directly caused by non-local energy transfer due to the three-wave near-resonant interactions of Rossby waves.

ETG turbulence in a tokamak pedestal

This paper explores the fundamental characteristics of electron-temperature-gradient (ETG)-driven turbulence in the tokamak pedestal. The extreme gradients in the pedestal produce linear instabilities and nonlinear turbulence that are distinct from the corresponding ETG phenomenology in the core plasma. The linear system exhibits multiple (greater than ten) unstable eigenmodes at each perpendicular wave vector, representing different toroidal and slab branches of the ETG instability. Proper orthogonal decomposition of the nonlinear fluctuations reveals no clear one-to-one correspondence between the linear and nonlinear modes for most wave vectors. Moreover, nonlinear frequencies deviate strongly from those of the linear instabilities, with spectra peaking at positive frequencies, which is opposite the sign of the ETG instability. The picture that emerges is one in which the linear properties are preserved only in a narrow range of k-space. Outside this range, nonlinear processes produce strong deviations from both the linear frequencies and eigenmode structures. This is interpreted in the context of critical balance, which enforces alignment between the parallel scales and fluctuation frequencies. We also investigate the nonlinear saturation processes. We observe a direct energy cascade from the injection scale to smaller scales in both perpendicular directions. However, in the bi-normal direction, there is also nonlocal inverse energy transfer to larger scales. Neither streamers nor zonal flows dominate the saturation.

Phase proper orthogonal decomposition of non-stationary turbulent flow

A phase proper orthogonal decomposition (phase POD) method is demonstrated utilizing phase averaging for the decomposition of spatiotemporal behavior of statistically non-stationary turbulent flows in an optimized manner. The proposed phase POD method is herein applied to a periodically forced statistically non-stationary lid-driven cavity flow, implemented using the snapshot proper orthogonal decomposition algorithm. Space-phase modes are extracted to describe the dynamics of the chaotic flow, in which four central flow patterns are identified for describing the evolution of the energetic structures as a function of phase. The modal building blocks of the energy transport equation are demonstrated as a function of the phase. The triadic interaction term can here be interpreted as the convective transport of bi-modal interactions. Non-local energy transfer is observed as a result of the non-stationarity of the dynamical processes inducing triadic interactions spanning across a wide range of mode numbers.

Radiative transfer in stars by feebly interacting bosons

Starting from first principles, we study radiative transfer by new feebly-interacting bosons (FIBs) such as axions, axion-like particles (ALPs), dark photons, and others. Our key simplification is to include only boson emission or absorption (including decay), but not scattering between different modes of the radiation field. Based on a given distribution of temperature and FIB absorption rate in a star, we derive explicit volume-integral expressions for the boson luminosity, reaching from the free-streaming to the strong-trapping limit. The latter is seen explicitly to correspond to quasi-thermal emission from a “FIB sphere” according to the Stefan-Boltzmann law. Our results supersede expressions and approximations found in the recent literature on FIB emission from a supernova core and, for radiatively unstable FIBs, provide explicit expressions for the nonlocal (“ballistic”) transfer of energy recently discussed in horizontal-branch stars.

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.

Spectral energy transfer in a viscoelastic homogeneous isotropic turbulence

Energy dynamics in elastoinertial turbulence is investigated by performing different direct numerical simulations of stationary, homogeneous isotropic turbulence for the range of Weissenberg numbers 0 ≤ Wi ≤ 9. Viscoelastic effects are described by the finite extensibility nonlinear elastic-Peterlin model. It is found that the presence of the polymer additives can nontrivially modify the kinetic energy dynamics by suppressing the rate of the kinetic energy transfer and altering the locality nature of this energy transfer. Spectral representation of the elastic field revealed that the elastic energy is also transferred locally through different elastic degrees of freedom via a dominantly forward energy cascade. Moreover, the elastic energy spectrum can display a power-law behavior, k−m, with the possibility of different scaling exponents depending on the Wi number. It is observed that the energy exchange between macro- and microstructures is a two-directional process: there is a dominant energy transfer from the solvent large-scale structures to the polymers alongside a weak energy transfer from polymers to the solvent small-scale structures. This energy exchange consists of three different fluxes. Two of these fluxes equally transfer a small fraction of the kinetic energy into the mean and fluctuating elastic fields. However, the main energy conversion takes place between fluctuating kinetic and elastic fields through a completely nonlocal energy transfer process.

Subcritical turbulent condensate in rapidly rotating Rayleigh–Bénard convection

The possibility of subcritical behaviour in the geostrophic turbulence regime of rapidly rotating thermally driven convection is explored. In this regime a non-local inverse energy transfer may compete with the more traditional and local direct cascade. We show that, even for control parameters for which no inverse cascade has previously been observed, a subcritical transition towards a large-scale vortex state can occur when the system is initialized with a vortex dipole of finite amplitude. This new example of bistability in a turbulent flow, which may not be specific to rotating convection, opens up new avenues for studying energy transfer in strongly anisotropic three-dimensional flows such as atmospheric or oceanic circulations.

Properties of hot-spot emission in a warm plastic-shell implosion on the OMEGA laser system

A warm plastic-shell implosion is performed on the OMEGA laser system. The measured corona plasma evolution and shell trajectory in the acceleration phase are reasonably simulated by the one-dimensional lilac simulation including the nonlocal and cross-beam energy transfer models. The results from analytical thin-shell model reproduce the time-dependent shell radius by lilac simulation and also the hot-spot x-ray-emissivity profile at stagnation predicted by spect3d. In the spect3d simulations within a clean implosion, a U-shaped hot-spot radius evolution can be observed with the Kirkpatrick-Baez microscope response (the photon energy is from 4 to 8 keV). However, a fading-away hot-spot radius evolution is measured in OMEGA warm plastic-shell implosion because of mixings. To recover the measured hot-spot x-ray emissivity profile at stagnation, a nonisobaric hot-spot model is built and the normalized hot-spot temperature, density, and pressure profiles (normalized to the corresponding target-center values) are obtained.

On non-local energy transfer via zonal flow in the Dimits shift

The two-dimensional Terry–Horton equation is shown to exhibit the Dimits shift when suitably modified to capture both the nonlinear enhancement of zonal/drift-wave interactions and the existence of residual Rosenbluth–Hinton states. This phenomenon persists through numerous simplifications of the equation, including a quasilinear approximation as well as a four-mode truncation. It is shown that the use of an appropriate adiabatic electron response, for which the electrons are not affected by the flux-averaged potential, results in an $\boldsymbol{E}\times \boldsymbol{B}$ nonlinearity that can efficiently transfer energy non-locally to length scales of the order of the sound radius. The size of the shift for the nonlinear system is heuristically calculated and found to be in excellent agreement with numerical solutions. The existence of the Dimits shift for this system is then understood as an ability of the unstable primary modes to efficiently couple to stable modes at smaller scales, and the shift ends when these stable modes eventually destabilize as the density gradient is increased. This non-local mechanism of energy transfer is argued to be generically important even for more physically complete systems.

Backscatter in stratified turbulence

In this paper, kinetic and potential energy transfers around a spectral test filter scale in direct numerical simulations of decaying stratified turbulence are studied in both physical and spectral domains. It is shown that while the domain-averaged effective subgrid scale energy transfer in physical space is a net downscale cascade, it is actually a combination of large values of downscale and upscale transfer, i.e. forward- and backscatter, in which the forward scatter is slightly dominant. Our results suggest that spectral backscatter in stratified turbulence depends on the buoyancy Reynolds number Reb and the filtering scale Δtest. When the test filter scale Δtest is around the dissipation scale Ld, transfer spectra show spectral backscatter from sub-filter to intermediate scales, as reported elsewhere. However, we find that this spectral backscatter is due to viscous effects at vertical scales around the test filter. It is also shown that there is a non-local energy transfer from scales larger than the buoyancy scale Lb to small scales. The effective turbulent Prandtl number spectra demonstrate that the assumption Prt≈1 is reasonable for the local energy transfer.

A measure of scale-dependent asymmetry in turbulent boundary layer flows: scaling and Reynolds number similarity

The distribution of temporal scale-dependent streamwise velocity increments is investigated in turbulent boundary layer flows at laboratory and atmospheric Reynolds numbers, using the St. Anthony Falls Laboratory wind tunnel and the Surface Layer Turbulence and Environmental Science Test dataset, respectively. The third-order moments of velocity increments, or asymmetry index $A(a,z)$, is computed for varying wall distance $z$ and time scale separation $a$, where it was observed to leave a robust, distinct signature in the form of a hump, independent of Reynolds number and located across the inertial range. The hump is observed in wall region limited to $z^{+}<5\times 10^{3}$, with a tendency to shift towards smaller time scales as the surface is approached ($z^{+}<70$). Comparing the two datasets, the hump, and its location, are found to obey inner wall scaling and is regarded as a genuine feature of the canonical turbulent boundary layer. The magnitude cumulant analysis of the scale-dependent velocity increments further reveals that intermittency is also enhanced near the wall, in the same flow region where the asymmetry signature was observed. The combination of asymmetry and intermittency is inferred to point at non-local energy transfer and scale coupling across a range of scales. From a turbulent structure perspective, such non-local energy transfer can be seen as the result of strong scale-interaction processes between outer scale motions in the logarithmic layer impacting and distorting smaller scales at the wall, through abrupt energy transfer across scales bypassing the typical energy cascade of the inertial range.

The finite element method for fractional non-local thermal energy transfer in non-homogeneous rigid conductors

In a non-local fractional-order model of thermal energy transport recently introduced by the authors, it is assumed that local and non-local contributions coexist at a given observation scale: while the first is described by the classical Fourier transport law, the second involves couples of adjacent and non-adjacent elementary volumes, and is taken as proportional to the product of the masses of the interacting volumes and their relative temperature, through a material-dependent, distance-decaying power-law function. As a result, a fractional-order heat conduction equation is derived. This paper presents a pertinent finite element method for the solution of the proposed fractional-order heat conduction equation. Homogenous and non-homogeneous rigid bodies are considered. Numerical applications are carried out on 1D and 2D bodies, including a standard finite difference solution for validation.

Poiseuille and Couette flows in the transitional and fully turbulent regime

We present an extensive compilation of direct numerical simulation (DNS) data for Poiseuille and Couette flows, from the laminar into the fully turbulent regime, with the goal of highlighting similarities and differences. The data suggest that, for a given bulk velocity, Couette flow yields less resistance than Poiseuille flow and greater turbulence kinetic energy, which may be beneficial for more efficient diffusion, thus suggesting the effectiveness of fluid transport devices based on moving belts as opposed to classical ducts. Both flows exhibit similar trends for the wall-parallel velocity variances, which increase logarithmically with the Reynolds number. The shear stress and the wall-normal stress tend to saturate faster in Couette flow, which can thus be regarded as a limit to which Poiseuille flow tends, in the limit of high Reynolds number. Excess production over dissipation is found in the outer part of Poiseuille and Couette flow, which is responsible for non-local transfer of energy. However, the structure of the core flow seems to attain an asymptotic state which consists of a parabolic and linear mean velocity profile, respectively, and it seems unlikely that substantial changes to this scenario will occur at Reynolds numbers reachable by DNS in the foreseeable future.

Proton-transfer mediated enhancement of nonlocal electronic relaxation processes in X-ray irradiated liquid water.

We have simulated the oxygen 1s Auger-electron spectra of normal and heavy liquid water using ab initio and quantum dynamical methods. The computed spectra are analyzed and compared to recently reported experimental data. The electronic relaxation in liquid water exposed to ionizing X-ray radiation is shown to be far more diverse and complex than anticipated and extremely different than for an isolated water molecule. A core-level ionized water molecule in the liquid phase, in addition to a local Auger process, relaxes through nonlocal energy and charge transfer, such as intermolecular Coulombic decay and electron-transfer mediated decay (ETMD). We evaluate the relative efficiencies for these three classes of relaxation processes. The quantitative estimates for the relative efficiencies of different electronic decay modes help determine yields of various reactive species produced by ionizing X-rays. The ETMD processes which are considered here for the first time in the core-level regime are found to have a surprisingly high efficiency. Importantly, we find that all nonlocal electronic relaxation processes are significantly enhanced by ultrafast proton transfer between the core-ionized water and neighboring molecules.

On quartet interactions in the California Current system

Abstract. Sea surface height (SSH) altimetry observations for 1992 to 2009 off California are used to show that observed quasi-zonal jets were likely driven by near-resonance interactions between different scales of the flow. Quartet (modulational) instability dominated and caused non-local transfer of energy from waves and eddies to biannual oscillations and quasi-zonal jets. Two types of quartets were identified: those composed of scales corresponding to (a) quasi-zonal jets, annual and semiannual Rossby waves and mesoscale eddies, and (b) biannual oscillations, semiannual Rossby waves and mesoscale eddies. The spectral centroid regularly shifted into the domain of low-order modes. However, the spectrum of SSHs does not demonstrate a power behavior. This says that the classical inverse cascade is absent. For a case with bottom friction, quartet instability required the existence of a certain level of dissipativity in the flow.

On the homogenization of turbulent flow structures in the wake of a model wind turbine

The structure of flow turbulence, measured experimentally, in the wake of a model wind turbine is investigated here through higher order scale-dependent statistics of the velocity increments and compared to the smooth wall turbulent boundary layer (base flow) case. The wind turbine wake flow is observed to possess higher turbulent kinetic energy, when compared to the base flow, though it contains more homogenized scale-dependent velocity increments, as confirmed via magnitude cumulant analysis of the streamwise velocities. Along with a reduction in intermittency (a measure of inhomogeneity) in the wake of the wind turbine, the asymmetry of the probability density functions of the velocity increments is also observed to be reduced. This is interpreted in terms of scale decoupling mechanisms and attenuating interactions and non-local energy transfer. In other words, wind turbines reduce the intermittency and asymmetry in the wake flow by breaking and/or deflecting the large-scale flow structures of the incoming flow, thus rendering the structure of the velocity fluctuations more homogenized as compared to the base flow. Experiments were conducted in a large scale, boundary layer wind tunnel at the St. Anthony Falls Laboratory.

Effective eddy viscosity in stratified turbulence

This paper investigates the effective eddy viscosity inferred from direct numerical simulations of decaying stratified and non-stratified turbulence. It is shown that stratification affects the horizontal eddy viscosity dramatically, by increasing non-local energy transfer between large and small horizontal scales. This non-local horizontal energy transfer is around 20% of the local horizontal energy transfer at the cutoff wavenumber kc = 40. The non-local horizontal energy transfer occurs at large vertical wavenumbers, which may be larger than the buoyancy wavenumber kb = N/urms, where N is the buoyancy frequency and urms is the root-mean-square velocity. By increasing the value of the test cutoff wavenumber kc from large scales to the dissipation range, the non-local horizontal eddy viscosity decreases and the local eddy viscosity is dominant. Overall, the presence of stratification can significantly change the features of subgrid-scale (SGS) motions. Current SGS models should, therefore, be modified for use in large-eddy simulation of stratified turbulence.

Microcavity controlled coupling of excitonic qubits

Controlled non-local energy and coherence transfer enables light harvesting in photosynthesis and non-local logical operations in quantum computing. This process is intuitively pictured by a pair of mechanical oscillators, coupled by a spring, allowing for a reversible exchange of excitation. On a microscopic level, the most relevant mechanism of coherent coupling of distant quantum bits—like trapped ions, superconducting qubits or excitons confined in semiconductor quantum dots—is coupling via the electromagnetic field. Here we demonstrate the controlled coherent coupling of spatially separated quantum dots via the photon mode of a solid state microresonator using the strong exciton–photon coupling regime. This is enabled by two-dimensional spectroscopy of the sample’s coherent response, a sensitive probe of the coherent coupling. The results are quantitatively understood in a rigorous description of the cavity-mediated coupling of the quantum dot excitons. This mechanism can be used, for instance in photonic crystal cavity networks, to enable a long-range, non-local coherent coupling.

Nonlocal effects in energy balance in an equilibrium plasma during its fast heating/cooling in tokamaks and stellarators

The long-standing problem of nonlocal energy transfer observed in a number of fast heating/cooling experiments in tokamaks and stellarators is discussed. The most representative and still unexplained are the results from cold-pulse experiments that demonstrate a rapid transient increase in the electron temperature in the plasma core in response to an abrupt cooling of the edge. This occurs on a timescale much faster than the diffusive one, which is incompatible with conventional local transport models. This paper contains a review of the most enigmatical observations and theoretical efforts to describe them, and offers an alternative theoretical approach to the problem. Its essential element is the incorporation of the induction effects and fast energy exchange between the plasma and the magnetic field into the traditional transport model. This makes an emphasis on the magnetic field as the main carrier of the interaction, which naturally explains the fast and nonlocal character of the process. The approach uses the ideas recently applied to the analysis of a closely related problem of ‘missing power’. Accordingly, the flux-conserving evolution of the plasma equilibrium and evaluation of the integral energy balance are parts of the analysis.