Incompressible turbulence as non-local field theory

It is well-known that incompressible turbulence is non-local in real space because sound speed is infinite in incompressible fluids. The equation in Fourier space indicates that it is non-local in Fourier space as well. However, the shell-to-shell energy transfer is local. Contrast this with Burgers equation which is local in real space. Note that the sound speed in Burgers equation is zero. In our presentation we will contrast these two equations using non-local field theory. Energy spectrum and renormalized parameters will be discussed.     

标量湍流的能量传输特性

应用直接数值模拟数据,从标量湍流传输的三波关系出发,进行湍流及标量湍流传输谱的多尺度分析,研究不同尺度间的能量传输性质,证实标量能量的传输与湍动能传输具有不同性质,大尺度速度脉动对标量传输有较大贡献,尤其是与标量小尺度脉动的相互作用,使标量模拟需要有比速度场更高的网格分辨率;并发现标量湍流的能量传输具有明显的非局部性;另外,定义了能量传输系数,发现在相同的Re数和Pe数条件下,标量湍流的对流惯性较速度脉动的惯性子区宽.     

Inverse energy transfer by near-resonant interactions with a damped-wave spectrum

The interaction of long-wavelength anisotropic drift waves with the plasma turbulence of electron density advection is shown to produce the inverse energy transfer that condenses onto zonal modes, despite the expectation of forward transfer on the basis of nonconservation of enstrophy. Wave triads with an unstable wave and two waves of a separate, damped spectrum carry the transfer, provided they satisfy a near-resonance condition dependent on turbulence level and wave number.     

Imprint of large-scale flows on turbulence

We investigate the locality of interactions in hydrodynamic turbulence using data from a direct numerical simulation on a grid of 1024(3) points; the flow is forced with the Taylor-Green vortex. An inertial range for the energy is obtained in which the flux is constant and the spectrum follows an approximate Kolmogorov law. Nonlinear triadic interactions are dominated by their nonlocal components, involving widely separated scales. The resulting nonlinear transfer itself is local at each scale but the step in the energy cascade is independent of that scale and directly related to the integral scale of the flow. Interactions with large scales represent 20% of the total energy flux. Possible explanations for the deviation from self-similar models, the link between these findings and intermittency, and their consequences for modeling of turbulent flows are briefly discussed.     

Nonlinear triad interactions and the mechanism of spreading in drift-wave turbulence

We present the results of a derivation of the fluctuation energy transport matrix for the two-field Hasegawa-Wakatani model of drift wave turbulence. The energy transport matrix is derived from a two-scale direct interaction approximation assuming weak turbulence. We examine different classes of triad interactions and show that radially extended eddies, as occurs in penetrative convection, are the most effective in turbulence spreading. We show that in the near-adiabatic limit internal energy spreads faster than the kinetic energy. Previous theories of spreading results are discussed in the context of weak turbulence theory.     

Free energy cascade in gyrokinetic turbulence

In gyrokinetic theory, the quadratic nonlinearity is known to play an important role in the dynamics by redistributing (in a conservative fashion) the free energy between the various active scales. In the present study, the free energy transfer is analyzed for the case of ion temperature gradient driven turbulence. It is shown that it shares many properties with the energy transfer in fluid turbulence. In particular, one finds a (strongly) local, forward (from large to small scales) cascade of free energy in the plane perpendicular to the background magnetic field. These findings shed light on some fundamental properties of plasma turbulence, and encourage the development of large-eddy-simulation techniques for gyrokinetics.     

On the self-energy of electrons in metals

The electron self-energy of unoccupied states is investigated taking into account dynamical screening and nonlocal exchange. To obtain agreement with experiment it is crucial to go beyond the framework of the homogeneous electron gas and include the nonlocal exchange with electrons in valence and core shells. This contribution of atomic origin gives rise to a considerable, almost linear energy dependence of the self-energy over a wide energy range in agreement with experimental findings for many substances and in disagreement with the local density approximation. Quantitative results are presented for Ag.     

Renormalization group theory for fluid and plasma turbulence

For the last several decades, renormalization group (RG, or RNG) methods have been applied to a wide variety of problems of turbulence in hydrodynamics and plasma physics. A comprehensive review of this work will be presented, covering RG methods in hydrodynamic turbulence and in turbulent systems with coupled fluctuating fields like magnetohydrodynamic (MHD) turbulence. This review will attempt to specifically consider several questions about RG: (1) Does RG provide an improvement over previous analytical theories like the direct interaction approximation, or is RG a useful simplification of those theories? (2) How are nonlocal, or ‘sweeping’ effects treated in RG formalisms, or are they ignored entirely? (3) Can RG theories treat both local and nonlocal interactions in turbulence?     

Compressible turbulence: the cascade and its locality

We prove that interscale transfer of kinetic energy in compressible turbulence is dominated by local interactions. In particular, our results preclude direct transfer of kinetic energy from large-scales to dissipation scales, such as into shocks, in high Reynolds number turbulence as is commonly believed. Our assumptions on the scaling of structure functions are weak and enjoy compelling empirical support. Under a stronger assumption on pressure dilatation cospectrum, we show that mean kinetic and internal energy budgets statistically decouple beyond a transitional conversion range. Our analysis establishes the existence of an ensuing inertial range over which mean subgrid scale kinetic energy flux becomes constant, independent of scale. Over this inertial range, mean kinetic energy cascades locally and in a conservative fashion despite not being an invariant.     

Multiwave non-linear couplings in elastic structures. Part II: two-dimensional example

The non-linear resonance coupling in a thin plate in the Kirchhoff-Love approximation is selected as a two-dimensional example of mechanical systems exhibiting a rich range of resonant wave-like phenomena. This is originally examined by use of Whitham's average-Lagrangian method. In particular, the existence of three basic resonant triads between longitudinal, shear and bending modes is shown. Some of these necessarily enter cascade wave processes related to the instability of some of the mode components of the triad under small perturbations. A short comparison with Kolmogorov's cascades of turbulence is given.     

EPR-detected photoinduced electron transfer in three structurally related molecular triads

A comparative electron paramagnetic resonance (EPR) study has been performed on a series of structurally related molecular triads which undergo photoinduced electron transfer and differ one from the other in terms of the acceptor or donor moieties. The molecular triads, C-P-C₆₀, TTF-P-C₆₀ and C-P-P_F, share the same free-base, tetraarylporphyrin (P) as the primary electron donor, which after light excitation initiates the electron transfer process, but differ either in terms of the electron acceptor (fullerene derivative, C₆₀, versus fluorinated free-base porphyrin, P_F), or in terms of the final electron donor (carotenoid polyene, C, versus tetrathiafulvalene, TTF). All these molecular triads can be considered artificial photosynthetic reaction centers in their ability to mimic several key properties of the reaction center primary photochemistry. Photoinduced charge separation and recombination have been followed by time-resolved EPR in a glass of 2-methyltetrahydrofuran and in the nematic phase of the uniaxial liquid crystal E-7. All the triads undergo photoinduced electron transfer, with the generation of charge-separated states in both the low-dielectric environment of the 2-methyl-tetrahydrofuran glass and in anisotropic E-7 medium. Different photochemical pathways have been recognized depending on the specific donor and acceptor moieties constituting the molecular triads. In the presence of the tetrathiafulvalene electron donor singlet- and triplet-initiated electron transfer routes are concurrently active. Recombination to the low-lying carotenoid triplet state occurs in the carotene-based triads, while singlet recombination is the only active route for the TTF-P-C₆₀ triad, where a low-lying triplet state is lacking. Long-lived charge separation has been observed in the case of TTF-P-C₆₀: about 8 μs for the singlet-born radical pair in the glassy isotropic matrix and about 7 μs for the triplet-born radical pair in the nematic phase of E-7. For all the molecular triads, a weak exchange interaction (J?1 G) between the electrons in the final spin-correlated radical pair has been evaluated by simulation of the EPR spectra, providing evidence for superexchange electronic interactions mediated by the tetraarylporphyrin bridge.     

Nonlinear Energy Cascading in Turbulence during the Internal Reconnection Event at the Sino-United Spherical Tokamak

The characteristics of the energy transfer and nonlinear coupling among edge electromagnetic turbulence in thermal quench sub-period of the internal reconnection event(IRE) are studied at the sino-united spherical tokamak device using multiple Langmuir and magnetic probe arrays. The wavelet bispectral analysis and the modified Kim method are applied to investigate linear growth/damping and nonlinear energy transfer rates, along with multi-field turbulence interactions. The results show a multi-field nonlinear energy transfer from electrostatic to magnetic turbulence that results in two-mode coupling in magnetic turbulence, which may play a crucial role to trigger the IRE.     

Relaxation processes in self-assembling triads based on porphyrin Zn-heterodimers

The directional self-assembly of nanosized, structurally organized triads is implemented in methylcyclohexane at 295 K, which is based on the two-point extra coordination of nonsymmetric, covalently bound heterodimers of Zn porphyrins to bipyridyl-substituted porphyrin free-base extra ligands. Based on experimental data and theoretical calculations, the structural organization is determined and information on the energetics of electronic interactions of components is obtained and the rate constants of the directional energy transfer (k ^ET ∼ 10¹¹ s⁻¹) and photoinduced electron transfer (k ^PET ∼ 2.7 × 10⁹ s⁻¹) are determined. The effects of the orientation of interacting macrocycles, the intercenter distances and the solvent temperature on the efficiency of relaxation processes in the triad is investigated.     

Stable periodic density waves in dipolar Bose-Einstein condensates trapped in optical lattices

Density-wave patterns in discrete media with local interactions are known to be unstable. We demonstrate that stable double- and triple-period patterns (DPPs and TPPs), with respect to the period of the underlying lattice, exist in media with nonlocal nonlinearity. This is shown in detail for dipolar Bose-Einstein condensates, loaded into a deep one-dimensional optical lattice. The DPP and TPP emerge via phase transitions of the second and first kind, respectively. The emerging patterns may be stable if the dipole-dipole interactions are repulsive and sufficiently strong, in comparison with the local repulsive nonlinearity. Within the set of the considered states, the TPPs realize a minimum of the free energy. A vast stability region for the TPPs is found in the parameter space, while the DPP stability region is relatively narrow. The same mechanism may create stable density-wave patterns in other physical media featuring nonlocal interactions.     

Asymptotic Analysis of a Slightly Rarefied Gas with Nonlocal Boundary Conditions

In this paper nonlocal boundary conditions for the Navier–Stokes equations are derived, starting from the Boltzmann equation in the limit for the Knudsen number being vanishingly small. In the same spirit of (Lombardo et al. in J. Stat. Phys. 130:69–82, 2008) where a nonlocal Poisson scattering kernel was introduced, a gaussian scattering kernel which models nonlocal interactions between the gas molecules and the wall boundary is proposed. It is proved to satisfy the global mass conservation and a generalized reciprocity relation. The asymptotic expansion of the boundary-value problem for the Boltzmann equation, provides, in the continuum limit, the Navier–Stokes equations associated with a class of nonlocal boundary conditions of the type used in turbulence modeling.     

Energy transfers in dynamos with small magnetic Prandtl numbers

We perform numerical simulation of dynamo with magnetic Prandtl number Pm = 0.2 on 1024³ grid, and compute the energy fluxes and the shell-to-shell energy transfers. These computations indicate that the magnetic energy growth takes place mainly due to the energy transfers from large-scale velocity field to large-scale magnetic field and that the magnetic energy flux is forward. The steady-state magnetic energy is much smaller than the kinetic energy, rather than equipartition; this is because the magnetic Reynolds number is near the dynamo transition regime. We also contrast our results with those for dynamo with Pm = 20 and decaying dynamo.     

Energy transfer and dual cascade in kinetic magnetized plasma turbulence

The question of how nonlinear interactions redistribute the energy of fluctuations across available degrees of freedom is of fundamental importance in the study of turbulence and transport in magnetized weakly collisional plasmas, ranging from space settings to fusion devices. In this Letter, we present a theory for the dual cascade found in such plasmas, which predicts a range of new behavior that distinguishes this cascade from that of neutral fluid turbulence. These phenomena are explained in terms of the constrained nature of spectral transfer in nonlinear gyrokinetics. Accompanying this theory are the first observations of these phenomena, obtained via direct numerical simulations using the gyrokinetic code AstroGK. The basic mechanisms that are found provide a framework for understanding the turbulent energy transfer that couples scales both locally and nonlocally.     

Equilibrium distribution of the wave energy in a carbyne chain

The steady-state energy distribution of thermal vibrations at a given ambient temperature has been investigated based on a simple mathematical model that takes into account central and noncentral interactions between carbon atoms in a one-dimensional carbyne chain. The investigation has been performed using standard asymptotic methods of nonlinear dynamics in terms of the classical mechanics. In the first-order nonlinear approximation, there have been revealed resonant wave triads that are formed at a typical nonlinearity of the system under phase matching conditions. Each resonant triad consists of one longitudinal and two transverse vibration modes. In the general case, the chain is characterized by a superposition of similar resonant triplets of different spectral scales. It has been found that the energy equipartition of nonlinear stationary waves in the carbyne chain at a given temperature completely obeys the standard Rayleigh–Jeans law due to the proportional amplitude dispersion. The possibility of spontaneous formation of three-frequency envelope solitons in carbyne has been demonstrated. Heat in the form of such solitons can propagate in a chain of carbon atoms without diffusion, like localized waves.     

Nonlinear damping of plasma zonal flows excited by inverse spectral transfer

Plasma zonal-flow excitation and saturation in fluid electron-drift-wave turbulence are studied spectrally. The zonal flow is a spectral condensation onto the zero-frequency linear-wave structure. In the representation diagonalizing the wave coupling that dominates interactions at long wavelengths, nonlinear triad interactions involving zero-frequency waves are greatly enhanced. Zonal modes are excited on both unstable and purely stable eigenmode branches. Coupling to the latter introduces robust, finite amplitude-induced damping of zonal flows, providing saturation.