Variable energy flux in turbulence

Abstract

In three-dimensional hydrodynamic turbulence forced at large length scales, a constant energy flux ${\Pi }_u$ flows from large scales to intermediate scales, and then to small scales. It is well known that for multiscale energy injection and dissipation, the energy flux ${\Pi }_u$ varies with scales. In this review we describe this principle and show how this general framework is useful for describing a variety of turbulent phenomena. Compared to Kolmogorov's spectrum, the energy spectrum steepens in turbulence involving quasi-static magnetofluid, Ekman friction, stable stratification, magnetohydrodynamics, and solution with dilute polymer. However, in turbulent thermal convection, in unstably stratified turbulence such as Rayleigh-Taylor turbulence, and in shear turbulence, the energy spectrum has an opposite behaviour due to an increase of energy flux with wavenumber. In addition, we briefly describe the role of variable energy flux in quantum turbulence, in binary-fluid turbulence including time-dependent Landau-Ginzburg and Cahn-Hillianrd equations, and in Euler turbulence.

arXiv comment69 pages

References in corpus (95)

• From Quantum Chaos and Eigenstate Thermalization to Statistical Mechanics and Thermodynamics
• Astrophysical magnetic fields and nonlinear dynamo theory
• Particles and fields in fluid turbulence
• A weak turbulence theory for incompressible MHD
• Cascades and transitions in turbulent flows
• High Reynolds number Taylor-Couette turbulence
• Introduction to quantum turbulence
• Statistical Theory of Magnetohydrodynamic Turbulence: Recent Results
• Shell to shell energy transfer in MHD, Part I: steady state turbulence
• Simulations of Bose fields at finite temperature
• Inverse energy cascade in three-dimensional isotropic turbulence
• Hyperviscosity, Galerkin truncation and bottlenecks in turbulence
• Spectra of turbulence in dilute polymer solutions
• Instantons in Burgers Equation
• Effective Dissipation and Turbulence in Spectrally Truncated Euler Flows
• Energy transfer in two-dimensional magnetohydrodynamic turbulence: formalism and numerical results
• Shell Models of Magnetohydrodynamic Turbulence
• Quantum turbulence in trapped atomic Bose-Einstein condensates
• Phenomenology of buoyancy-driven turbulence: recent results
• Manifestations of Drag Reduction by Polymer Additives in Decaying, Homogeneous, Isotropic Turbulence
• The imprint of large-scale flows on turbulence
• Energy Spectrum of Buoyancy-Driven Turbulence
• Far Dissipation Range of Turbulence
• Polymers in Fluid Flows
• Statistical equilibria of large scales in dissipative hydrodynamic turbulence
• Energy Flux and Bottleneck Effect in Turbulence
• Heat transport in boiling turbulent Rayleigh-Bénard convection
• Non-Kolmogorov cascade of helicity driven turbulence
• Intermittency exponents and energy spectrum of the Burgers and KPZ equations with correlated noise
• Strong anisotropy in quasi-static magnetohydrodynamic turbulence for high interaction parameters
• Scaling of heat flux and energy spectrum for "very large" Prandtl number convection
• Anisotropy in Quasi-Static Magnetohydrodynamic Turbulence
• Two-dimensional Turbulence in Symmetric Binary-Fluid Mixtures: Coarsening Arrest by the Inverse Cascade
• Evidence for Bolgiano-Obukhov scaling in rotating stratified turbulence using high-resolution direct numerical simulations
• Energy Spectra of Developed Turbulencein Helium Superfluids
• Convective turbulent viscosity acting on equilibrium tidal flows: new frequency scaling of the effective viscosity
• Local shell-to-shell energy transfer via nonlocal Interactions in fluid turbulence
• Resonance phenomenon for the Galerkin-truncated Burgers and Euler equations
• On the energy spectrum of rapidly rotating forced turbulence
• Exact Resummations in the Theory of Hydrodynamic Turbulence: I The Ball of Locality and Normal Scaling
• Revisiting Bolgiano-Obukhov scaling for moderately stably stratified turbulence
• Energy transfer in turbulence under rotation
• Turbulence and coarsening in active and passive binary mixtures
• Applicability of Taylor's hypothesis in thermally driven turbulence
• Energy Spectra and Fluxes in Dissipation Range of Turbulent and Laminar Flows
• Anisotropic energy transfers in quasi-static magnetohydrodynamic turbulence
• Why, how and when MHD turbulence at low $Rm$ becomes three-dimensional
• Variable enstrophy flux and energy spectrum in two-dimensional turbulence with Ekman friction
• Energy Spectra of Quantum Turbulence: Large-scale Simulation and Modeling
• Dissipation range of the energy spectrum in high Reynolds number turbulence
• Statistical features of rapidly rotating decaying turbulence: enstrophy and energy spectra, and coherent structures
• Quantum turbulence in quantum gases
• Energy and enstrophy spectra and fluxes for the inertial-dissipation range of two-dimensional turbulence
• Turbulence and Multiscaling in the Randomly Forced Navier Stokes Equation
• Near isotropic behaviour of turbulent thermal convection
• Modeling quasi-static magnetohydrodynamic turbulence with variable energy flux
• Quantum turbulence at finite temperature: the two-fluids cascade
• Energy Cascade and Intermittency in Helically Decomposed Navier-Stokes Equations
• Dynamic anisotropy in MHD turbulence induced by mean magnetic field
• The inverse cascade of magnetic helicity in magnetohydrodynamic turbulence
• Rotating Taylor-Green Flow
• Discontinuous transition from direct to inverse cascade in three-dimensional turbulence
• Field theoretic calculation of scalar turbulence
• Exact Resummations in the Theory of Hydrodynamic Turbulence: II A Ladder to Anomalous Scaling
• Large-scale intermittency of liquid-metal channel flow in a magnetic field
• Dispersive bottleneck delaying thermalization of turbulent Bose-Einstein Condensates
• Computing the Scaling Exponents in Fluid Turbulence from First Principles: Demonstration of Multi-scaling
• Experimental Study of the Bottleneck in Fully Developed Turbulence
• From two-dimensional to three-dimensional turbulence through two-dimensional three-component flows
• Exact Resummations in the Theory of Hydrodynamic Turbulence: III. Scenarios for Anomalous Scaling and Intermittency
• Self-organised criticality and 1/f noise in single-channel current of voltage-dependent anion channel
• On the thermal equilibrium state of large scale flows
• Inverse cascade of energy in helical turbulence
• The Viscous Lengths in Hydrodynamic Turbulence are Anomalous Scaling Functions
• Shell model of superfluid turbulence
• Kinetic energy spectra and flux in turbulent phase-separating symmetric binary-fluid mixtures
• Fusion Rules in Navier-Stokes Turbulence: First Experimental Tests
• Phase transition in time-reversible Navier-Stokes equations
• Anomalous vortex ring velocities induced by thermally-excited Kelvin waves and counterflow effects in superfluids
• How vortices and shocks provide for a flux loop in two-dimensional compressible turbulence
• 1/f noise and long-term memory of coherent structures in a turbulent shear flow
• Asymmetric energy transfers in driven nonequilibrium systems and arrow of time
• Universal Scaling Laws for Large Events in Driven Nonequilibrium Systems
• Comparison of Theory and Direct Numerical Simulations of Drag Reduction by Rodlike Polymers in Turbulent Channel Flows
• Gyrokinetic turbulence: between idealized estimates and a detailed analysis of nonlinear energy transfers
• Evolution of similarity lengths in anisotropic magnetohydrodynamic turbulence
• Intra-scales energy transfer during the evolution of turbulence in a trapped Bose-Einstein condensate
• Phenomenology of two-dimensional stably stratified turbulence under large-scale forcing
• Enstrophy transfers in helical turbulence
• Turbulent drag reduction in magnetohydrodynamic and quasi-static magnetohydrodynamic turbulence
• Similarities between the structure functions of thermal convection and hydrodynamic turbulence
• On uniqueness of transfer rates in magnetohydrodynamic turbulence
• Contrasting turbulence in stably stratified flows and thermal convection
• Helicoidal particles in turbulent flows with multi-scale helical injection
• Euler Turbulence and thermodynamic equilibrium

Cited by in corpus (10)

• Intermittency, fluctuations and maximal chaos in an emergent universal state of active turbulence
• Statistical Equilibrium of Large Scales in Three-Dimensional Hydrodynamic Turbulence
• Hydrodynamic Entropy and Emergence of Order in Two-dimensional Euler Turbulence
• Equilibrium states of Burgers and KdV equations
• Baroclinic interaction of forced shock waves with random thermal gradients
• Nonlinear mode coupling and energetics of driven magnetized shear-flow turbulence
• Taylor's Frozen-in Hypothesis for Magnetohydrodynamic turbulence and Solar Wind
• A revisit of generalized scaling of forced turbulence through flux analysis
• Magnetohydrodynamic Turbulence: Chandrasekhar's Contributions \& Beyond
• Quad-cascade picture of electrokinetic turbulence