Victor S. L’vov

Wave Turbulence Under Parametric Excitation

. . . . . . . . . . . . . . 6 Advanced S-Theory: Supplementary Sections 121 6.1 Ground State Evolution of System . . . . . . . . . . . . . . . . . with Increasing Pumping Amplitude 123 6.1.1 Ground State of Parametric Waves . . . . . . for Complex Pair Interaction Amplitudes 124 . . . . . . 6.1.2 The Second and Intermediate Thresholds 125 6.1.3 Nonlinear Behavior . . . of Non-Analytic Pair Interaction Amplitudes 128 6.2 Influence of Nonlinear Damping . . . . . . . . . . . . . . . . . . . . . . . . . . on Parametric Excitation 132 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.2.1 Simple Theory 132 6.2.2 Influence of Non-Analyticity . . . . . . . . . . . . . . . . . . . . . . on Nonlinear Damping 135 6.3 Parametric Excitation Under the Feedback Effect on Pumping . . . . . . . . . . . . . . 139 6.3.1 Harniltonian of the Problem . . . . . . . . . . . . . . . . . . 139 . . . 6.3.2 General Analysis of the Equations of Motion 141 6.3.3 First-Order Processes . . . . . . . . . . . . . . . . . . . . . . . . 143 6.3.4 SecondOrder Processes . . . . . . . . . . . . . . . . . . . . . . 146 6.4 Nonlinear Theory of Parametric wave Excitation at Finite Temperatures . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147 6.4.1 Different Time Correlators and Frequency Spectrum . . . . . . . . . . . . . . . . . . . . 147 . . . . . 6.4.2 Basic Equations of Temperature S-Theory 146 6.4.3 Separation of Waves into Parametric and Thermal 150 6.4.4 Two-Dimensional Reduction of Basic Equations . 151 6.4.5 Distribution of Parametric Waves in k . . . . . . . . . 152 6.4.6 Spectrum of Pararnctr-ic Waves . . . . . . . . . . . . . . . 153 6.4.7 Heating Below Threshold . . . . . . . . . . . . . . . . . . . . 153 6.4.8 Influence of Thermal Bath on Total Characteristics 153 6.5 Introduction to Spatially Inhomogeneous S-Theory . . . . . 155 6.5.1 Basic Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155 6.5.2 Parametric Threshold in Inhomogeneous Media . 157 . . . 6.5.3 Stationary State in Non-Homogeneous Media 160 6.6 Nonlinear Behavior of Parametric Waves from Various Branches. Asymmetrical S-Theory . . . . . . . . . . . 165 6.6.1 Derivation of Basic Equations . . . . . . . . . . . . . . . . 165 6.6.2 Stationary States in Isotropic Case . . . . . . . . . . . . 167 6.7 Parametric Excitation of Waves by Noise Pumping . . . . 172 6.7.1 Equations of S-Theory Under Noise Pumping . . 173 6.7.2 Distribution of Parametric Waves ! 6 Advanced S-Theory: i Supplementary Sections / I

Drag reduction by polymers in turbulent channel flows: Energy redistribution between invariant empirical modes

We address the phenomenon of drag reduction by a dilute polymeric additive to turbulent flows, using direct numerical simulations (DNS) of the FENE-P model of viscoelastic flows. It had been amply demonstrated that these model equations reproduce the phenomenon, but the results of DNS were not analyzed so far with the goal of interpreting the phenomenon. In order to construct a useful framework for the understanding of drag reduction we initiate in this paper an investigation of the most important modes that are sustained in the viscoelastic and Newtonian turbulent flows, respectively. The modes are obtained empirically using the Karhunen-Loéve decomposition, allowing us to compare the most energetic modes in the viscoelastic and Newtonian flows. The main finding of the present study is that the spatial profile of the most energetic modes is hardly changed between the two flows. What changes is the energy associated with these modes, and their relative ordering in the decreasing order from the most energetic to the least. Modes that are highly excited in one flow can be strongly suppressed in the other, and vice versa. This dramatic energy redistribution is an important clue to the mechanism of drag reduction as is proposed in this paper. In particular, there is an enhancement of the energy containing modes in the viscoelastic flow compared to the Newtonian one; drag reduction is seen in the energy containing modes rather than the dissipative modes, as proposed in some previous theories.

Spectrum of Kelvin-wave turbulence in superfluids

We derive a type of kinetic equation for Kelvin waves on quantized vortex filaments with random large-scale curvature, that describes step-by-step (local) energy cascade over scales caused by 4-wave interactions. Resulting new energy spectrum ELN(k) ∝ k−5/3 must replace in future theory (e.g., in finding the quantum turbulence decay rate) the previously used spectrum EKS(k) ∝ k−7/5, which was recently shown to be inconsistent due to nonlocality of the 6-wave energy cascade.

Energy spectra of developed superfluid turbulence

Turbulence spectra in superfluids are modified by the nonlinear energy dissipation caused by the mutual friction between quantized vortices and the normal component of the liquid. We have found a new state of fully developed turbulence, which occurs in some range of two Reynolds parameters characterizing the superfluid flow. This state displays both the Kolmogorov-Obukhov 5/3-scaling law Ek ∝ k−5/3 and a new “3-scaling law” Ek ∝ k−3, each in a well-separated range of k.

Energy- and Flux-Budget Turbulence Closure Model for Stably Stratified Flows. Part II: The Role of Internal Gravity Waves

We advance our prior energy- and flux-budget (EFB) turbulence closure model for stably stratified atmospheric flow and extend it to account for an additional vertical flux of momentum and additional productions of turbulent kinetic energy (TKE), turbulent potential energy (TPE) and turbulent flux of potential temperature due to large-scale internal gravity waves (IGW). For the stationary, homogeneous regime, the first version of the EFB model disregarding large-scale IGW yielded universal dependencies of the flux Richardson number, turbulent Prandtl number, energy ratios, and normalised vertical fluxes of momentum and heat on the gradient Richardson number, Ri. Due to the large-scale IGW, these dependencies lose their universality. The maximal value of the flux Richardson number (universal constant ≈0.2–0.25 in the no-IGW regime) becomes strongly variable. In the vertically homogeneous stratification, it increases with increasing wave energy and can even exceed 1. For heterogeneous stratification, when internal gravity waves propagate towards stronger stratification, the maximal flux Richardson number decreases with increasing wave energy, reaches zero and then becomes negative. In other words, the vertical flux of potential temperature becomes counter-gradient. Internal gravity waves also reduce the anisotropy of turbulence: in contrast to the mean wind shear, which generates only horizontal TKE, internal gravity waves generate both horizontal and vertical TKE. Internal gravity waves also increase the share of TPE in the turbulent total energy (TTE = TKE + TPE). A well-known effect of internal gravity waves is their direct contribution to the vertical transport of momentum. Depending on the direction (downward or upward), internal gravity waves either strengthen or weaken the total vertical flux of momentum. Predictions from the proposed model are consistent with available data from atmospheric and laboratory experiments, direct numerical simulations and large-eddy simulations.

Supercurrent in a room-temperature Bose-Einstein magnon condensate

Studies of supercurrent phenomena, such as superconductivity and superfluidity, are usually restricted to cryogenic temperatures, but evidence suggests that a magnon supercurrent can be excited in a Bose–Einstein magnon condensate at room temperature.

Exact solution for the energy spectrum of Kelvin-wave turbulence in superfluids

We study the statistical and dynamical behavior of turbulent Kelvin waves propagating on quantized vortices in superfluids and address the controversy concerning the energy spectrum that is associated with these excitations. Finding the correct energy spectrum is important because Kelvin waves play a major role in the dissipation of energy in superfluid turbulence at near-zero temperatures. In this paper, we show analytically that the solution proposed by [L’vov and Nazarenko, JETP Lett. 91, 428 (2010)] enjoys existence, uniqueness, and regularity of the prefactor. Furthermore, we present numerical results of the dynamical equation that describes to leading order the nonlocal regime of the Kelvin-wave dynamics. We compare our findings with the analytical results from the proposed local and nonlocal theories for Kelvin-wave dynamics and show an agreement with the nonlocal predictions. Accordingly, the spectrum proposed by L’vov and Nazarenko should be used in future theories of quantum turbulence. Finally, for weaker wave forcing we observe an intermittent behavior of the wave spectrum with a fluctuating dissipative scale, which we interpreted as a finite-size effect characteristic of mesoscopic wave turbulence.

Direct energy cascade in two-dimensional compressible quantum turbulence

We numerically study two-dimensional quantum turbulence with a Gross-Pitaevskii model. With the energy initially accumulated at large scale, quantum turbulence with many quantized vortex points is generated. Due to the lack of enstrophy conservation in this model, direct energy cascade with a Kolmogorov-Obukhov energy spectrum E(k){proportional_to}k{sup -5/3} is observed, which is quite different from two-dimensional incompressible classical turbulence in the decaying case. A positive value for the energy flux guarantees a direct energy cascade in the inertial range (from large to small scales). After almost all the energy at the large scale cascades to the small scale, the compressible kinetic energy realizes the thermodynamic equilibrium state without quantized vortices.

Drag reduction by microbubbles in turbulent flows : The limit of minute bubbles

Drag reduction by microbubbles is a promising engineering method for improving ship performance. A fundamental theory of the phenomenon is lacking, however, making actual design quite haphazard. We offer here a theory of drag reduction by microbubbles in the limit of very small bubbles, when the effect of the bubbles is mainly to normalize the density and the viscosity of the carrier fluid. The theory culminates with a prediction of the degree of drag reduction given the concentration profile of the bubbles. Comparisons with experiments are discussed and the road ahead is sketched.

The universal scaling exponents of anisotropy in turbulence and their measurement

Correlation functions of non‐scalar fields in isotropic hydrodynamicturbulence are characterized by a set of universal exponents. These exponents also characterize the rate of decay of the effects of anisotropic forcing in developed turbulence. These exponents are important for the general theory of turbulence, and for modelinganisotropic flows. We propose methods for measuring these exponents by designing new laboratory experiments.