# Hydrodynamic Turbulence: a 19th Century Problem with a Challenge for the 21st Century

@inproceedings{Lvov1996HydrodynamicTA, title={Hydrodynamic Turbulence: a 19th Century Problem with a Challenge for the 21st Century}, author={Victor S. L’vov and Itamar Procaccia}, year={1996} }

Sir Horace Lamb once said “I am an old man now, and when I die and go to Heaven there are two matters on which I hope enlightenment. One is quantum electro-dynamics and the other is turbulence of fluids. About the former, I am really rather optimistic” [1]. Possibly Lamb’s pessimism about turbulence was short-sighted. There exist signs that the two issues that concerned Lamb are not disconnected. The connections have been brewing for a while, and began to take clearer form recently. They…

## 12 Citations

### Review of ‘ Turbulence and Shell Models ’ by

- Physics
- 2012

The problem of hydrodynamic Navier-Stokes turbulence is considered to be one of the last open problems of classical mechanics, and also one of the most tantalizing ones. According to an often-told…

### The Century of Turbulence Theory: The Main Achievements and Unsolved Problems

- Art
- 2001

The flows of fluids actually met both in nature and engineering practice are turbulent in the overwhelming majority of cases. Therefore, in fact the humanity began to observe the turbulence phenomena…

### Remarks on the Frisch framework of hydrodynamic turbulence and the quasi-Lagrangian formulation

- Environmental Science, Mathematics
- 2005

In this paper, we revisit the claim that the Eulerian and quas i-L grangian same time correlation tensors are equal. This statement allows us to tran sform the results of an MSR quasi-Lagrangian…

### On the elimination of the sweeping interactions from theories of hydrodynamic turbulence

- Environmental Science
- 2007

### Experimental investigation of the turbulent cascade development by injection of single large-scale Fourier modes

- PhysicsExperiments in Fluids
- 2020

The current work presents an experimental investigation of the dynamic interactions between flow scales caused by repeated actions of the nonlinear term of the Navier–Stokes equation. Injecting a…

### Different intermittency for longitudinal and transversal turbulent fluctuations

- Physics
- 1997

Scaling exponents of the longitudinal and transversal velocity structure functions in numerical Navier?Stokes turbulence simulations with Taylor?Reynolds numbers up to Relambda = 110 are determined…

### Winterberg’s Conjectured Breaking of the Superluminal Quantum Correlations over Large Distances

- Physics
- 2008

Abstract
We elaborate further on a hypothesis by Winterberg that turbulent fluctuations of the zero point field may lead to a breakdown of the superluminal quantum correlations over very large…

### Passive Scalars in Turbulent Flows

- Physics
- 2000

▪ Abstract Passive scalar behavior is important in turbulent mixing, combustion, and pollution and provides impetus for the study of turbulence itself. The conceptual framework of the subject,…

### A novel laser Doppler anemometer (LDA) for high-accuracy turbulence measurements

- Physics
- 2019

A transparently functioning novel LDA, utilizing advanced technologies and up-to-date hardware and software has therefore been developed to enhance the measurement quality and the dynamic range.

## References

SHOWING 1-10 OF 28 REFERENCES

### Statistical Fluid Mechanics: The Mechanics of Turbulence

- Physics, Engineering
- 1971

This book, originally published in Moscow in 1965, is of interest to a wide scientific and technical audience, including geophysicists, meteorologists, aerodynamicists, chemical, mechanical, and…

### Fluid Mechanics in the First Half of this Century

- Physics
- 1969

THE FIRST DECADE The opening decade of the twentieth century was a period of progress in fluid mechanics. Much was begun that was to continue for many years. Most of the great discoverers in the…

### Exact resummations in the theory of hydrodynamic turbulence. I. The ball of locality and normal scaling.

- PhysicsPhysical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics
- 1995

It is proven that the resulting perturbation theory is free of divergences, both in large and in small spatial separations, and argued that the real space-time formalism that is developed here offers a clear and intuitive understanding of every diagram in the theory, and of every element in the diagrams.

### Multicomponent turbulence, the spherical limit, and non-Kolmogorov spectra.

- MathematicsPhysical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics
- 1995

A set of models for homogeneous, isotropic turbulence is considered in which the Navier-Stokes equations for incompressible fluid flow are generalized to a set of N coupled equations in N velocity…

### Exact Resummations in the Theory of Hydrodynamic Turbulence: 0. Line-Resummed Diagrammatic Perturbation Approach

- Physics
- 1995

The lectures presented by one of us (IP) at the Les Houches summer school dealt with the scaling properties of high Reynolds number turbulence in fluid flows. The results presented are available in…

### Intermittent turbulence in self-similar cascades: divergence of high moments and dimension of the carrier

- PhysicsJournal of Fluid Mechanics
- 1974

Kolmogorov's ‘third hypothesis’ asserts that in intermittent turbulence the average ε of the dissipation ε, taken over any domain D, is ruled by the lognormal probability distribution. This…

### Towards a nonperturbative theory of hydrodynamic turbulence: Fusion rules, exact bridge relations, and anomalous viscous scaling functions.

- MathematicsPhysical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics
- 1996

It is demonstrated that every nth-order correlation function of velocity differences Fn(R1,R2,...) exhibits its own crossover length h n to dissipative behavior as a function of, say, R1, this length depends on n and on the remaining separations R2,R3,... .

### Exact resummations in the theory of hydrodynamic turbulence. III. Scenarios for anomalous scaling and intermittency.

- PhysicsPhysical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics
- 1996

It is shown that nonperturbative effects may introduce multiscaling with the renormalization scale being the infrared outer scale of turbulence $L$.

### Measurements of the Kolmogorov constant and intermittency exponent at very high Reynolds numbers

- Physics, Environmental Science
- 1994

Characteristics of turbulence in the inertial range are experimentally studied in the atmospheric surface layer over the range of the Taylor microscale based Reynolds number Rλ≊(2.8–12.7)×103 and in…