# 2D turbulence in physical scales of the Navier-Stokes equations

@article{Dascaliuc20112DTI, title={2D turbulence in physical scales of the Navier-Stokes equations}, author={Radu Dascaliuc and Zoran Grujic}, journal={arXiv: Analysis of PDEs}, year={2011} }

Local analysis of the two dimensional Navier-Stokes equations is used to obtain estimates on the energy and enstrophy fluxes involving Taylor and Kraichnan length scales and the size of the domain. In the framework of zero driving force and non-increasing global energy, these bounds produce sufficient conditions for existence of the direct enstrophy and inverse energy cascades. Several manifestations of locality of the fluxes under these conditions are obtained. All the scales involved are…

## One Citation

### Coherent Vortex Structures and 3D Enstrophy Cascade

- Physics
- 2011

Existence of 2D enstrophy cascade in a suitable mathematical setting, and under suitable conditions compatible with 2D turbulence phenomenology, is known both in the Fourier and in the physical…

## References

SHOWING 1-10 OF 26 REFERENCES

### Energy Cascades and Flux Locality in Physical Scales of the 3D Navier-Stokes Equations

- Physics
- 2011

Rigorous estimates for the total – (kinetic) energy plus pressure – flux in $${\mathbb{R}^3}$$ are obtained from the three dimensional Navier-Stokes equations. The bounds are used to establish a…

### Statistical Estimates for the Navier–Stokes Equations and the Kraichnan Theory of 2-D Fully Developed Turbulence

- Physics, Environmental Science
- 2002

A mathematical formulation of the Kraichnan theory for 2-D fully developed turbulence is given in terms of ensemble averages of solutions to the Navier–Stokes equations. A simple condition is given…

### Navier-Stokes equations

- Mathematics, Physics
- 1992

A criterion is given for the convergence of numerical solutions of the Navier-Stokes equations in two dimensions under steady conditions. The criterion applies to all cases, of steady viscous flow in…

### On universal relations in 2-D turbulence

- Physics
- 2010

A rigorous study of universal laws of 2-D turbulence is presented
for time independent forcing at all length scales.
Conditions for energy and enstrophy cascades are derived, both for a general…

### Energy conservation and Onsager's conjecture for the Euler equations

- Mathematics
- 2007

Onsager conjectured that weak solutions of the Euler equations for incompressible fluids in conserve energy only if they have a certain minimal smoothness (of the order of 1/3 fractional derivatives)…

### Local Structure Of Turbulence in an Incompressible Viscous Fluid at Very Large Reynolds Numbers

- Mathematics
- 1991

§1. We denote by ua(P) = ua(xl, x2, x3, t), a= 1,2,3, the velocity components at time t at a point with rectangular Cartesian coordinates xi, x2, x3. When studying turbulence it is natural to regard…

### Inertial Ranges in Two‐Dimensional Turbulence

- Physics, Environmental Science
- 1967

Two‐dimensional turbulence has both kinetic energy and mean‐square vorticity as inviscid constants of motion. Consequently it admits two formal inertial ranges, E(k)∼e2/3k−5/3 and E(k)∼η2/3k−3, where…

### Counterbalanced interaction locality of developed hydrodynamic turbulence.

- PhysicsPhysical review. A, Atomic, molecular, and optical physics
- 1992

It is shown that the condition of infrared locality of interaction (with larger k,-eddies) could give only the upper restriction for the exponent, and it is proved that any reasonable dimension function D( h) provides locality whatever small h is considered.

### Diffusion Approximation for Two‐Dimensional Turbulence

- Physics, Environmental Science
- 1968

A diffusion approximation to inertial energy transfer in two‐dimensional isotropic turbulence is derived in such a way that energy and squared vorticity are conserved. The −53 and −3 power inertial…