# Inverse versus direct cascades in turbulent advection

@article{Chertkov1998InverseVD, title={Inverse versus direct cascades in turbulent advection}, author={Michael Chertkov and Igor V. Kolokolov and M. Vegrassola}, journal={Physical Review Letters}, year={1998}, volume={80}, pages={512-515} }

A model of scalar turbulent advection in compressible flow is analytically investigated. It is shown that, depending on the dimensionality d of space and the degree of compressibility of the smooth advecting velocity field, the cascade of the scalar is direct or inverse. If d . 4 the cascade is always direct. For a small enough degree of compressibility, the cascade is direct again. Otherwise it is inverse; i.e., very large scales are excited. The dynamical hint for the direction of the cascade…

## 46 Citations

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## References

SHOWING 1-10 OF 40 REFERENCES

Inverse cascade and intermittency of passive scalar in one-dimensional smooth flow

- Mathematics, Physics
- 1997

Random advection of a Lagrangian tracer scalar field $\ensuremath{\theta}(t,x)$ by a one-dimensional, spatially smooth and short-correlated in time velocity field is considered. Scalar fluctuations…

STRUCTURES AND INTERMITTENCY IN A PASSIVE SCALAR MODEL

- Physics
- 1997

Perturbative expansions for intermittency scaling exponents in the Kraichnan passive scalar model [Phys. Rev. Lett. 72, 1016 (1994)] are investigated. A one-dimensional compressible model is…

Statistics of a passive scalar advected by a large-scale two-dimensional velocity field: Analytic solution.

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

The change of variables that allows one to map the matrix problem onto a scalar one is found and to prove the central limit theorem for the stretching rate statistics, valid for any finite correlation time of the velocity field.

Small‐Scale Structure of a Scalar Field Convected by Turbulence

- Physics
- 1968

Batchelor's theory of the turbulent straining of small‐spatial‐scale amplitude variations of a convected scalar field is re‐examined to see the effects of fluctuation of the rates of strain in space…

Anomalous scaling of the passive scalar.

- Physics, MedicinePhysical review letters
- 1995

Anomalous inertial range scaling of structure functions is established for a model of advection of a passive scalar by a random velocity field and for all but the second structure functions the anomalous exponents are nonvanishing.

Small-scale variation of convected quantities like temperature in turbulent fluid Part 1. General discussion and the case of small conductivity

- Physics
- 1959

When some external agency imposes on a fluid large-scale variations of some dynamically passive, conserved, scalar quantity θ like temperature or concentration of solute, turbulent motion of the…

Inertial Ranges in Two‐Dimensional Turbulence

- Physics
- 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…

Normal and anomalous scaling of the fourth-order correlation function of a randomly advected passive scalar.

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

Advection of a passive scalar θ in d = 2 by a large-scale velocity field rapidly changing in time is considered and analytically the simultaneous fourth-order correlation function of θ is obtained.

Turbulence without pressure.

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

It is demonstrated that the breakdown of Galilean invariance is responsible for intermittency and the operator product expansion is established, and the effects of pressure can be turned on perturbatively.