# SHELL MODELS OF ENERGY CASCADE IN TURBULENCE

@article{Biferale2003SHELLMO, title={SHELL MODELS OF ENERGY CASCADE IN TURBULENCE}, author={Luca Biferale}, journal={Annual Review of Fluid Mechanics}, year={2003}, volume={35}, pages={441-468} }

▪ Abstract We review the most important theoretical and numerical results obtained in the realm of shell models for the energy-turbulent cascade. We mainly focus here on those results that had or will have some impact on the fluid-dynamics community. In particular, we address the problem of small-scale intermittency by discussing energy–helicity interactions, energy-dissipation multifractality, and universality of intermittency, i.e., independence of anomalous scaling exponents from large-scale…

## 269 Citations

### Anomalous scaling and universality in hydrodynamic systems with power-law forcing

- Physics
- 2004

The problem of the interplay between normal and anomalous scaling in turbulent systems stirred by a random forcing with a power-law spectrum is addressed. We consider both linear and nonlinear…

### Dynamic scaling in rotating turbulence: A shell model study.

- PhysicsPhysical review. E
- 2022

We investigate the scaling form of appropriate timescales extracted from time-dependent correlation functions in rotating turbulent flows. In particular, we obtain precise estimates of the dynamic…

### Bridging inertial and dissipation range statistics in rotating turbulence

- Physics
- 2019

We perform a multifractal analysis of rotating turbulence to obtain an estimate of the (anomalous) scaling exponents in the inertial range in terms of the generalised dimensions associated with the…

### Hidden scale invariance of intermittent turbulence in a shell model

- Engineering
- 2020

It is known that scale invariance is broken in the developed hydrodynamic turbulence due to intermittency, substantiating complexity of turbulent flows. Here we challenge the concept of broken scale…

### Dynamical scaling and intermittency in shell models of turbulence.

- PhysicsPhysical review. E, Statistical, nonlinear, and soft matter physics
- 2005

It is shown that by slowing down the energy-transfer mechanism for fixed energy flux, intermittency decreases and eventually disappears, supporting the conjecture that intermittency can be observed only if energy is flowing towards faster and faster scales of motion.

### Optimal thermalization in a shell model of homogeneous turbulence

- Physics
- 2015

We investigate the turbulence-induced dissipation of the large scales in a statistically homogeneous flow using an ‘optimal closure,’ which one of us (BT) has recently exposed in the context of…

### Model for intermittency of energy dissipation in turbulent flows.

- PhysicsPhysical review. E, Statistical, nonlinear, and soft matter physics
- 2006

It is suggested that the proposed dynamical model could represent a useful tool to simulate the intermittent structure of turbulent energy dissipation in those high-Reynolds-number astrophysical fluids where impulsive energy release processes can be associated with the dynamics of the turbulent cascade.

### Inverse energy cascade in nonlocal helical shell models of turbulence.

- PhysicsPhysical review. E, Statistical, nonlinear, and soft matter physics
- 2015

A modified version of helical shell models for turbulence with nonlocal triadic interactions is introduced, showing that there exists a class of models that exhibits a statistically stable inverse energy cascade, in close analogy with that predicted for the Navier-Stokes equations restricted to the same helical interactions.

## References

SHOWING 1-10 OF 84 REFERENCES

### Intermittency in the large-N limit of a spherical shell model for turbulence

- Physics, Mathematics
- 1997

A spherical shell model for turbulence, obtained by coupling N replicas of the Gledzer, Okhitani and Yamada shell model, is considered. Conservation of energy and of a helicity-like invariant is…

### Statistical mechanics of shell models for two-dimensional turbulence.

- Physics, Environmental SciencePhysical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics
- 1994

The main result is that the observed state is well described as a formal statistical equilibrium, closely analogous to the approach to two-dimensional ideal hydrodynamics of Onsager, Hopf and Lee.

### Intermittency in Turbulence

- Physics
- 2002

We present a detailed review of recent developments in the statistical approach to fully developed turbulence. We address both ideal situations such as “homogeneous and isotropic turbulence” as well…

### Cascades of energy and helicity in the GOY shell model of turbulence

- Physics
- 1997

The effect of extreme hyperviscous damping, νknp,p=∞ is studied numerically in the GOY shell model of turbulence. It has resently been demonstrated [Leveque and She, Phys. Rev. Lett. 75, 2690 (1995)]…

### Cascades and statistical equilibrium in shell models of turbulence.

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

The GOY shell model simulating the cascade processes of turbulent flow has two inviscid invariants governing the dynamical behavior, and the multi fractality of the enstrophy dissipation seems to be related to the ratio of typical timescales of the different shell velocities.

### Shell model for turbulent advection of passive-scalar fields.

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

A shell model for the small-scale statistics of a scalar field passively carried by a three-dimensional turbulent fluid is introduced and it is found to exhibit an intermittency correction to the 5/3 Obukhov-Corrsin power law for the power spectrum of a passive scalar.

### Instanton calculus in shell models of turbulence

- PhysicsPhysical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics
- 2000

A statistical theory of singular structures whose dynamics in the inertial range includes interactions with a background of fluctuations is proposed by modeling the incoherent background as a Gaussian white-noise forcing of small strength Gamma.

### Anomalous scaling in a model of hydrodynamic turbulence with a small parameter

- Physics
- 1999

The major difficulty in developing theories for anomalous scaling in hydrodynamic turbulence is the lack of a small parameter. In this letter we introduce a shell model of turbulence that exhibits…

### Energy spectra in a model for convective turbulence.

- PhysicsPhysical review letters
- 1992

The energy cascade in both hydrodynamic and hydromagnetic Boussinesq convection is investigated at large Rayleigh numbers, using a scalar model for turbulence and derives dissipative cutoff wave numbers that are consistent with these spectra.