Jean-Philippe Laval

Influence of turbulence on the dynamo threshold.

We use direct and stochastic numerical simulations of the magnetohydrodynamic equations to explore the influence of turbulence on the dynamo threshold. In the spirit of the Kraichnan-Kazantsev model, we model the turbulence by a noise, with given amplitude, injection scale, and correlation time. The addition of a stochastic noise to the mean velocity significantly alters the dynamo threshold and increases it for any noise at large scale. For small-scale noise, the result depends on its correlation time and on the magnetic Prandtl number.

Direct numerical simulation of a separated channel flow with a smooth profile

A direct numerical simulation (DNS) of a channel flow with one curved surface was performed at moderate Reynolds number (Re τ = 395 at the inlet). The adverse pressure gradient was obtained by a wall curvature through a mathematical mapping from physical coordinates to Cartesian ones. The code, using spectral spanwise and normal discretization, combines the advantage of a good accuracy with a fast integration procedure compared to standard numerical procedures for complex geometries. The turbulent flow slightly separates on the profile at the lower curved wall and is at the onset of separation at the opposite flat wall. The thin separation bubble is characterized with a reversal flow fraction. Intense vortices are generated not only near the separation line on the lower wall but also at the upper wall. Turbulent normal stresses and kinetic energy budget are investigated along the channel.

LES modeling of converging-diverging turbulent channel flow

The paper presents the results of the application of large-eddy simulation (LES) to turbulent channel flow with a varying pressure gradient obtained by an appropriately specified shape of one of the walls. The main objective of the paper is to assess various subgrid scale (SGS) models implemented in two different codes as well as to assess the sensitivity of the predictive accuracy to grid resolution. Additionally, the role of SGS viscosity, controlled by a constant parameter of the SGS model, was investigated. The simulations were performed with inlet conditions corresponding to two Reynolds numbers: and . The consistency and the accuracy of simulations are evaluated using direct numerical simulation (DNS) results. It is demonstrated that all SGS models require a comparable minimum grid refinement in order to capture accurately the recirculation region. Such a test case with a reversal flow, where the turbulence transport is dictated by the dynamics of the large-scale eddies, is well suited to demonstrat...

Bifurcations and dynamo action in a Taylor–Green flow

We report successive bifurcations in direct numerical simulations (DNSs) of a Taylor–Green flow, in both a hydro- and a magneto-hydrodynamic case. Hydrodynamic bifurcations occur in between different metastable states with different dynamo action, and are triggered by the numerical noise. The various states encountered range from stationary to chaotic or turbulent through possible oscillatory states. The corresponding sequence of bifurcations is reminiscent of the sequence obtained in the von Karman (VK) flow, at aspect ratio Γ=2 (Nore et al 2003 J. Fluid Mech. 477 51). We then use kinematic simulations to compute the dynamo thresholds of the different metastable states. A more detailed study of the turbulent state reveals the existence of two windows of dynamo action. Stochastic numerical simulations are then used to mimic the influence of turbulence on the dynamo threshold of the turbulent state. We show that the dynamo threshold is increased (respectively decreased) by the presence of large scale (resp. small scale) turbulent velocity fluctuations. Finally, DNSs of the magneto-hydrodynamic equations are used to explore the linear and nonlinear stage of the dynamo instability. In the linear stage, we show that the magnetic field favours the bifurcation from the basic state directly towards the turbulent or chaotic stable state. The magnetic field can also temporarily stabilize a metastable state, resulting in cycles of dynamo action, with different Lyapunov exponents. The critical magnetic Reynolds number for dynamo action is found to increase strongly with the Reynolds number. Finally, we provide a preliminary study of the saturation regime above the dynamo threshold. At large magnetic Prandtl number, we have observed two main types of saturations, in agreement with an analytical prediction of Leprovost and Dubrulle (2005 Eur. Phys. J. B 44 395): (i) intermittent dynamo, with vanishing most probable value of the magnetic energy; (ii) dynamo with non vanishing mean value of the magnetic energy. We describe a sequence of bifurcation of the dynamo at low Reynolds number and at increasing magnetic Prandtl number, where the dynamo switches from stationary mode to chaotic modes in a complex manner, involving intermittency in a way reminiscent to what is observed in dynamical systems with low number of degrees of freedom.

Non-local two-dimensional turbulence and Batchelor's regime for passive scalars

We study small-scale two-dimensional non-local turbulence, where interaction of small scales with large vortices dominates in the small-scale dynamics, by using a semi-classical approach developed in Dyachenko, Nazarenko & Zakharov (1992), Nazarenko, Zabusky & Scheidegger (1995), Dubrulle & Nazarenko (1997) and Nazarenko, Kevlahan & Dubrulle (1999). Also, we consider a closely related problem of passive scalars in Batchelors regime, when the Schmidt number is much greater than unity. In our approach, we do not perform any statistical averaging, and most of our results are valid for any form of the large-scale advection. A new invariant is found in this paper for passive scalars when their initial spectrum is isotropic. It is shown, analytically, numerically and using a dimensional argument, that there is a spectrum corresponding to an inverse cascade of the new invariant, which scales like k[minus sign]1 for turbulent energy and k1 for passive scalars. For passive scalars, the k1-spectrum was first found by Kraichnan (1974) in the special case of advection [delta]-correlated in time, and until now it was believed to correspond to an absolute thermodynamic equilibrium and not a cascade. We also obtain, both analytically and numerically, power-law spectra of decaying two-dimensional turbulence, k[minus sign]2, and passive scalar, k0.

Dynamical modeling of sub-grid scales in 2D turbulence

We develop a new numerical method which treats resolved and sub-grid scales as two different fluid components evolving according to their own dynamical equations. These two fluids are nonlinearly interacting and can be transformed one into another when their scale becomes comparable to the grid size. Equations describing the two-fluid dynamics were rigorously derived from Euler equations [B. Dubrulle, S. Nazarenko, Physica D 110 (1997) 123‐138] and they do not involve any adjustable parameters. The main assumption of such a derivation is that the large-scale vortices are so strong that they advect the sub-grid scales as a passive scalar, and the interactions of small scales with small and intermediate scales can be neglected. As a test for our numerical method, we performed numerical simulations of 2D turbulence with a spectral gap, and we found a good agreement with analytical results obtained for this case by Nazarenko and Laval [Non-local 2D turbulence and passive scalars in Batchelor’s regime, J. Fluid Mech., in press]. We used the two-fluid method to study three typical problems in 2D dynamics of incompressible fluids: decaying turbulence, vortex merger and forced turbulence. The two-fluid simulations performed on at 128 2 and 256 2 resolution were compared with pseudo-spectral simulations using hyperviscosity performed at the same and at much higher resolution. This comparison shows that performance of the two-fluid method is much better than one of the pseudo-spectral method at the same resolution and comparable computational cost. The most significant improvement is observed in modeling of the small-scale component, so that effective inertial interval increases by about two decades compared to the high-resolution pseudo-spectral method. Using the two-fluid method, we demonstrated that the k 3 tail always exists for the energy spectrum, although its amplitude is slowly decreasing in decaying turbulence.

On the relation between kinetic energy production in adverse-pressure gradient wall turbulence and streak instability

A direct numerical simulation (DNS) of a turbulent channel flow with a lower curved wall is performed at Reynolds number Re τ≃617 at inlet. This adverse-pressure gradient turbulent flow is characterized by strong peaks of turbulent kinetic energy at both walls, as a consequence of the breakdown of more organized flow structures. To elucidate the underlying instability scenario, low-speed streak structures are extracted from the turbulent flow field and base flows formed with conditional streak averages, superimposing the mean streamwise velocity profile, are used for linear stability analyses. The size and shape of the counter-rotating streamwise vortices associated with the instability modes are shown to be reminiscent of the coherent vortices emerging from the streak skeletons in the direct numerical simulation. The distance of the streaks centre from the wall is used as a criterion for the conditional averages and the corresponding streak base flows are characterised by more or less pronounced contour...

A model for rapid stochastic distortions of small-scale turbulence

We present a model describing the evolution of the small-scale Navier–Stokes turbulence due to its stochastic distortion by much larger turbulent scales. This study is motivated by numerical findings (Laval et al. Phys. Fluids vol. 13, 2001, p. 1995) that such interactions of separated scales play an important role in turbulence intermittency. We introduce a description of turbulence in terms of the moments of

A New Dynamical Subgrid Model for the Planetary Surface Layer. Part I: The Model and A Priori Tests

k

The streamwise turbulence intensity in the intermediate layer of turbulent pipe flow

-space quantities using a method previously developed for the kinematic dynamo problem (Nazarenko et al. Phys. Rev. E vol. 68, 2003, 0266311). Working with the