On the nature of turbulence

A mechanism for the generation of turbulence and related phenomena in dissipative systems is proposed.The research was supported by the Netherlands Organisation for the Advancement of Pure Research (Z.W.O.).     

On the peculiar nature of turbulence in planetary dynamos

Under the combined constraints of rapid rotation, sphericity, and magnetic field, motions in planetary cores get organized in a peculiar way. Classical hydrodynamic turbulence is not present, but turbulent motions can take place under the action of the buoyancy and Lorentz forces. Laboratory experiments, such as the rotating spherical magnetic Couette DTS experiment in Grenoble, help us understand what motions take place in planetary core conditions. To cite this article: H.-C. Nataf, N. Gagnière, C. R. Physique 9 (2008).     

On the chaotic nature of turbulence observed in benchmark analysis of nonlinear plasma simulation

Simulational results of two dissipative interchange turbulence (Rayleigh-Taylor-type instability with dissipation) models with the same physics are compared. The convective nonlinearity is the nonlinear mechanism in the models. They are shown to have different time evolutions in the nonlinear phase due to the different initial value which is attributed to the initial noise. In the first model (A), a single pressure representing the sum of the ion and electron components is used (one-fluid model). In the second model (B) the ion and electron components of the pressure fields are independently solved (two-fluid model). Both models become physically identical if we set ion and electron pressure fields to be equal in the model (B). The initial conditions only differ by the infinitesimally small initial noise due to the roundoff errors which comes from the finite difference but not the differentiation. This noise grows in accordance with the nonlinear development of the turbulence mode. Interaction with an intrinsic nonlinearity of the system makes the noise grow, whose contribution becomes almost the same magnitude of the fluctuation itself in the results. The instantaneous deviation shows the chaotic characteristics of the turbulence. (c) 1997 American Institute of Physics.     

Intermittent nature of acceleration in near wall turbulence

Using direct numerical simulation of a fully developed turbulent channel flow, we investigate the behavior of acceleration near a solid wall. We find that acceleration near the wall is highly intermittent and the intermittency is in large part associated with the near wall organized coherent turbulence structures. We also find that acceleration of large magnitude is mostly directed towards the rotation axis of the coherent vortical structures, indicating that the source of the intermittent acceleration is the rotational motion associated with the vortices that causes centripetal acceleration.     

On the lagrangian turbulence in continua

Lagrangian turbulence in continua is introduced as a failure of euclidian metric of a material (frozen) system of coordinates. Criteria of such a turbulence for fluids and solids are derived.     

On the decay law of quasi-two-dimensional turbulence

Laboratory measurements of decaying quasi-two-dimensional turbulence in thin fluid layers with various depths have been performed. It has been shown that decay at large Reynolds numbers corresponds to a non-linear bottom friction with the coefficient satisfying the law λ ∼ (ν/h ²)^1/2|K|^1/4 following from theoretical estimates, where K is the Okubo-Weiss function depending on the enstrophy and degree of ellipticity of vortices. It has been shown that the structure of the flow changes in the decay process.     

On the nature of pulsars

The paper contains a relatively non-technical summary of some recent work by the author and Jeremy Butterfield. The goal is to find a way of assigning meaningful truth values to propositions in quantum theory: something that is not possible in the normal, instrumentalist interpretation. The key mathematical tool is presheaf theory where multi-valued, contextual truth values arise naturally. We show how this can be applied to quantum theory, with the ‘contexts’ chosen to be Boolean subalgebras of the set of all projection operators.     

On MRI turbulence quantification

Turbulent flow, characterized by velocity fluctuations, accompanies many forms of cardiovascular disease and may contribute to their progression and hemodynamic consequences. Several studies have investigated the effects of turbulence on the magnetic resonance imaging (MRI) signal. Quantitative MRI turbulence measurements have recently been shown to have great potential for application both in human cardiovascular flow and in engineering flow. In this article, potential pitfalls and sources of error in MRI turbulence measurements are theoretically and numerically investigated. Data acquisition strategies suitable for turbulence quantification are outlined. The results show that the sensitivity of MRI turbulence measurements to intravoxel mean velocity variations is negligible, but that noise may degrade the estimates if the turbulence encoding parameter is set improperly. Different approaches for utilizing a given amount of scan time were shown to influence the dynamic range and the uncertainty in the turbulence estimates due to noise. The findings reported in this work may be valuable for both in vitro and in vivo studies employing MRI methods for turbulence quantification.     

On a symmetry of turbulence

This paper presents results on symmetries of the spectrum of singularities for random cascades found in the statistical theory of turbulence. It is shown that empirical dimension curves possess a natural symmetry whose presence restricts the class of allowable probability distributions of the cascade generator in a simple manner. In particular, necessary and sufficient conditions on the probability distribution of the generator are obtained for symmetry of the singularity spectrum within a large class of cascade models.     

On the generation and maintenance of waves and turbulence in simulations of free-surface turbulence

One of the challenges in numerical simulation of wave–turbulence interaction is the precise setup and maintenance of wave and turbulence fields. In this paper, we investigate techniques for the generation and suppression of specific surface wave modes, the generation of turbulence in an inhomogeneous physical domain with a wavy boundary-fitted grid, and the generation and maintenance of waves and turbulence during the complex wave–turbulence interaction process. We apply surface pressure to generate and suppress waves. Based on the solution of linearized Cauchy–Poisson problem, we derive three pressure expressions, which lead to a δ-function method, a time-segment method, and a gradual method. Numerical experiments show that these methods generate waves as specified and eliminate spurious waves effectively. The nonlinear wave effect is accounted for with a time-relaxation method. For turbulence generation, we extend the linear forcing method to an inhomogeneous physical domain with a curvilinear computational grid. Effects of force distribution and computational grid distortion are examined. For wave–turbulence interaction, we develop an algorithm to instantaneously identify specific progressive and standing waves. To precisely control the wave amplitude in a complex turbulent flow field, we further develop an energy controlling method. Finally, a simulation example of wave–turbulence interaction is presented. Results show that turbulence has unique features in the presence of waves. Velocity fluctuations are found to be strongly dependent on the wave phase; variations of these fluctuations are explained by the pressure–strain correlation associated with the wave-induced strain field.     

On the third moments in helical turbulence

The evolution of the correlation characteristics in homogeneous helical turbulence is studied. Additional Kármán-Howarth-type equations describing the evolution of the mixed correlation tensor of the velocity and vorticity are obtained. In the helical scaling region, the solution of the obtained equation gives the exact relation between the antisymmetric component of a rank-three correlation tensor and the average dissipation of helicity; this relation is a kind of analog of Kolmogorov’s well-known 4/5 law [A. N. Kolmogrov, Dokl. Akad. Nauk SSSR 32(1), 19 (1941)]. Pis’ma Zh. éksp. Teor. Fiz. 63, No. 10, 768–772 (25 May 1996)