Extension of the KDO turbulence/transition model to account for roughness

Wall roughness significantly influences both laminar-turbulent transition process and fully developed turbulence. A wall roughness extension for the KDO turbulence/transition model is developed. The roughness effect is introduced via the modification of the k and νt boundary conditions. The wall is considered to be lifted to a higher position. The difference between the original position and the higher position, named as equivalent roughness height, is linked to the actual roughness height. The ratio between the two heights is determined by reasoning. With such a roughness extension, the predictions of the KDO RANS model agree well with the measurements of turbulent boundary layer with a sand grain surface, while the KDO transition model yields accurate cross-flow transition predictions of flow past a 6:1 spheroid.

A nonlinear wave coupling algorithm and its programing and application in plasma turbulences

The fully developed turbulence can be regarded as a nonlinear system, with wave coupling inside, which causes the nonlinear energy transfer, and drives the turbulence to develop further or be suppressed. Spectral analysis is one of the most effective methods to study turbulence system. In order to apply it in the study of the nonlinear wave coupling process of edge plasma turbulence, an efficient algorithm based on spectral analysis technology was proposed to solve the nonlinear wave coupling equation. The algorithm is based on a mandatory temporal static condition after separating the nonideal spectra from the ideal spectra. The realization idea and programing flow were given. According to the characteristics of plasma turbulence, the simulation data were constructed and used to verify the algorithm and its implementation program. The simulation results and examples showed the accuracy of the algorithm and the corresponding program, which could play a great role in the study of the energy transfer in edge plasma turbulences. As an application, the energy cascade analysis of typical edge plasma turbulence was carried out using the results of a case calculation. Consequently, a physical image of the energy transfer in a kind of fully developed turbulence was constructed, which confirmed that the energy transfer in this turbulent system was from lower- to higher-frequency regions and from linear growing to damping waves.

Properties of Hall-MHD Turbulence at Sub-Ion Scales: Spectral Transfer Analysis

We present results of a multiscale study of Hall-magnetohydrodynamic (MHD) turbulence, carried out on a dataset of compressible nonlinear 2D Hall-MHD numerical simulations of decaying Alfvénic turbulence. For the first time, we identify two distinct regimes of fully developed turbulence. In the first one, the power spectrum of the turbulent magnetic fluctuations at sub-ion scales exhibits a power law with a slope of ∼−2.9, typically observed both in solar wind and in magnetosheath turbulence. The second regime, instead, shows a slope of −7/3, in agreement with classical theoretical models of Hall-MHD turbulence. A spectral-transfer analysis reveals that the latter regime occurs when the energy transfer rate at sub-ion scales is dominated by the Hall term, whereas in the former regime, the governing process is the dissipation (and the system exhibits large intermittency). Results of this work are relevant to the space plasma community, as they may potentially reconcile predictions from theoretical models with results from numerical simulations and spacecraft observations.

Nonlinear amplification in hydrodynamic turbulence

Using direct numerical simulations performed on periodic cubes of various sizes, the largest being $8192^3$ , we examine the nonlinear advection term in the Navier–Stokes equations generating fully developed turbulence. We find significant dissipation even in flow regions where nonlinearity is locally absent. With increasing Reynolds number, the Navier–Stokes dynamics amplifies the nonlinearity in a global sense. This nonlinear amplification with increasing Reynolds number renders the vortex stretching mechanism more intermittent, with the global suppression of nonlinearity, reported previously, restricted to low Reynolds numbers. In regions where vortex stretching is absent, the angle and the ratio between the convective vorticity and solenoidal advection in three-dimensional isotropic turbulence are statistically similar to those in the two-dimensional case, despite the fundamental differences between them.

Extension of the KDO Turbulence/Transition Model to Account for Roughness

Wall roughness significantly influences both laminar-turbulent transition process and fully developed turbulence. This work has developed a wall roughness extension for the KDO turbulence/transition model. The roughness effect is introduced via the modification of the k and νt boundary conditions, i.e., the wall is considered to be raised at an extra height. The equivalent roughness height is linked to the actual roughness height, and the ratio between them is determined by reasoning. With such a roughness extension, the predictions of the KDO RANS model agree well with the measurements of turbulent boundary layer with a sand grain surface, while the KDO transition model yields accurate cross-flow transition predictions of flow past a 6:1 spheroid.

A Study of RANS Turbulence Models in Fully Turbulent Jets: A Perspective for CFD-DEM Simulations

This paper presents an analysis of linear viscous stress Favre averaged turbulence models for computational fluid dynamics (CFD) of fully turbulent round jets with a long straight tube geometry in the near field. Although similar work has been performed in the past with very relevant solutions, considerations were not given for the issues and limitations involved with coupling between an Eulerian and Lagrangian phase, such as in fully two-way coupled CFD-DEM. These issues include limitations on solution domain, mesh cell size, wall modelling, and momentum coupling between the two phases in relation to the particles size. Therefore, within these considerations, solutions are provided to the Navier–Stokes equations with various turbulence models using a three-dimensional wedge long straight tube geometry for fully developed turbulence flow. Simulations are performed with a Reynolds number of 13,000 and 51,000 using two different tube diameters. It is found that a modified k-ε turbulence model achieved the most agreeable results for both the velocity and turbulent flow fields between these two flow regimes, while a modified k-ω SST/BSL also provided suitable results.

A Study of RANS Turbulence Models in Fully Turbulent Jets: A Perspective for CFD-DEM Simulations

This paper presents an analysis of linear viscous stress Favre-Averaged turbulence models for computational fluid dynamics (CFD) of fully turbulent round jets with a long straight tube geometry in the near field. Although similar work has been performed in the past with very relevant solutions, considerations were not given for the issues and limitations involved with coupling between an Eulerian and Lagrangian phase, such as in fully two-way coupled CFD-DEM. These issues include limitations on solution domain, mesh cell size, wall modelling, and momentum coupling between the two phases in relation to the particles size. Therefore, within these considerations, solutions are provided to the Navier-Stokes equations with various turbulence models using a three-dimensional wedge long straight tube geometry for fully developed turbulence flow. Simulations are performed with a Reynolds number of 15000 and 50000 using two different tube diameters. It is found that a modified k−ε turbulence model achieved the most agreeable results for both the velocity and turbulent flow fields between these two flow regimes, while a modified k−ω SST/BSL also provided suitable results.

Turbulence of Capillary Waves on Shallow Water

We consider the developed turbulence of capillary waves on shallow water. Analytic theory shows that an isotropic cascade spectrum is unstable with respect to small angular perturbations, in particular, to spontaneous breakdown of the reflection symmetry and generation of nonzero momentum. By computer modeling we show that indeed a random pumping, generating on average zero momentum, produces turbulence with a nonzero total momentum. A strongly anisotropic large-scale pumping produces turbulence whose degree of anisotropy decreases along a cascade. It tends to saturation in the inertial interval and then further decreases in the dissipation interval. Surprisingly, neither the direction of the total momentum nor the direction of the compensated spectrum anisotropy is locked by our square box preferred directions (side or diagonal) but fluctuate.

Multifractals, free turbulence decay laws and the Scaling Gyroscopes Cascade model

<p>Turbulence being a dissipative system decays when being "free", i.e. without any force. The law of this decay has been intriguing for quite a while. Assuming that for vanishing viscosity, the whole spectrum is self-similar, as well as stationary for low wave numbers/large eddies  (E(k,t) ≈C<sub>S</sub> k<sup>S</sup>, k → 0) , it was shown [1] that the total energy of turbulence has a power-law decay: E(t) = ∫ E(k,t) dk ≈ t<sup>-a(s)</sup>: a(s) =2(s+1)/(s+3) . This was particularly thought to be relevant for s=4, C<sub>4</sub> being proportional to the Loitsianski integral, assumed to be time-invariant [2]. However, it was shown with the help of the eddy-damped quasi-normal Markovian (EDQNM) [3] that there is an energy backscatter term transferring energy from energy-containing eddies by nonlocal triads interactions to large eddies, which behaves like T<sub>NL</sub>≈ k<sup>4</sup> and therefore prevents the invariance of the Loitsianski integral. This implies that the theoretical exponent a(s) = 2(s+1)/(s+3)  is only valid for s<4 and that a(s) =a(4)=-(10-2γ)/7 for s≥ 4 with C<sub>4</sub>(t) ≈ t <sup>γ</sup>, γ>0. The turbulence decay is therefore slower than previously expected for s ≥ 4 due to the backscatter term that progressively stores energy in large eddies. <br>EDQNM provides the estimate γ ≈ 0.16. However, a strong limitation of EDQNM and similar models (e.g. Direct Interaction Approximation, Test Field Model) is that these models are not able to represent intermittency, which is a fundamental phenomenon of turbulence [4] and this could bring into questions the previous results. We, therefore, investigate this question with the Scaling Gyroscopes Cascade (SGC) model [5], which is based on nonlocal interactions and display multifractal intermittency [6]. We first theoretically argue that SGC confirms the existence of the backscatter term, but the turbulence decay is no longer smooth but occurs by puffs and we provide numerical evidence of this.</p><p>Keywords: Loitsianski integral; intermittency; infrared spectrum; SGC model; energy decay</p><p>[1]M. Lesieur and D. Schertzer, ‘‘Amortissement auto-similaire d’une turbulence a‘ grand nombre de Reynolds,’’ J. Mec. 17, 609 1978 .</p><p>[2]Davidson, P. A. (2000). Was Loitsyansky correct? A review of the arguments. <em>Journal of Turbulence</em>, <em>1</em>(1), 006-006.</p><p>[3]Frisch, U., Lesieur, M.,Schertzer, D. (1980). Comments on the quasi- normal Markovian approximation for fully-developed turbulence. Jour- nal of Fluid Mechanics, 97(1), 181-192.</p><p>[4]Morf, R. H., Orszag, S. A., Frisch, U. (1980). Spontaneous singularity in three-dimensional inviscid, incompressible ow. Physical Review Letters, 44(9), 572.</p><p>[5]Chigirinskaya, Y., Schertzer, D.,  Lovejoy, S. (1997). Scaling gyroscopes cascade: universal multifractal features of 2-D and 3-D turbulence. <em>Fractals and Chaos in Chemical Engineering. World Scientific, Singapore</em>, 371-384.</p><p>[6]Chigirinskaya, Y.,  Schertzer, D. (1997). Cascade of scaling gyroscopes: Lie structure, universal multifractals and self-organized criticality in turbulence. In <em>Stochastic Models in Geosystems</em> (pp. 57-81). Springer, New York, NY.</p>

Observations of shock propagation through turbulent plasma in the solar corona

<p>Eruptive activity in the solar corona can often lead to the propagation of shockwaves. In the radio domain the primary signature of such shocks are type II radio bursts, observed in dynamic spectra as bands of emission slowly drifting towards lower frequencies over time. These radio bursts can sometimes have inhomogeneous and fragmented fine structure, but the cause of this fine structure is currently unclear. Here we observe several type II radio bursts on 2019-March-20th using the New Extension in Nancay Upgrading LOFAR (NenuFAR), a radio interferometer observing between 10-85 MHz. We show  that the distribution of size-scales of density perturbations associated with the fine structure of one type II follows a power law with a spectral index of -1.71, which closely matches the value of -5/3 expected of fully developed turbulence. We determine this turbulence to be upstream of the shock, in background coronal plasma at a heliocentric distance of ~2 R<sub>sun</sub>. The observed inertial size-scales of the turbulent density inhomogeneities range from ~62 Mm to ~209 km. This shows that type II fine structure and fragmentation can be due to shock propagation through an inhomogeneous and turbulent coronal plasma, and we discuss the implications of this on electron acceleration in the coronal shock.</p>