Wouter J. T. Bos

Spectral imbalance and the normalized dissipation rate of turbulence

The normalized turbulent dissipation rate Cϵ is studied in decaying and forced turbulence by direct numerical simulations, large-eddy simulations, and closure calculations. A large difference in the values of Cϵ is observed for the two types of turbulence. This difference is found at moderate Reynolds number, and it is shown that it persists at high Reynolds number, where the value of Cϵ becomes independent of the Reynolds number, but is still not unique. This difference can be explained by the influence of the nonlinear cascade time that introduces a spectral disequilibrium for statistically nonstationary turbulence. Phenomenological analysis yields simple analytical models that satisfactorily reproduce the numerical results. These simple spectral models also reproduce and explain the increase of Cϵ at low Reynolds number that is observed in the simulations.

Dynamics of spectrally truncated inviscid turbulence

The evolution of the turbulent energy spectrum for the inviscid spectrally truncated Euler equations is studied by closure calculations. The observed behavior is similar to the one found in direct numerical simulations [Cichowlas, Bonaititi, Debbasch, and Brachet, Phys. Rev. Lett. 95, 264502 (2005)]. A Kolmogorov spectral range and an equipartition range are observed simultaneously. Between these two ranges a “quasi-dissipative” zone is present in the kinetic energy spectrum. The time evolution of the wave number that marks the beginning of the equipartition range is analyzed and it is shown that spectral nonlocal interactions are governing this evolution.

Reynolds number dependency of the scalar flux spectrum in isotropic turbulence with a uniform scalar gradient

In this paper, the eddy-damped quasi-normal Markovian closure is used to study the behavior of the scalar flux spectrum in isotropic turbulence as the Reynolds number Reλ varies in a range between 30 and 107. The different contributions to the evolution equation of the scalar flux spectrum are studied. One-dimensional spectra are in good agreement with direct numerical simulation (DNS) and experiments at moderate Reλ. The closure shows that at high Reynolds numbers, a K−7∕3 scaling is found for the scalar flux spectrum, in agreement with Lumley’s prediction [Phys. Fluids 10, 855 (1967)], but enormous Reλ are needed before it can be clearly observed. In the range of wind tunnel experiments, the spectral exponent for the scalar flux is closer to −2 in agreement with existing measurements [Mydlarski and Warhaft, J. Fluid Mech. 358, 135 (1998)]. The results for the molecular dissipation of scalar flux are in agreement with the DNS results of Overholt and Pope [Phys. Fluids A 8, 3128 (1996)]. The large Reλ beh...

On the behavior of the velocity-scalar cross correlation spectrum in the inertial range

The velocity-scalar cross spectrum (or scalar flux spectrum) is generally presumed to have a K−7/3 wavenumber dependence in the inertial range, in agreement with the dimensional analysis proposed by Lumley [Phys. Fluids 10, 855 (1967)]. Such a behavior is, however, clearly not observed in experiments in which spectra closer to K−2 (or even less steep) are generally found. It is shown in the paper that dimensional analysis is compatible with a K−2 scaling if a spectral flux of the velocity-scalar cross correlation is introduced. An analysis of the different terms in the equation of the scalar flux spectrum shows that two nonlinear contributions can be identified: a transfer term and the pressure contribution. Direct numerical simulations and large eddy simulation calculations are performed to obtain spectral information about the scalar flux spectrum and to analyze some key properties of the associated nonlinear transfer and pressure terms.

Reynolds number effect on the velocity increment skewness in isotropic turbulence

Second and third order longitudinal structure functions and wavenumber spectra of isotropic turbulence are computed using the eddy-damped quasi-normal Markovian model (EDQNM) and compared to results of the multifractal formalism. It is shown that both the multifractal model and EDQNM give power-law corrections to the inertial range scaling of the velocity increment skewness. For the multifractal formalism, this is an intermittency correction that persists at any high Reynolds number. For EDQNM, this correction is a finite Reynolds number effect, and it is shown that very high Reynolds numbers are needed for this correction to become insignificant with respect to intermittency corrections. Furthermore, the two approaches yield realistic behavior of second and third order statistics of the velocity fluctuations in the dissipative and near-dissipative ranges. Similarities and differences are highlighted, in particular, the Reynolds number dependence.

Inertial range scaling of scalar flux spectra in uniformly sheared turbulence

A model based on two-point closure theory of turbulence is proposed and applied to study the Reynolds number dependency of the scalar flux spectra in homogeneous shear flow with a cross-stream uniform scalar gradient. For the cross-stream scalar flux, in the inertial range the spectral behavior agrees with classical predictions and measurements. The streamwise scalar flux is found to be in good agreement with the results of atmospheric measurements. However, both the model results and the atmospheric measurements disagree with classical predictions. A detailed analysis of the different terms in the evolution equation for the streamwise scalar flux spectrum shows that nonlinear contributions are governing the inertial subrange of this spectrum and that these contributions are relatively more important than for the cross-stream flux. A new expression for the scalar flux spectra is proposed. It allows us to unify the description of the components in one single expression, leading to a classical K−7∕3 inertia...

Extreme Lagrangian Acceleration in Confined Turbulent Flow

A Lagrangian study of two-dimensional turbulence for two different geometries, a periodic and a confined circular geometry, is presented to investigate the influence of solid boundaries on the Lagrangian dynamics. It is found that the Lagrangian acceleration is even more intermittent in the confined domain than in the periodic domain. The flatness of the Lagrangian acceleration as a function of the radius shows that the influence of the wall on the Lagrangian dynamics becomes negligible in the center of the domain, and it also reveals that the wall is responsible for the increased intermittency. The transition in the Lagrangian statistics between this region, not directly influenced by the walls, and a critical radius which defines a Lagrangian boundary layer is shown to be very sharp with a sudden increase of the acceleration flatness from about 5 to about 20.

The role of coherent vorticity in turbulent transport in resistive drift-wave turbulence

The coherent vortex extraction method, a wavelet technique for extracting coherent vortices out of turbulent flows, is applied to simulations of resistive drift-wave turbulence in magnetized plasma (Hasegawa-Wakatani system). The aim is to retain only the essential degrees of freedom, responsible for the transport. It is shown that the radial density flux is carried by these coherent modes. In the quasi-hydrodynamic regime, coherent vortices exhibit depletion of the polarization-drift nonlinearity and vorticity strongly dominates strain, in contrast to the quasiadiabatic regime.

Rapid generation of angular momentum in bounded magnetized plasma

Direct numerical simulations of two-dimensional decaying MHD turbulence in bounded domains show the rapid generation of angular momentum in nonaxisymmetric geometries. It is found that magnetic fluctuations enhance this mechanism. On a larger time scale, the generation of a magnetic angular momentum, or angular field, is observed. For axisymmetric geometries, the generation of angular momentum is absent; nevertheless, a weak magnetic field can be observed. The derived evolution equations for both the angular momentum and angular field yield possible explanations for the observed behavior.

A single-time two-point closure based on fluid particle displacements

A new single-time two-point closure is proposed, in which the equation for the two-point correlation between the displacement of a fluid particle and the velocity allows one to estimate a Lagrangian timescale. This timescale is used to specify the nonlinear damping of triple correlations in the closure. A closed set of equations is obtained without ad hoc constants. Taking advantage of the analogy between particle displacements and scalar fluctuations in isotropic turbulence subjected to a mean scalar gradient, the model is numerically integrated. Results for the energy spectrum are in agreement with classical scaling predictions. An estimate for the Kolmogorov constant is obtained.