Lukas Liechtenstein

Nonlinear formation of structures in rotating stratified turbulence

Nonlinear approaches such as direct numerical simulations (DNS) yield a characteristic structuring in homogeneous turbulence as a result of modified dynamics under the effect of rotation and stable stratification. The structures are elongated for dominant rotation or flat when stratification dominates. Nonlinearity is essential for constructing these anisotropic Eulerian features, which we quantify by single and two-point second-order statistics. Linear approaches such as rapid distorsion theory (RDT) and kinematic simulations (KS) do not reproduce these effects at all. However, when looking at Lagrangian statistics, both linear and nonlinear models seem to yield very similar anisotropic trends. In order to investigate this paradox, we consider statistically homogeneous turbulence with vertical stable stratification characterized by the Brunt–Väisälä frequency N and vertical system rotation with frequency Ω in the Boussinesq system of equations. For different values of the ratio 2 Ω/N, we compare Eulerian and Lagrangian statistics. The detailed dynamics of energy is studied by splitting the velocity in toroidal and poloidal modes, which we put in relation with the wave/vortex linear decomposition. From DNS, the results for dominant stratification show a large disequilibrium of anisotropy between the toroidal and poloidal parts. For dominant rotation, angular spectra show an equidistribution of energy between poloidal and toroidal parts, with non-isotropic angular distribution of the energy density down to the smallest scales. Regarding Lagrangian statistics, DNS results are compared with two linear models based on RDT and KS, respectively. The linear models reproduce extremely well the oscillations and confinement of vertical one-point dispersion when stratification is present. Horizontal diffusion laws compare well in a qualitative way. However, quantitative differences can be detected.

On the structure and dynamics of sheared and rotating turbulence : Direct numerical simulation and wavelet-based coherent vortex extraction

The influence of rotation on the structure and dynamics of sheared turbulence is investigated using a series of direct numerical simulations. Five cases are considered: turbulent shear flow without rotation, with moderate rotation, and with strong rotation, where the rotation configuration is either parallel or antiparallel. For moderate rotation rates an antiparallel configuration increases the growth of the turbulent kinetic energy, while the parallel case reduces the growth as compared to the nonrotating case. For strong rotation rates decay of the energy is observed, linear effects dominate the flow, and the vorticity probability density functions tend to become Gaussian. Visualizations of vorticity show that the inclination angle of the vortical structures depends on the rotation rate and orientation. Coherent vortex extraction, based on the orthogonal wavelet decomposition of vorticity, is applied to split the flow into coherent and incoherent parts. It was found that the coherent part preserves the...

Refined vorticity statistics of decaying rotating three-dimensional turbulence

The influence of background rotation on all nontrivial third-order vorticity correlations is studied for an unbounded incompressible homogeneous turbulent flow, using pseudo-spectral direct numerical simulation. The behaviour of third-order vorticity correlations is found to be consistent with exact theoretical predictions presented herein for axisymmetric turbulence without mirror symmetry. Particular attention is given to the vertical vorticity skewness S ω3. Its dependence on the viscosity, the initial value of the velocity gradient skewness, and the background rotation rate has been thoroughly investigated. The initial growth rate of S ω3 provides evidence for a power-law behaviour proportional to t 0.75 ± 0.1 for all considered cases, in agreement with recent experimental results by Morize et al. [Phys. Fluids 17 (2005) 095105]. It is also found that higher background rotation rates – implying more linearity – result in lower final values of while lower viscosities and lower initial (absolute) values of the velocity derivative skewness both yield higher final values of S ω3.

A Model for the Far-Field Anisotropic Acoustic Emission of Rotating Turbulence

The isotropy of homogeneous turbulence can be broken in flows subject to background rotation. This results in the anisotropic structuration, with large-scale vortices elongated along the rotation axis, and inertial waves with anisotropic mixing properties. Considered as acoustic sources, these anisotropic structures produce noise with characteristics different from the acoustic emission of isotropic turbulence. We propose a computationally efficient model that helps to assess these differences, and to quantify the properties of noise produced by anisotropic turbulence. The simplified configuration is homogeneous turbulence submitted to rotation, for which we evaluate the far-field acoustic emission. A combination of two models is used: Lighthill’s acoustic analogy, for the computation of far-field sound emission, and Kinematic Simulation, a stochastic model for homogeneous turbulence, adapted for rotation. The sound spectrum dependence on the rotation rate and the directivity of acoustic intensity are studied and shown to differ from an isotropic emission.