Session Q39: Stratified and Buoyancy Driven Flow

The evolution of flow structures and energy exchange in forced rotating stratified turbulence

We investigate the long-time evolution of the rotating stratified turbulence, concerning the flow structures and the exchange between kinetic and potential energy e_KtoP. Numerical simulations of forced three-dimensional homogeneous rotating stratified turbulence are performed at a high hyperviscous Reynolds number and low Rossby number for a sequence of Froude numbers. In the presence of stratification, with two box scale structures with opposite signs of vertical vorticity formed at later times, there are short and small vortices spreading over the flow field. Compared with anticyclonic vortices, cyclonic vortices are lack in number, easier to grow up or merge, and form the box-scale structure earlier. Moreover, the intense area of e_KtoP is associated with the cyclonic structures. We also find a relation between vertical vorticity and the distribution of the density during the evolution of turbulence, which is serviceable for modeling density by velocity.   

Non-Oberbeck-Boussinesq effects and prediction of the bulk temperature in turbulent Rayleigh-Benard convection

We report results of a complementary experimental and numerical study of turbulent non-Oberbeck-Boussinesq Rayleigh-Benard convection (NOB RBC) in pressurized sulfur hexafluoride (SF6). The measurements are conducted in a cylindrical cell of a height 2.2m and diameter 1.1m in the Uboot of the Max Planck Turbulence Facility in  Göttingen and direct numerical simulations (DNS) are performed with the Goldfish code, for a wide range of Rayleigh numbers and different NOB conditions. The numerical and experimental results are compared with predictions for the bulk and the reference temperatures of the top and bottom boundary layers made in Weiss, He, Ahlers, Bodenschatz, Shishkina, J. Fluid Mech., 2018.

  

The accessibility of strongly stratified turbulence in towed-sphere wakes

The strongly stratified turbulence (SST) flow regime (Brethouwer et al. 2007) is characterized by small turbulent horizontal Froude number, i.e. Fr_h « 1, and large buoyancy Reynolds number, i.e. Re_hFr_h² » 1, two quantities that could vary significantly with time in temporally evolving free-shear turbulent flows, such as a towed-sphere wake. We investigate a large-eddy simulation dataset of stratified towed-sphere wakes of varying Reynolds number, Re ≡ UD/ν = [5×10³, 10⁵, 4×10⁵], and Froude number, Fr ≡ 2U/(ND) = [4,16,64], where U is tow speed, D is sphere diameter and N is buoyancy frequency. By examining relevant stratified turbulence parameters in appropriately defined phase diagrams, we show that these wakes can indeed access the SST regime if ReFr^-2/3 > O(10³). The length of time during which the wake turbulence would operate within this regime also depends strongly on Re and Fr. This analysis constitutes a first attempt to obtain a predictive capability of stratified wake turbulence in terms of Re, while extending the investigations of SST from space-filling homogeneous turbulence to a canonical inhomogeneous free-shear flow.

Directional energy flux in anisotropic turbulence

In Navier-Stokes turbulence, energy is transferred among three wave numbers via a triad interaction.  The energy flux, which should be equal to the total energy dissipation rate if the energy transfer is local in the wavenumber space, plays a key role in the energy-cascading process that makes the self-similar structures in turbulent flows.  The energy flux for a wave number in isotropic turbulence systems is given by a scalar and is independent of the magnitude of the wavenumbers in the inertial subrange.  On the other hand, the energy flux in anisotropic turbulence systems depends on the directions as well as the magnitudes of the wave numbers, and should be a vector.  The energy flux vector in the anisotropic systems cannot be uniquely determined in a similar way used for the isotropic energy flux, which is obtained from the scalar energy transfer rate according to the continuity equation of energy.  In this work, we propose a way to determine the energy flux vector in anisotropic turbulence by using the pseudo-inverse matrix, which selects the minimal-norm vector, and will discuss the validity of the energy flux vector in rotating turbulence.   

On the Orientation of Vortical Structures in Homogeneous Turbulent Shear Flows with Stable Stratification or System Rotation

The orientation of vortical structures in homogeneous turbulent shear flows with stable stratification or system rotation is studied using results from direct numerical simulations. Inclined structures are observed in the plane of shear and the three-dimensional two-point autocorrelation coefficient of vorticity magnitude is computed to quantify their orientation. Isosurfaces of the autocorrelation coefficient closely resemble an ellipsoid with its major axis oriented into the direction of the structures. A least-squares fit of an ellipsoid to the isosurfaces is performed and the major axis is determined. From the major axis, the inclination angle of the structures is computed. The inclination angle is observed to have a similar dependence on the Richardson number Ri, in the case of stratified shear flows, and on the rotation to shear rate ratio f/S, in the case of rotating shear flows, as the growth rate of the turbulent kinetic energy. Therefore, the structure orientation in homogeneous turbulent shear flows appears to be directly related to the dynamics of the flows.

  

Three-dimensional numerical simulation of MHD turbulent shear flows

Flow of an electrically conducting fluid in a cylindric container is analysed with direct numerical simulations (DNS). The flow geometry and the value of the injected current density(I) or magnetic fields(B) are corresponding to the experiment of Messadek(2002) . In this work, the cases with injected radius r_e=0.054m  and 1T≤B ≤3T, 3A≤ I ≤20A have been selected to investigate, in which parameter space turbulence regime is  well-established, whereas Hartmann layers remain laminar. Via a visualization way, we find that the flow experiences a complex evolution and the tendency of large structures variation with the increasing of I and B. The mean velocity profiles exhibit that the thickness of free shear layer is increased by the turbulence. For the present parameter space, the angular momentum of the numerics agrees well with that of the experiments and theoretical solutions. DNS shows that the energy spectra exhibits a power law close to k^-5/3 when the Joule dissipation is weak and close to k^-3 when it is significant, which appears consistent with the theory and the experimental results of Messadek(2002).   

Study of convection in rotating flow in a new configuration with bi-directional temperature gradients

Laboratory experiments were conducted in a novel configuration, comprising of non-homogeneously heated rotating cylindrical annulus, to study dynamics of rotating convection. Temperature time series measurements and flow visualization were done over a range of Taylor number, Ta (spanning 6.5 X 10⁸ - 2.7 X 10⁹)  and Rayleigh number, Ra (spanning 2.2 X 10⁸- 6.2 X 10⁸). Localized temperature time series data acquired by thermocouples, two point correlations of temperature data, Nusselt number characteristics, PIV imaging combined with 2D axisymmetric ANSYS Fluent simulation were used to understand the physics of baroclinic instabilities, convective structures and their interaction. Overall, it is speculated that heat transport in this new configuration is governed by the co-existence and interplay of convective plumes (above the heating zone that aid in the vertical transport of heat) and baroclinic waves/eddies (which aid in the horizontal transport of cold and hot fluids between the annuli). The two point temperature correlations show that these waves break into eddies as the value of Ta increases, which closely simulates the dynamics of geophysical motions. Scaling for the proposed system is derived and validated with thermal measurements.