Session MC: Turbulence Simulations VI

The Effect of the Prandtl Number on the Turbulent Wake in a Stratified Fluid

Direct Numerical Simulations are employed to study the effect of the Prandtl number on the towed wake in a stratified fluid. Historically, the majority of stratified wake simulations are performed at a Prandtl number of 1 due to the high numerical cost of simulating larger Prandtl numbers. This makes the assumption that the Prandtl number makes only a small difference in the behavior of the wake. It is well known that the Prandtl number impacts the scale of fluctuations but it is not known how the coupling between kinetic and potential energy at different Prandtl numbers will impact the lifetime of the wake. These numerical simulations were designed to improve understanding of this aspect of the wake evolution. Data is presented for a number of mean and turbulent quantities such as the wake width, wake height, peak defect velocity, velocity fluctuations and turbulent fluxes. Simulations were conducted at a Reynolds number of 10,000 for a range of Prandtl numbers: 0.2, 1, 7, where 7 is a reasonable value for the ocean.   

Dynamics of a Stratified Layer with Horizontal Shear

Direct Numerical Simulations of a temporally evolving uniformly stratified layer with horizontal shear provide insight into the dynamics of common oceanographic and atmospheric flows. The evolution of the stratified horizontal shear layer is investigated along with the importance of coherent vortical structures to Reynolds stresses, dissipation, correlations, spectra, and energy budgets. Novel vortex eduction techniques are employed to isolate coherent structures from the incoherent background flow. Additionally, the effect of rotation is examined with Rossby numbers appropriate for sub-mesoscale flows.   

Direct Numerical Simulations of unstratified and stratified wakes at Re=50,000

Direct numerical simulations (DNS) of axisymmetric wakes with and without initial net momentum are performed at Re=50,000 on a grid with approximately 2 billion grid points. The present study focuses on this difference in the presence of stratification and attempts to elucidate the effects of buoyancy. Similarities and differences are characterized by the evolution of maxima, area integrals and spatial distributions of mean and turbulence statistics. Buoyancy allows a wake to survive longer in a stratified fluid by reducing the correlation responsible for the mean-to-turbulence energy transfer in the vertical direction. This effect is especially important in the case with zero initial net-momentum because it allows regions of positive and negative momentum to become decoupled in the vertical direction and decay with different rates. The role of internal waves in the energetics is determined and it is found that they are responsible for sustaining turbulence at the wake periphery long after the shear production has subsided. The non-equilibrium region of the Re =50,000 wake is found to exhibit a time span when, although the turbulence is strongly stratified as indicated by small Froude number, the turbulent dissipation rate exhibits inertial scaling.   

Numerical simulations of the Lorentz force flowmeter

We investigate the turbulent flow of a liquid metal in a circular pipe under the influence of a localized magnetic field. The magnetic system consists in one or several coils wrapped around the pipe. The electric current in the coils generates a magnetic field that interacts with the velocity of the flow. Eddy currents are thus induced in the flow, and create a Lorentz force. In previous works, we showed that the Lorentz force acting on a coil is proportional to the mean velocity of the flow. Therefore, the measurement of this force allows an accurate determination of the mean flow rate. Here, we consider complex distributions of the magnetic field by using multiple coils, and analyse their influence on the measurement. The influence of some parameters of the coils system, such as the coil radius, is also addressed. The results are based on numerical computations performed with a second-order collocated finite volume method.   

Direct numerical simulation of magnetohydrodynamic flow in a toroidal duct

Magnetohydrodynamics studies the interaction between the motion of electrically conducting fluids and magnetic fields. When the magnetic Reynolds number of the flow is small, which is typical for laboratory-scale experiments and many industrial applications, we can invoke the quasi-static approximation, which states that the induced magnetic field is negligible compared to the externally applied one. In this work, we consider numerical simulations of quasi-static MHD duct flow in a toroidal duct of square cross-section. The choice of this particular geometry was inspired by a recent experimental investigation (P. Moresco and T. Alboussi\`ere, J. Fluid. Mech. 2004) of the instability of the Hartmann layers. The scope of this work is however a more moderate regime in terms of Reynolds and Hartmann number, so that the Coriolis force will also play an important role, as expressed by the Elsasser number. We investigate the transition of the flow and the turbulent statistics as a function of the aforementioned parameters.   

Spectral study of anisotropic magnetohydrodynamic turbulence

A spectral analysis of anisotropic magneto-hydrodynamic turbulence, in presence of a constant magnetic field, is presented using direct numerical simulations. A method of decomposing the spectral space into ring structures is presented and the energy transfers between such rings are studied. This decomposition method takes into account the angular dependency of transfer functions in anisotropic systems, while it allows to recover easily the known shell-to-shell transfers in the limit of isotropic turbulence. For large values of the constant magnetic field, the dominant energy transfers appear to be in the direction perpendicular to the mean magnetic field. The linear transfer due to the constant magnetic also appear to be important in redistributing the energy between the velocity and the magnetic fields.   

Direct numerical and large eddy simulations of decaying magnetohydrodynamic turbulence at low magnetic Reynolds number

A series of direct numerical simulations (DNS) is performed for decaying homogeneous magnetohydrodynamic (MHD) turbulence at low magnetic Reynolds number ($Re_m << 1$) with different strengths of magnetic field. The initially-isotropic turbulence problem has a Taylor scale Reynolds number ($Re_{\lambda}$) of $220$. Comparisons of decay rates, energy spectra and even higher-order statistics such as structure functions and skewness factors are made between the varying magnetic field cases. Furthermore, the phenomenon of anisotropy, that is developed due to the introduction of the magnetic field is investigated by comparing anisotropy coefficients based on velocities and their gradients. Large eddy simulations (LES) using the classical non-dynamic Smagorinsky model are also conducted for the highest magnetic field case and results are in excellent agreement with the corresponding DNS.   

Direct Numerical Simulation for the MHD Homogeneous Shear Turbulence with the Several Parameter Sets

The MHD homogeneous shear turbulent flows with the several initial ratios of the magnetic energy to the kinetic energy, magnetic Prandtl number, shear rates and initial profiles of the cross helicity are investigated by means of the direct numerical simulation. The transformation term between the kinetic and magnetic energy, which is closely connected with the Lorenz force, plays an important role of the interaction between the velocity and magnetic fields. In the cases of the large initial energy ratio and high magnetic Prandtl number, the magnetic energy is converted into the kinetic one and from the result of the energy spectrum budget this converting phenomenon occurs over the wide length scale. On the other hand, the inverse conversion is caused in the large scale in the case of the small initial energy ratio, small magnetic Prandtl number and the high shear rate. The difference among the initial cross helicity has an influence on the time development of the mean quantities immediately after the calculation start.   

Rayleigh-Taylor turbulence in presence of stratification

We present numerical results on 2 dimensional Rayleigh-Taylor turbulence in presence of density stratification, up to Atwood =0.4. Numerical algorithm is based on a fully consistent Thermal Lattice Boltzmann code for an ideal gas. We study both how the mixing layer depends on stratification and small-scale temperature, density and velocity fluctuations, confirming a Bolgiano scaling scenario for two dimensional RT turbulence.   

Prediction of pressure fluctuations in turbulent flows using the immersed boundary method

The immersed boundary (IB) method has been widely used to model flow problems in complex geometries. We investigate the capability of the IB method to predict wall pressure fluctuations in turbulent flows. We introduce a new numerical treatment of the cells crossed by the IB that ensures mass consrvation and provides accurate evaluation of the wall pressure. The present approach has been successfully validated through computations of the space-time correlations of the wall-pressure fluctuations. Compared to the original IB method (Fadlun et al., 2000), the present approach shows better agreement with the standard DNS results. When applied to turbulent flow around an airfoil, the computed flow statistics - the mean/RMS and power spectra of the wall pressure - are in good agreement with the LES performed on body- fitted mesh and experiment (Roger and Moreau, 2004).