Mini-workshop on Turbulence, Fluid and Magnetohydrodynamics (The 7th of July)

The Computational Fluid Dynamics group at the Department of Applied Mathematics will host a mini-workshop on Fluid, Turbulence and Magnetohydrodynamics on the 7th of July. The workshop will take place in the Lecture Theatre 3 at Hicks Building. Researchers from outside Sheffield and the Department of Applied Mathematics will present their recent works. You are cordially invited to join us. No registration is needed.

The timetable is available below, and can also be downloaded on the right. For more information, please contact Dr. Yi Li.

The workshop is supported by EPSRC through the Bridging the Gap grant, Royal Society, and the Department of Applied Mathematics.

9:00-9:30 Coffee at the Common Room (I14)
9:30-10:30 Wind turbine array fluid dynamics: measurements and modeling issues
  Charles Meneveau (The Johns Hopkins University, USA)
  The presentation will summarize results from ongoing wind tunnel measurements to characterize the boundary layer structure associated with arrays of wind turbines. A rough-wall turbulent boundary layer is created in the Corrsin wind tunnel to replicate atmospheric turbulent boundary layer (ATBL) conditions and to study the interaction between the ATBL and an array of wind turbines. An active grid, vertical strakes and surface roughness are combined to create mean velocity and Reynolds stresses profiles that resemble those of an ATBL. Wind-turbine models, scaled down about 850 times from real life length scales, use three bladed rotors with a diameter D = 12cm. Various statistics such as plane averaged mean velocities and turbulence quantities are documented, as well as wake profiles to quantify wake recovery. In a related project, Large Eddy Simulations using the drag disk concept are performed. The model is implemented within a Large Eddy Simulation of an array of wind turbines. The budgets of kinetic energy are analyzed in detail (This work is a collaboration with L. Castillo, R. Cal, J. Lebron, H.S. Kang, and M. Calaf, and is supported by the National Science Foundation).
10:30-11:30 Mixing and quasi-modes in two-dimensional planar vortices
  Andrew Gilbert (University of Exeter)
  When an inviscid Gaussian vortex in the plane is perturbed, for example by a weak, transient external strain field, the perturbation shows an exponential decay as the vortex relaxes to axisymmetry. Although such a vortex can easily be shown to possess no normal modes and only continuous spectrum, there is a complex `growth' rate that can be found by analytic continuation as a so-called Landau pole --- it has negative real part and so in fact corresponds to exponential decay. This exponential decay does not correspond to a classical normal mode, but what is described as a quasi-mode. This finding, which goes back to Briggs, Daugherty and Levy (1970), with recent key contributions by Balmforth, Le Dizes, Shecter and co-workers, is relevant to understanding much of the physics of planar vortices, for example the formation of long-lived cat's eyes when the external applied strain exceeds some threshold.

In this talk I will outline the background to these problems and some of our recent investigations into the dynamics of planar vortices, including recent work on how the spreading of vorticity through mixing interacts with stability and dynamics, giving rise to phenomena such as vorticity staircases. This is joint work with Andrew Bassom (Perth, Australia) and Matthew Turner (EPSRC supported).
11:30-11:50 Coffee break at the Common Room (I14)
11:50-12:30 Blow-up Problems in Fluid Mechanics: a Case Study
  Koji Ohkitani(University of Sheffield)
  We consider a family of 2D fluid equations, which include the 2D Euler and the surface quasi-geostrophic (SQG) equations. In dissipative cases (hypo-viscosity), an oscillatory damping is observed in long-time evolution, both below/above the criticality. This suggests all-time regularity even for supercritical cases, but with a complicated transient. For inviscid cases, the growth rates of scalar gradient in Lp are compared within the family; in particular, the 2D Euler grows faster than SQG. This order is reversed in maximum norm.
12:30-2:00 Lunch
2:00-3:00 Synthetic Turbulence using a Minimal Lagrangian Map
  Carlos Rosales (Universidad Tecnica Federico Santa Maria, Chile)
  Methods available to generate synthetic vector fields as surrogates for turbulent velocity fields are not able to reproduce the non-Gaussian statistics of turbulence nor to produce phase coherency. This talk will present a method recently introduced to generate non-Gaussian synthetic vector fields (called MLM). The method is based on a minimal Lagrangian map, by which an initial Gaussian field generated using random-phase Fourier modes, is deformed over a multiplicity of spatial scales. This is done by moving fluid particles of a sequence of low-pass filtered fields for some scale-dependent time-interval, interpolating onto regular grids and enforcing the divergence-free condition.

The results show that vector fields obtained in this way display many statistical and structural properties observed in real turbulence, which cannot be reproduced by Gaussian fields with random phases. The MLM-generated fields are used as initial conditions in DNS and LES of decaying isotropic turbulence, yielding more realistic evolution and significantly shortened initial adjustment periods when compared with initializations using Gaussian fields. It is also found that the Lagrangian map time scale is crucial in determining anomalous scaling properties in the inertial range. Using the Eulerian sweeping time scale non-Gaussian statistics and realistic geometric features are reproduced at each scale, but anomalous exponent are not observed. Conversely, if the appropriate Kolmogorov inertial-range turnover time scale is used, fields with realistic anomalous scaling are generated. In the same way, the intermittency and multifractal nature of energy dissipation is found to be quite realistic, as well as the properties of the pressure field derived from the synthetic velocity field. Finally, preliminary results from ongoing research on synthetic passive scalar fields generated by this procedure also show realistic statistics.
3:00-3:30 Microfluidics for Rheology
  Julia M. Rees, Hemaka C. H. Bandulasena and William B. Zimmerman
(University of Sheffield)
  A novel methodology for calculating the rheological parameters of non-Newtonian power law fluids will be explained. The fidelity of finite element modelling of the Navier Stokes equations for reproducing the velocity fields of such a fluid in a microfluidic T-junction has been verified by comparing numerical simulations with experimental observations obtained using micron resolution particle image velocimetry (-PIV). As the pressure-driven fluid is forced to turn the corner of the T-junction, a range of shear rates, and therefore viscosities, is produced within the flow system. Thus we have a set up whereby potentially the rheological profile of a power law fluid could be established from a single experiment. An inverse method based on finding the mapping between the statistical moments of field variables and the constitutive parameters of the viscosity profile demonstrated that such a system could potentially be used for the design of an efficient microfluidic rheometer.
3:30-3:50 Coffee break at the Common Room (I14)
3:50-4:40 Modelling multi-scale interaction in sheared turbulence: transport barriers, self-organisation, and intermittency
  Eun-jin Kim (University of Sheffield)
  Understanding multi-scale interactions is an outstanding problem in turbulence. Despite complex nonlinear dynamics, coherent structures such as shear flows (vortices, differential rotation, zonal flows, etc) often form from small-scale turbulence, which then fundamentally modify the turbulence property of small-scales. For instance, shear flows can dramatically quench turbulent mixing and transport, thereby triggering the formation of transport barriers. As small-scale turbulence influenced by shear flows in turn feedbacks on the dynamics of shear flows, the evolution of the two is closely linked. One of remarkable consequence of such mutual interaction is self-organisation, which provides a powerful paradigm for understanding complexity in many systems (e.g. population, forest fires, reaction-diffusion). In particular, self-organisation has emerged as one of the key physical processes governing transport and mixing in laboratory and astrophysical fluids. A non-perturbative statistical theory [probability distribution functions (PDFs)] is absolutely necessary for a proper modelling of self-organisation due to inherent intermittency.

In this talk, I will first review our recent works on the effects of shear flows on turbulent transport, and then present a statistical theory of self-organisation of shear flows. In particular, a non-perturbative method based on a coherent structure is utilised for the prediction of the PDFs, showing strongly intermittent tails. I will comment on implications of these results for the dynamics and the role of shear flows, which is vital not only in momentum transport, but also in transporting chemical species and controlling mixing of other quantities (e.g. air pollution, weather control).
4:40-5:10 Zero molecular diffusion and real turbulent dispersion
  Nils Mole (University of Sheffield)
  I consider the dispersion of contaminants in turbulent flows at high P\'{e}clet number. Except at the smallest scales, molecular diffusion acts slowly by comparison with turbulent advection. Molecular diffusion is still important because it is the only means by which the concentration in a fluid particle can be changed. Exact solution of the full problem, including both turbulent advection and molecular diffusion, is not possible because of the well-known turbulence closure problem. But exact results for moments and the probability density function (pdf) of concentration can be derived
for the hypothetical case of zero diffusivity. For high P\'{e}clet number these results can be expected to hold in certain ranges of space and time with only slight modification. I outline the results in the absence of molecular diffusion, and consider how the results for the moments can be modified to account for the presence of slowly acting diffusion. The corresponding form of the pdf is considered, and results for large concentrations are presented.
5:10-5:40 Vorticity, geometrical statistics, and subgrid-scale helicity dissipation in isotropic helical turbulence
  Yi Li (University of Sheffield)
  Helicity is defined as the scalar product between velocity and vorticity. It is an invariant of the Euler equation, and has been observed to play important roles in magnetohydrodynamics, geophysical flows. Recent results indicate that it also has effects on the regularity of the solutions to the NS equations. In this talk, a recent study of isotropic helical hydrodynamic turbulence fields is presented. The helical turbulence fields are generated by direct numerical simulations of the NS equations with constant helicity input. The helicity cascade from large scales to small scales is studied using a filtering approach. The emphasis is on the effects of helicity on the geometrical statistics of the vorticity field. It is shown that helicity cascade is related to the symmetric part of the gradient of the vorticity field, which is a symmetric tensor. It is found that, in helical turbulence, the eigenvalues of this tensor show skewed distribution, so that the intermediate eigenvalue of the tensor is more probable to be negative. It is also shown that, in helical turbulence, the vorticity tends to align more closely with its increasing direction, and that these properties of the vorticity field in helical turbulence are one of the mechanisms to generate helicity cascade.




Downloads