Round Tables TMB July – 07 August 2009 ICTP, Trieste, Italy You are welcome to add your questions, comments, concerns for consideration at Round Tables to be held on 30 July and 06 August 2009, Please save your changes.

Dear TMB … Some thoughts for the Round Table. Turbulence and mixing were studied for a long time while TMB is a new conference/community. The solid foundation of previous studies of turbulence in various areas (mechanics, physics, astrophysics, applied mathematics, etc) is very important but the most interesting role for TMB would be to look at new, emerging areas that may become "classical" one day. I suggest to exchange opinions on what these new emerging areas could be.

I may have missed the detailed information about those sessions. I am mainly interested in mean-field modeling of astrophysical MHD processes.

(1) What progress has been made in our understanding of the coexistence of coherent structures and scale invariant features of turbulence? How do they feed off each other? Are there circumstances where there is a description that is viable where their interactions can be isolated and thus serve as a viable reduction scheme? Here I have in mind large scale-dependent-vorticity and scale invariant features at finer scales. How does this differ in 2D and 3D? (2) How do plasmas and ordinary fluids differ in terms of their turbulence properties? To what extent do the studies of one really feed into an understanding of the other and when is that just wishful thinking? How would one isolate plasma features of turbulence, related to kinetic effects, wave-particle interactions, long range EM forces, vs the mundane features of shear fighting shocks and vorticity generation type scenarios?

Some issues for round-table discussion: 1) Computers have become large and fast enough to allow large-eddy simulation (LES) of fairly complex practical turbulent flow problems. 2) Super-grid scale. Recognition of sensitivity of turbulent flows to initial and boundary conditions leads to importance of characterizing and modeling these conditions in reasonable fashion if any sort of meaningful (predictive) LES experiments are to be attempted. Moreover, because regarding these conditions as stochastic is very likely unavoidable in practical applications, assessment of uncertainties of LES predictions becomes a very important issue. 3) Sub-grid scale. Unless we deal with grid resolutions that amount to carrying out "coarse DNS", implicit subgrid contributions due to discretization interfere with the explicit modeling. Otherwise, for most practical under-resolved situations, smart mixed explicit/implicit subgrid models should be our main focus. We should make the most of what numerics can do implicitly by itself and "mix" it with explicit models acting in collaborative (non-interfering) fashion when the latter are needed (e.g., near walls, combustion) ~V which of course, is easier said than done...

Re Round Table: […] Current topics of interest in fusion plasma physics may include: Physics on the transport time scale (much longer than the autocorrelation time of the turbulence): - Is nonlinear gyrokinetics adequate for the calculation of macroscopic electric fields and plasma rotation? - How does one effectively do an economical simulation on the transport time scale? Edge physics of tokamaks: - How does one simulate the edge (which is a very complicated boundary layer with complicated magnetic geometry, fluctuations of order unity, etc.)? - How does one describe analytically the generation rate of coherent structures ("blobs") in tokamak edge turbulence?

Regarding Round Tables, and your question " what issues/problems would you consider as the most important for the field ?", I have no simple answer. But if I have to say something, I would like to say the following: I would like to understand canonical turbulent flows. Then an interesting question may be, "what are canonical turbulent flows,? And in which sense are they considered or qualified to be canonical".

Subject: Discussion Topic for Rayleigh-Taylor Mixing Issues in the Simulation of Turbulent Mixing This discussion will start with posing some central questions: 1. What are the factors (physical and numerical) which influence the overall mixing rate, for example the RT alpha? 2. What type of simulations are needed to compute molecular mixing rates, such as chemical reaction rates in turbulent mixing, especially for rapid mixing over short time scales? 3. How is the high Schmidt number limit or immiscible case to be handled? 4. Are there ideas for new experiments? Usually discussions on these topics will concentrate on the importance of a chacterization of the initial conditions, which while random, will have a statistical signature, and on the scale breaking physical properties, such as fluid transport or surface tension. Additionally, for simulations, the numerical scale breaking analogs of fluid transport and surface tension play a role. Simulations for the RT alpha have given very different values based on different numerical strategies. Successful agreement with experiment has been obtained from: 1. Front Tracking, to control numerical mass diffusion 2. Particle methods, which also control numerical mass diffusion, and in addition are a totally different numerical method 3. Very high levels of mesh refinement (DNS) combined with experimental characterization (statistically) of the initial conditions. What conclusions can we draw from these simulations, and from many others which do not agree with experiment, and apparently no longer try to?

COMMENTS on Issues in Simulations of Turbulent Mixing N1-4 on page An attempt of answer would be the following: The $\alpha_{RT}$ parameter depends on nine dimensionless parameters:$$\alpha_{RT} = \alpha_{RT} ( \At, \Sr, \gamma_{H,L}, L_{H,L}, \Rey, \Sc, \Pr)$$,with the following meaning: the Atwood number, $\At$; the stratification, $\Sr$; the ratio of specific heats for the two gases, $\gamma_{H,L}$, the vertical thickness $L_{H,L}$ of the heavy and light fluid, respectively, the Reynolds number, $\Rey$, the Schmidt number, $\Sc$, and the Prandtl number, $\Pr$. At the limit of small stratifications ($ \Sr \rightarrow 0$), small compressibiities $\gamma_{H,L}$ large enough $\Rey \rightarrow \infty$ (so that Schmidt and Prandtl numbers are small), one recovers the classical value for $alpha_{RT}$. Indeed, it remains the cases of large Schmidt numbers COMMENTS on agreements with experiments: A work of comparison of numerical methods should be done. In particular, comparison with highly resolved simulations with low order methods and high order numerical schemes has to be done. Some talks of TMB-09 are dealing with this problematic. Some comparison are underway in the IWPCTM meeting.

-theoretical concepts applicable for non-equilibrium processes -RTI/ KHI / RMI / MRI and other instabilities -nonlinear dynamics: theory versus model with adjustable parameters Numerics -conservation laws; ill-posedness; sensitivity to boundary and initial conditions -good schemes versus affordable computations -molecular dynamics versus continuous fluid dynamics, range of applicability of Navier-Stokes equations -computational limits: can the simulations substitute the theory and the experiments? Theory Data analysis -availability of data to a wide community -data storage and transfer, post-processing and real-time processing -quality and information capacity of data sets

Experiments How good (i.e. reliable and repeatable) are the observations and diagnostics of non-equilibrium turbulent processes? -criteria for the estimate of information capacity of data sets, including dynamic range, spatio-temporal resolution, accuracy, precision, control, data rate acquisition -“records” (extreme parameter regime) versus “diagnostics” (data quality) -closer connection to high-technologies and application of advanced diagnostic opportunities? It may be not enough to “buy” the “instrumentation expertise”… -verification and validation of theories and models -development of a concept of “model experiments”