Hello, A change in allocation has been requested: Requester: paul (Mark Paul) Project: Chaos Title: Spatiotemporal chaos and turbulence in fluids Description: This is a continuing project with this year's allocation request building upon last year's progress. All of our calculations use spectral element methods to explore the spatiotemporal chaos and turbulence of fluid systems. The code nek5000 has previously demonstrated scalability and efficiency for the specific problems that we are interested in. We continue to make significant progress on the numerical simulation of Rayleigh-Benard convection for experimentally realistic conditions. Rayleigh-Benard convection is the buoyancy induced convection that occurs when a fluid layer is heated uniformly from below. We are most interested in cases where the fluid dynamics of the convection layer is chaotic or turbulent. Specifically, the code integrates the three-dimensional time-dependent Boussinesq equations, any associated reaction-diffusion-advection equations for the transport of scalar quantities of interest, and the linearized tangent-space equations for computing Lyapunov diagnostics. The code is geometrically flexible and can handle a number of experimentally appropriate boundary conditions. The Lyapunov diagnostics we can compute include the spectrum of Lyapunov exponents and vectors that can be used to provide fundamental insights into the complex dynamics that include the fractal dimension and the location of fast growing perturbations. In this allocation we propose to continue exploring the following problems. 1) Transport in chaotic flow fields In this project we are interested in exploring the transport dynamics of a scalar species when the underlying fluid dynamics are spatiotemporally chaotic. There are a number of situations in which this is important and we will explore two in particular. First, is the combustion of premixed gases in a chaotic flow field. Second, is the motion of swimming microorganisms in a fluid layer. Both of these situations can be described by an additional reaction-diffusion-advection equation that is solved simultaneously with the Boussinesq equations that describe the fluid motion of Rayleigh-Benard convection. The nek5000 code already has this apability and our proposed work does not involve significant additional code development. Over the past year we have explored a number of validation cases to ensure the accuracy of the code for the parameter space that we are interested in. We have computed the transport of a passive scalar quantity in a large shallow fluid layer that is undergoing spiral defect chaos. This allowed us to connect our work with previous calculations in the literature (Chiam et al, Physical Review E, 036205, 2005). This has also provided a baseline computation of the passive transport of a scalar quantity. This baseline computation allows for an important for comparison with the cases where the scalar quantity is not passive but active which we will continue to explore in this allocation. A specific case of interest is the combustion of a scalar quantity in a chaotic flow field. We have begun these calculations and validated the basic approach. With this allocation we will explore the parameter space to quantify the transport of an active scalar. In particular we are interested i n cases of small Lewis and large Damkohler numbers that are most closely related to experiment. 2) Quantifying spatiotemporal chaos In this effort we will perform large scale numerical simulations of chaotic fluid convection for the precise conditions of experiment. We will explore large cylindrical domains with aspect ratios of 30 and larger for very long times (several horizontal diffusion times). We are particularly interested in using and developing diagnostics that shed physical insight upon fundamental features of the underlying high-dimensional chaos. We will use our current capability to compute the Lyapunov exponents, Lyapunov vectors, and the fractal dimension (all using the Gram-Schmidt approach) for a range of conditions of current experimental interest in the convection community. One aspect we will focus upon is using the temporal and spatial averages of the leading order Lyapunov vector to quantify regions and dynamics of interest. We are interested in searching for a connection between these Lyapunov based diagnostics, which can only be computed and are not accessible to experiment, with quantities and diagnostics that can be measured in experiment. We will also develop and explore new diagnostics such as covariant Lyapunov vectors to quantify the spatial disorder in the patterns. The covariant Lyapunov vectors are much more difficult to calculate than the Gram-Schmidt based Lyapunov vectors but have the benefit of providing all of the directions of perturbation growth in the high dimensional phase space (called Oseledec's splitting). The covariant Lyapunov vectors have not been calculated for an experimentally accessible fluid system and have the potential to provide new and important insights into the regions and directions that contribute most to the chaos. In order to connect with experiment we are also going to explore the use of realistic boundary conditions such as walls of finite thermal conductivity and varying fluid properties. 3) Turbulent thermal convection. We would like to continue our three-dimensional numerical simulations of fully turbulent Rayleigh-Benard convection cells for higher Rayleigh numbers (10E10) and lower Prandtl number (0.02-0.7). Simulations have never been performed at such high Rayleigh numbers, system size and Prandtl number. This is exactly the region where there is disagreement between theory and experiments, and there is evidence of a trend towards disagreement by our simulation results at lower Rayleigh number. By going to higher Rayleigh number, we will be able to resolve the disagreements and develop a fuller understanding of turbulence. Many experiments are currently being performed in the proposed regime (and even higher Rayleigh number), but this system is not well understood theoretically. Thermal plumes are present in turbulent convection as a means of heat transport. In addition, a large-scale circulation (LSC) has been found, which sweeps the thermal plumes along like leaves in a wind. This LSC is not steady and also undergoes chaotic, abrupt reversals. Visualizations are extremely difficult in experiments, so numerical simulations are essential for bridging the gap between experiment and theory. Heat transport measurements can also be determined from these simulations and compared to experiments and theoretical predictions. Thin thermal and viscous boundary layers are present, and we can perform a detailed analysis of these boundary layers, which are key to understanding the nature of turbulence in these cells. Finally Lyapunov exponents can be computed for these systems and a correlation is expected between the time dependence of the LSC and the time dependence of one of the Lyapunov exponents. Turbulent Rayleigh-Benard systems have application to such diverse phenomena as weather forecasting and the reversal of the earth's magnetic field. URL: More information can be found at the following URL's Janet Scheel http://faculty.oxy.edu/jscheel/research.html Mark Paul http://www.me.vt.edu/mpaul Paul Fischer http://www.mcs.anl.gov/~fischer/ Allocation request: 150,000 Transport in chaotic convection 150,000 Covariant Lyapunov vectors and exponents 150,000 Turbulent thermal convection 450,000 Total Request Current: undetermined amount Justification: N/A Requested: 250000 A specific reason has been given: We would like to request an additional 250,000 core hours on fusion to continue our current projects. All 3 of our current investigations are making very good progress and require more hours to continue. This supplemental allocation should cover these investigations until the next allocation cycle upon which we are planning to submit a renewal. A brief description of the investigations are: 1) Turbulent Rayleigh-Benard convection at very low Prandtl number. 2) Transport of an active scalar in chaotic convection. 3) Using Lyapunov based diagnostics to probe the dynamics of chaotic convection to compare directly with experiment. All of these projects involve student research projects that are in progress and are central to publications that are in progress, and to presentations that will be given at upcoming conferences including the American Physical Society's Division of Fluid Dynamics meeting. These supplemental hours are very important for the progress of these and will allow us to continue to push forward to generate new physical insights. If there is any further information we can provide please do not hesitate to ask. This needs to be approved and the final allocation amount decided upon. Thank You, The LCRC Accounts System