Hello, A yearly allocation for the LCRC cluster has been requested with the following updated information: Submitter/PI: Mark Paul Project Name: Chaos Division: MCS Project title: Spatiotemporal chaos and turbulence in fluids Associated funding: DOE DE-FG03-98ER14891, DE-FG02-98ER14892, NSF CTS-0604376, NSF CBET-0747727, NSF CDI-1125302. Other Systems: NERSC, ops.phys.oxy.edu (128 node linux cluster at Occidental College) Science: This work is a computational effort to push as deeply as is currently possible toward a quantitative understanding of how complex dynamics (i.e., spatiotemporal chaos and turbulence) arise in spatially-extended nonequilibrium systems that are at the frontiers of numerous science and technological problems. Project 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. During the previous year's allocation we successfully validated our numerical approach through a careful series of numerical tests. During this year's allocation we will continue with production level simulations for very large spatial domains that include a range of transport dynamics to study. We are most interested in the parameter regime where the time scales of the chaotic convective fluid motion, the reaction of the scalar species, and the diffusion of the scalar species are comparable. We have already successfully performed preliminary calculations on blues. We would like to compute the transport in a cylindrical domain of aspect ratio of 40 over a range of Lewis, Damkohler, and Rayleigh numbers. There are may open challenges and open questions regarding the active transport of a scalar species in a chaotic flow field. Nearly all current work to date in the literature has focussed upon the case of simple periodic flow fields. With our work we proposed to explore well into the chaotic regime and to quantify the dynamics of transport. 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 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 are in direct communication with experimentalists interested in comparing the results of our simulations with experimental measurements. We have identified several important test problems to explore that we will focus upon during this allocation. We have already performed test runs of blues and the runs requested for this allocation do not require significant code development. We have developed the ability to compute the 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. Our current code is a serial implementation of the algorithm. We intend to parallelize the code in order to explore much larger systems. 3) Turbulent thermal convection. We would like to continue our three-dimensional numerical simulations of fully turbulent Rayleigh-Benard convection cells for lower Prandtl number (0.021). By going to very low Prandtl number, we will explore a region of parameter space that has not been well-studied, either experimentally or numerically. Low Prandtl number has direct application to convection in liquid metals, and can also shed light on the convection in the earth’s liquid metal core and in the sun and other stars which can have even lower Prandtl numbers. We would also like to perform simulations of turbulent RBC at moderate Prandtl number (0.7) and Rayleigh number (10^7-10^{10}). Many experiments are currently being performed in this moderate Prandtl number regime (and for even higher Rayleigh numbers), 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. Project URL: Current FY Hours Used: undetermined amount New FY Requested allocation: 480000 Q1: 120000 Q2: 120000 Q3: 120000 Q4: 120000 Justification: Not required for our request. Thank You, The LCRC Accounts System