Publications

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One of the authors previously conjectured that the wrinkling of propagating fronts by weak random advection increases the bulk propagation rate (turbulent burning velocity) in proportion to the 4/3 power of the advection strength. An exact derivation of this scaling is reported. The analysis shows that the coefficient of this scaling is equal to the energy density of a lower-dimensional Burgers fluid with a white-in-time forcing whose spatial structure is expressed in terms of the spatial autocorrelation of the flow that advects the front. The replica method of field theory has been used to derive an upper bound on the coefficient as a function of the spatial autocorrelation. High precision numerics show that the bound is usefully sharp. Implications for strongly advected fronts (e.g., turbulent flames) are noted.

Recent work suggests that cloud effects remain one of the largest sources of uncertainty in model-based estimates of climate sensitivity. In particular, the entrainment rate in stratocumulus-topped mixed layers needs better models. More than thirty years ago a clever laboratory experiment was conducted by McEwan and Paltridge to examine an analog of the entrainment process at the top of stratiform clouds. Sayler and Breidenthal extended this pioneering work and determined the effect of the Richardson number on the dimensionless entrainment rate. The experiments gave hints that the interaction between molecular effects and the one-sided turbulence seems to be crucial for understanding entrainment. From the numerical point of view large-eddy simulation (LES) does not allow explicitly resolving all the fine scale processes at the entrainment interface. Direct numerical simulation (DNS) is limited due to the Reynolds number and is not the tool of choice for parameter studies. Therefore it is useful to investigate new modeling strategies, such as stochastic turbulence models which allow sufficient resolution at least in one dimension while having acceptable run times. We will present results of the One-Dimensional Turbulence stochastic simulation model applied to the experimental setup of Sayler and Breidenthal. The results on radiatively induced entrainment follow quite well the scaling of the entrainment rate with the Richardson number that was experimentally found for a set of trials. Moreover, we investigate the influence of molecular effects, the fluids optical properties, and the artifact of parasitic turbulence experimentally observed in the laminar layer. In the simulations the parameters are varied systematically for even larger ranges than in the experiment. Based on the obtained results a more complex parameterization of the entrainment rate than currently discussed in the literature seems to be necessary.

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A novel multi-scale approach for extending the one-dimensional turbulence (ODT) model of [A.R. Kerstein. One-dimensional turbulence: model formulation and application to homogeneous turbulence, shear flows, and buoyant stratified flows, J. Fluid Mech. 392 (1999) 277] to treat turbulent flow in three-dimensional (3D) domains is described. In this model, here called ODTLES, 3D aspects of the flow are captured by embedding three, mutually orthogonal, one-dimensional ODT domain arrays within a coarser 3D mesh. The ODTLES model is obtained by developing a consistent approach for dynamically coupling the different ODT line sets to each other and to the large scale processes that are resolved on the 3D mesh. The model is implemented computationally and its performance is tested by performing simulations of decaying isotropic turbulence at two different Reynolds numbers and comparing to the experimental data of [H. Kang, S. Chester, C. Meneveau. Decaying turbulence in an active-grid-generated flow and comparisons with large-eddy simulations, J. Fluid Mech. 480 (2003) 129; G. Comte-Bellot, S. Corrsin, Simple Eulerian correlation of full-and narrow band velocity signals in grid-generated 'isotropic' turbulence, J. Fluid Mech. 48 (1971) 273]. © 2008 Elsevier B.V.

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There are two principal scientific objectives in the study of Type Ia supernovae - first, a better understanding of these complex explosions from as near first principles as possible, and second, enabling the more accurate utilization of their emission to measure distances in cosmology. Both tasks lend themselves to large scale numerical simulation, yet take us beyond the current frontiers in astrophysics, combustion science, and radiation transport. Their study requires novel approaches and the creation of new, highly scalable codes. © 2009 IOP Publishing Ltd.

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A recently established mathematical equivalence-between weakly perturbed Huygens fronts (e.g., flames in weak turbulence or geometrical-optics wave fronts in slightly nonuniform media) and the inviscid limit of white-noise-driven Burgers turbulence-motivates theoretical and numerical estimates of Burgers-turbulence properties for specific types of white-in-time forcing. Existing mathematical relations between Burgers turbulence and the statistical mechanics of directed polymers, allowing use of the replica method, are exploited to obtain systematic upper bounds on the Burgers energy density, corresponding to the ground-state binding energy of the directed polymer and the speedup of the Huygens front. The results are complementary to previous studies of both Burgers turbulence and directed polymers, which have focused on universal scaling properties instead of forcing-dependent parameters. The upper-bound formula can be heuristically understood in terms of renormalization of a different kind from that previously used in combustion models, and also shows that the burning velocity of an idealized turbulent flame does not diverge with increasing Reynolds number at fixed turbulence intensity, a conclusion that applies even to strong turbulence. Numerical simulations of the one-dimensional inviscid Burgers equation using a Lagrangian finite-element method confirm that the theoretical upper bounds are sharp within about 15% for various forcing spectra (corresponding to various two-dimensional random media). These computations provide a quantitative test of the replica method. The inferred nonuniversality (spectrum dependence) of the front speedup is of direct importance for combustion modeling. © 2008 The American Physical Society.

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One of the authors previously conjectured that the wrinkling of propagating fronts by weak random advection increases the bulk propagation rate (turbulent burning velocity) in proportion to the 4/3 power of the advection strength. An exact derivation of this scaling is reported. The analysis shows that the coefficient of this scaling is equal to the energy density of a lower-dimensional Burgers fluid with a white-in-time forcing whose spatial structure is expressed in terms of the spatial autocorrelation of the flow that advects the front. The replica method of field theory has been used to derive an upper bound on the coefficient as a function of the spatial auto-correlation. High precision numerics show that the bound is usefully sharp. Implications for strongly advected fronts (e.g., turbulent flames) are noted.

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