Scaling of acceleration in locally isotropic turbulence

The variances of the fluid-particle acceleration and of the pressure-gradient and viscous force are given. The scaling parameters for these variances are velocity statistics measureable with a single-wire anemometer. For both high and low Reynolds numbers, asymptotic scaling formulas are given; these agree quantitatively with DNS data. Thus, the scaling can be presumed known for all Reynolds numbers. Fluid-particle acceleration variance does not obey K41 scaling at any Reynolds number; this is consistent with recent experimental data. The non-dimensional pressure-gradient variance named lambda-sub{T} /lambda-sub{P} is shown to be obsolete.Comment: in press, J. Fluid Mech.; 7pages, 2 figure

Equations relating structure functions of all orders

The hierarchy of exact equations is given that relates two-spatial-point velocity structure functions of arbitrary order with other statistics. Because no assumption is used, the exact statistical equations can apply to any flow for which the Navier-Stokes equations are accurate, and they apply no matter how small the number of samples in the ensemble. The exact statistical equations can be used to verify DNS computations and to detect their limitations. For example,if DNS data are used to evaluate the exact statistical equations, then the equations should balance to within numerical precision, otherwise a computational problem is indicated. The equations allow quantification of the approach to local homogeneity and to local isotropy. Testing the balance of the equations allows detection of scaling ranges for quantification of scaling-range exponents. The second-order equations lead to Kolmogorov's equation. All higher-order equations contain a statistic composed of one factor of the two-point difference of the pressure gradient multiplied by factors of velocity difference. Investigation of this pressure-gradient-difference statistic can reveal much about two issues: 1) whether or not different components of the velocity structure function of given order have differing exponents in the inertial range, and 2) the increasing deviation of those exponents from Kolmogorov scaling as the order increases. Full disclosure of the mathematical methods is in xxx.lanl.gov/list/physics.flu-dyn/0102055.Comment: The Laplacians of structure functions in Table 1 are herein correct and extended to order 8, but were incorrect in the journal publication JFM 2001, 8 pages, no figures. arXiv admin note: text overlap with arXiv:physics/010205

Exact Second-Order Structure-Function Relationships

Equations that follow from the Navier-Stokes equation and incompressibility but with no other approximations are "exact.". Exact equations relating second- and third-order structure functions are studied, as is an exact incompressibility condition on the second-order velocity structure function. Opportunities for investigations using these equations are discussed. Precisely defined averaging operations are required to obtain exact averaged equations. Ensemble, temporal, and spatial averages are all considered because they produce different statistical equations and because they apply to theoretical purposes, experiment, and numerical simulation of turbulence. Particularly simple exact equations are obtained for the following cases: i) the trace of the structure functions, ii) DNS that has periodic boundary conditions, and iii) an average over a sphere in r-space. The last case (iii) introduces the average over orientations of r into the structure function equations. The energy dissipation rate appears in the exact trace equation without averaging, whereas in previous formulations energy dissipation rate appears after averaging and use of local isotropy. The trace mitigates the effect of anisotropy in the equations, thereby revealing that the trace of the third-order structure function is expected to be superior for quantifying asymptotic scaling laws. The orientation average has the same property.Comment: no figure

Opportunities for use of exact statistical equations

Exact structure function equations are an efficient means of obtaining asymptotic laws such as inertial range laws, as well as all measurable effects of inhomogeneity and anisotropy that cause deviations from such laws. "Exact" means that the equations are obtained from the Navier-Stokes equation or other hydrodynamic equations without any approximation. A pragmatic definition of local homogeneity lies within the exact equations because terms that explicitly depend on the rate of change of measurement location appear within the exact equations; an analogous statement is true for local stationarity. An exact definition of averaging operations is required for the exact equations. Careful derivations of several inertial range laws have appeared in the literature recently in the form of theorems. These theorems give the relationships of the energy dissipation rate to the structure function of acceleration increment multiplied by velocity increment and to both the trace of and the components of the third-order velocity structure functions. These laws are efficiently derived from the exact velocity structure function equations. In some respects, the results obtained herein differ from the previous theorems. The acceleration-velocity structure function is useful for obtaining the energy dissipation rate in particle tracking experiments provided that the effects of inhomogeneity are estimated by means of displacing the measurement location.Comment: accepted by Journal of Turbulenc

Length Scales of Acceleration for Locally Isotropic Turbulence

Length scales are determined that govern the behavior at small separations of the correlations of fluid-particle acceleration, viscous force, and pressure gradient. The length scales and an associated universal constant are quantified on the basis of published data. The length scale governing pressure spectra at high wave numbers is discussed. Fluid-particle acceleration correlation is governed by two length scales; one arises from the pressure gradient, the other from the viscous force.Comment: 2 figures, 4 pages. Physical Review Letters, accepted August 200

Inactivation of gadd45a Sensitizes Epithelial Cancer Cells to Ionizing Radiation In vivo Resulting in Prolonged Survival

Ionizing Radiation (IR) therapy is one of the most commonly used treatments for cancer patients. The responses of tumor cells to IR are often tissue specific and depend on pathway aberrations present in the tumor. Identifying molecules and mechanisms that sensitize tumor cells to IR provides new potential therapeutic strategies for cancer treatment. In this study, we used two genetically engineered mouse (GEM) carcinoma models, brain choroid plexus (CPC) and prostate to test the impact of inactivating gadd45a, a DNA damage response p53 target gene, on tumor responses to IR We show that gadd45a deficiency significantly increases tumor cell death after radiation. Impact on survival was assessed in the CPC model and was extended in IR-treated mice with gadd45a deficiency compared to those expressing wild type gadd45a. These studies demonstrate a significant effect of gadd45a inactivation in sensitizing tumor cells to IR, implicating gadd45a as a potential drug target in radiotherapy management