Approximating turbulent and non-turbulent events with the Tensor Train decomposition method

Low-rank multilevel approximation methods are often suited to attack high-dimensional problems successfully and they allow very compact representation of large data sets. Specifically, hierarchical tensor product decomposition methods, e.g., the Tree-Tucker format and the Tensor Train format emerge as a promising approach for application to data that are concerned with cascade-of-scales problems as, e.g., in turbulent fluid dynamics. Beyond multilinear mathematics, those tensor formats are also successfully applied in e.g., physics or chemistry, where they are used in many body problems and quantum states. Here, we focus on two particular objectives, that is, we aim at capturing self-similar structures that might be hidden in the data and we present the reconstruction capabilities of the Tensor Train decomposition method tested with 3D channel turbulence flow data

Minimal model for aeolian sand dunes

We present a minimal model for the formation and migration of aeolian sand dunes. It combines a perturbative description of the turbulent wind velocity field above the dune with a continuum saltation model that allows for saturation transients in the sand flux. The latter are shown to provide the characteristic length scale. The model can explain the origin of important features of dunes, such as the formation of a slip face, the broken scale invariance, and the existence of a minimum dune size. It also predicts the longitudinal shape and aspect ratio of dunes and heaps, their migration velocity and shape relaxation dynamics. Although the minimal model employs non-local expressions for the wind shear stress as well as for the sand flux, it is simple enough to serve as a very efficient tool for analytical and numerical investigations and to open up the way to simulations of large scale desert topographies.Comment: 19 pages, 22 figure

Formation of Large-Scale Semi-Organized Structures in Turbulent Convection

A new mean-field theory of turbulent convection is developed. This theory predicts the convective wind instability in a shear-free turbulent convection which causes formation of large-scale semi-organized fluid motions in the form of cells or rolls. Spatial characteristics of these motions, such as the minimum size of the growing perturbations and the size of perturbations with the maximum growth rate, are determined. This study predicts also the existence of the convective shear instability in a sheared turbulent convection which results in generation of convective shear waves with a nonzero hydrodynamic helicity. Increase of shear promotes excitation of the convective shear instability. Applications of the obtained results to the atmospheric turbulent convection and the laboratory experiments on turbulent convection are discussed. This theory can be applied also for the describing a mesogranular turbulent convection in astrophysics.Comment: 16 pages, 10 figures, REVTEX4, PHYSICAL REVIEW E, v. 67, in press (2003

Long Hole Film Cooling Dataset for CFD Development - Flow and Film Effectiveness

An experiment investigating flow and heat transfer of long (length to diameter ratio of 18) cylindrical film cooling holes has been completed. In this paper, the thermal field in the flow and on the surface of the film cooled flat plate is presented for nominal freestream turbulence intensities of 1.5 and 8 percent. The holes are inclined at 30 deg above the downstream direction, injecting chilled air of density ratio 1.0 onto the surface of a flat plate. The diameter of the hole is 0.75 in. (approx. 0.02 m) with center to center spacing (pitch) of 3 hole diameters. Coolant was injected into the mainstream flow at nominal blowing ratios of 0.5, 1.0, 1.5, and 2.0. The Reynolds number of the freestream was approximately 11,000 based on hole diameter. Thermocouple surveys were used to characterize the thermal field. Infrared thermography was used to determine the adiabatic film effectiveness on the plate. Hotwire anemometry was used to provide flowfield physics and turbulence measurements. The results are compared to existing data in the literature. The aim of this work is to produce a benchmark dataset for Computational Fluid Dynamics (CFD) development to eliminate the effects of hole length to diameter ratio and to improve resolution in the near-hole region. In this report, a Time Filtered Navier Stokes (TFNS), also known as Partially Resolved Navier Stokes (PRNS), method that was implemented in the Glenn-HT code is used to model coolant-mainstream interaction. This method is a high fidelity unsteady method that aims to represent large scale flow features and mixing more accurately

Revisiting the Local Scaling Hypothesis in Stably Stratified Atmospheric Boundary Layer Turbulence: an Integration of Field and Laboratory Measurements with Large-eddy Simulations

The `local scaling' hypothesis, first introduced by Nieuwstadt two decades ago, describes the turbulence structure of stable boundary layers in a very succinct way and is an integral part of numerous local closure-based numerical weather prediction models. However, the validity of this hypothesis under very stable conditions is a subject of on-going debate. In this work, we attempt to address this controversial issue by performing extensive analyses of turbulence data from several field campaigns, wind-tunnel experiments and large-eddy simulations. Wide range of stabilities, diverse field conditions and a comprehensive set of turbulence statistics make this study distinct

Developments in turbulence research: a review based on the 1999 Programme of the Isaac Newton Institute, Cambridge

Recent research is making progress in framing more precisely the basic dynamical and statistical questions about turbulence and in answering them. It is helping both to define the likely limits to current methods for modelling industrial and environmental turbulent flows, and to suggest new approaches to overcome these limitations. Our selective review is based on the themes and new results that emerged from more than 300 presentations during the Programme held in 1999 at the Isaac Newton Institute, Cambridge, UK, and on research reported elsewhere. A general conclusion is that, although turbulence is not a universal state of nature, there are certain statistical measures and kinematic features of the small-scale flow field that occur in most turbulent flows, while the large-scale eddy motions have qualitative similarities within particular types of turbulence defined by the mean flow, initial or boundary conditions, and in some cases, the range of Reynolds numbers involved. The forced transition to turbulence of laminar flows caused by strong external disturbances was shown to be highly dependent on their amplitude, location, and the type of flow. Global and elliptical instabilities explain much of the three-dimensional and sudden nature of the transition phenomena. A review of experimental results shows how the structure of turbulence, especially in shear flows, continues to change as the Reynolds number of the turbulence increases well above about 104 in ways that current numerical simulations cannot reproduce. Studies of the dynamics of small eddy structures and their mutual interactions indicate that there is a set of characteristic mechanisms in which vortices develop (vortex stretching, roll-up of instability sheets, formation of vortex tubes) and another set in which they break up (through instabilities and self- destructive interactions). Numerical simulations and theoretical arguments suggest that these often occur sequentially in randomly occurring cycles. The factors that determine the overall spectrum of turbulence were reviewed. For a narrow distribution of eddy scales, the form of the spectrum can be defined by characteristic forms of individual eddies. However, if the distribution covers a wide range of scales (as in elongated eddies in the ‘wall’ layer of turbulent boundary layers), they collectively determine the spectra (as assumed in classical theory). Mathematical analyses of the Navier–Stokes and Euler equations applied to eddy structures lead to certain limits being defined regarding the tendencies of the vorticity field to become infinitely large locally. Approximate solutions for eigen modes and Fourier components reveal striking features of the temporal, near-wall structure such as bursting, and of the very elongated, spatial spectra of sheared inhomogeneous turbulence; but other kinds of eddy concepts are needed in less structured parts of the turbulence. Renormalized perturbation methods can now calculate consistently, and in good agreement with experiment, the evolution of second- and third-order spectra of homogeneous and isotropic turbulence. The fact that these calculations do not explicitly include high-order moments and extreme events, suggests that they may play a minor role in the basic dynamics. New methods of approximate numerical simulations of the larger scales of turbulence or ‘very large eddy simulation’ (VLES) based on using statistical models for the smaller scales (as is common in meteorological modelling) enable some turbulent flows with a non-local and non-equilibrium structure, such as impinging or convective flows, to be calculated more efficiently than by using large eddy simulation (LES), and more accurately than by using ‘engineering’ models for statistics at a single point. Generally it is shown that where the turbulence in a fluid volume is changing rapidly and is very inhomogeneous there are flows where even the most complex ‘engineering’ Reynolds stress transport models are only satisfactory with some special adaptation; this may entail the use of transport equations for the third moments or non-universal modelling methods designed explicitly for particular types of flow. LES methods may also need flow-specific corrections for accurate modelling of different types of very high Reynolds number turbulent flow including those near rigid surfaces.This paper is dedicated to the memory of George Batchelor who was the inspiration of so much research in turbulence and who died on 30th March 2000. These results were presented at the last fluid mechanics seminar in DAMTP Cambridge that he attended in November 1999