Wavelet transforms and their applications to MHD and plasma turbulence: a review

Wavelet analysis and compression tools are reviewed and different applications to study MHD and plasma turbulence are presented. We introduce the continuous and the orthogonal wavelet transform and detail several statistical diagnostics based on the wavelet coefficients. We then show how to extract coherent structures out of fully developed turbulent flows using wavelet-based denoising. Finally some multiscale numerical simulation schemes using wavelets are described. Several examples for analyzing, compressing and computing one, two and three dimensional turbulent MHD or plasma flows are presented.Comment: Journal of Plasma Physics, 201

A Multiresolution Census Algorithm for Calculating Vortex Statistics in Turbulent Flows

The fundamental equations that model turbulent flow do not provide much insight into the size and shape of observed turbulent structures. We investigate the efficient and accurate representation of structures in two-dimensional turbulence by applying statistical models directly to the simulated vorticity field. Rather than extract the coherent portion of the image from the background variation, as in the classical signal-plus-noise model, we present a model for individual vortices using the non-decimated discrete wavelet transform. A template image, supplied by the user, provides the features to be extracted from the vorticity field. By transforming the vortex template into the wavelet domain, specific characteristics present in the template, such as size and symmetry, are broken down into components associated with spatial frequencies. Multivariate multiple linear regression is used to fit the vortex template to the vorticity field in the wavelet domain. Since all levels of the template decomposition may be used to model each level in the field decomposition, the resulting model need not be identical to the template. Application to a vortex census algorithm that records quantities of interest (such as size, peak amplitude, circulation, etc.) as the vorticity field evolves is given. The multiresolution census algorithm extracts coherent structures of all shapes and sizes in simulated vorticity fields and is able to reproduce known physical scaling laws when processing a set of voriticity fields that evolve over time

Some Observations of Flow Patterns and Statistical Properties of Three Component Flows

Vertical air-water flows, solids-water flows and three component air-solids-water flows were investigated in a Three Component Flow Facility. Visual observations of the flow patterns show that three component flows undergo transition and can exhibit strong unsteady vortical motions. Measurements of the fluctuations in cross-sectionally averaged volume fraction measurements were made. The statistical properties of the fluctuations are presented in terms of their amplitude and coherent time scale in the form of the Signal To Noise Ratio (STNR) and the Time Constant (symbol), respectively. Remarkably, the solids-water flows and the dispersed bubbly air-water flows exhibit almost identical values of STNR for the same volume fraction. Equally remarkable in the linear relationship between the Time Constant and the mean bubble or particle velocity; this relationship is found to have the same constant of proportionality for both species in the well behaved disperse regime. In the two-component churn-turbulent and the three-component agitated vortical regimes, the variables (symbol) and STNR significantly deviate from their dispersed regime values. The onset of large coherent structures characteristic of these regimes is reflected by a rise in the amplitude of the fluctuations and a marked increase in their coherent time scale. The results of this study demonstrate the large information content in the fluctuations of the measured quantity, both as a flow regime indicator and as a measure of flow quantities in two- and three-component flows

Separation between coherent and turbulent fluctuations. What can we learn from the Empirical Mode Decomposition?

The performances of a new data processing technique, namely the Empirical Mode Decomposition, are evaluated on a fully developed turbulent velocity signal perturbed by a numerical forcing which mimics a long-period flapping. First, we introduce a "resemblance" criterion to discriminate between the polluted and the unpolluted modes extracted from the perturbed velocity signal by means of the Empirical Mode Decomposition algorithm. A rejection procedure, playing, somehow, the role of a high-pass filter, is then designed in order to infer the original velocity signal from the perturbed one. The quality of this recovering procedure is extensively evaluated in the case of a "mono-component" perturbation (sine wave) by varying both the amplitude and the frequency of the perturbation. An excellent agreement between the recovered and the reference velocity signals is found, even though some discrepancies are observed when the perturbation frequency overlaps the frequency range corresponding to the energy-containing eddies as emphasized by both the energy spectrum and the structure functions. Finally, our recovering procedure is successfully performed on a time-dependent perturbation (linear chirp) covering a broad range of frequencies.Comment: 23 pages, 13 figures, submitted to Experiments in Fluid

Investigation of flow structures involved in sound generation by two- and three-dimensional cavity flows

Proper Orthogonal Decomposition and Stochastic Estimation are combined to shed some light on the link between organized flow structures and noise generation by turbulent flows. Proper Orthogonal Decomposition (POD) is firstly used to extract selected flow events. Based on the knowledge of these structures, the Quadratic Stochastic Estimation of the acoustic pressure field is secondly performed. Both procedures are successively applied to two- and three-dimensional numerical databases of a flow over a cavity. It is demonstrated that POD can extract selected aerodynamic events which can be associated with selected frequencies in the acoustic spectra. Reconstructed acoustic fields also indicate the aerodynamic events which are responsible of the main energy of the noise emission. Such mathematical tools offer new perspectives in analysing flow structures involved in sound generation by turbulent flows and in the experimental design of a flow control strategy

Conditional vorticity budget of coherent and incoherent flow contributions in fully developed homogeneous isotropic turbulence

We investigate the conditional vorticity budget of fully developed three-dimensional homogeneous isotropic turbulence with respect to coherent and incoherent flow contributions. The Coherent Vorticity Extraction based on orthogonal wavelets allows to decompose the vorticity field into coherent and incoherent contributions, of which the latter are noise-like. The impact of the vortex structures observed in fully developed turbulence on statistical balance equations is quantified considering the conditional vorticity budget. The connection between the basic structures present in the flow and their statistical implications is thereby assessed. The results are compared to those obtained for large- and small-scale contributions using a Fourier decomposition, which reveals pronounced differences

The role of coherent vorticity in turbulent transport in resistive drift-wave turbulence

The coherent vortex extraction method, a wavelet technique for extracting coherent vortices out of turbulent flows, is applied to simulations of resistive drift-wave turbulence in magnetized plasma (Hasegawa-Wakatani system). The aim is to retain only the essential degrees of freedom, responsible for the transport. It is shown that the radial density flux is carried by these coherent modes. In the quasi-hydrodynamic regime, coherent vortices exhibit depletion of the polarization-drift nonlinearity and vorticity strongly dominates strain, in contrast to the quasiadiabatic regime

Sensing array for coherence analysis of modulated aquatic chemical plumes

An electrochemical sensor array can provide information about the spatial and temporal distribution of chemicals in liquid turbulent plumes. Planar laser induced fluorescence (PLIF) and amperometric sensor arrays were used to record signals from modulated chemical plumes released into a recirculating aquatic flume. Coherence analysis was applied to extract the frequency components contained in the sensor response. Effects due to release distance, modulation frequency, and array orientation were investigated. This study has demonstrated that frequency encoded information can be extracted from a turbulent chemical plume using an array of amperometric sensors with optimized three-dimensional geometry and tuning.M.S.Committee Chair: Janata, Jiri; Committee Member: Lyon, Andrew; Committee Member: Weissburg, Mar