Showing papers on "Dynamic mode decomposition published in 2011"

Applications of the dynamic mode decomposition

Abstract: The decomposition of experimental data into dynamic modes using a data-based algorithm is applied to Schlieren snapshots of a helium jet and to time-resolved PIV-measurements of an unforced and harmonically forced jet. The algorithm relies on the reconstruction of a low-dimensional inter-snapshot map from the available flow field data. The spectral decomposition of this map results in an eigenvalue and eigenvector representation (referred to as dynamic modes) of the underlying fluid behavior contained in the processed flow fields. This dynamic mode decomposition allows the breakdown of a fluid process into dynamically revelant and coherent structures and thus aids in the characterization and quantification of physical mechanisms in fluid flow.

Application of the dynamic mode decomposition to experimental data

Abstract: The dynamic mode decomposition (DMD) is a data-decomposition technique that allows the extraction of dynamically relevant flow features from time-resolved experimental (or numerical) data. It is based on a sequence of snapshots from measurements that are subsequently processed by an iterative Krylov technique. The eigenvalues and eigenvectors of a low-dimensional representation of an approximate inter-snapshot map then produce flow information that describes the dynamic processes contained in the data sequence. This decomposition technique applies equally to particle-image velocimetry data and image-based flow visualizations and is demonstrated on data from a numerical simulation of a flame based on a variable-density jet and on experimental data from a laminar axisymmetric water jet. In both cases, the dominant frequencies are detected and the associated spatial structures are identified.

Non-normality of thermoacoustic interactions: an experimental investigation

Abstract: An experimental investigation of the non-normal nature of thermoacoustic interactions in an electrically heated horizontal Rijke tube is performed. Since non-normality and the associated transient growth are linear phenomena, the experiments have to be confined to the linear regime. The bifurcation diagram for the subcritical Hopf bifurcation into a limit cycle behavior has been determined, after which the amplitude levels, for which the system acts linearly, have been identified for dierent power inputs to the heater. There are two main objectives for this experimental investigation. The first one deals with the extraction of the linear eigenmodes associated with the acoustic pressure from experimental data. This is accomplished by the Dynamic Mode Decomposition (DMD) technique applied in the linear regime. The non-orthogonality between the eigenmodes is determined for various values of heater power. The second objective is to identify evidence of transient perturbation growth in the system. The total acoustic energy in the duct has been monitored as the thermoacoustic system has been initialized by linear combinations of the two dominant eigenmodes. Transient growth, on the order of previous theoretical studies, has been found, and its parameter dependence on amplitude ratio and phase angle of the initial eigenmode components has been determined. This study represents the first experimental confirmation of non-normality in thermoacoustic systems.

Investigation of wall-bounded turbulent flow using Dynamic mode decomposition

Abstract: Dynamics mode decomposition (DMD) which is a method to construct a linear mapping describing the dynamics of a given time-series of any quantities is applied to the analysis of a turbulent channel flow. The flow fields are generated by direct numerical simulations for the friction Reynolds number Re? = 190. The time-series of the flow fields in a short time-interval in the order of the wall-unit time-scale and in a small spatial domain that encloses a single near-wall structure are used as the inputs to DMD. In some datasets, linearly growing modes that seem to contribute to the well-known self-sustained cycle of the flow structures near the wall are detected.

Using principal component analysis and dynamic mode decomposition to analyze spatio-temporal data

Abstract: We study two methods to analyze spatio-temporal data. To describe data, we use principal component analysis. To predict data, we use dynamic mode decomposition. We compute numerical solutions of the complex Ginzburg-Landau equation and we use that numerical solution as data. Using principal component analysis we identify a low-dimensional subspace spanned by only 3 principal components. Using these 3 principal components we can reconstruct the original data matrix with approximately 2% error, and construct out-of-sample data with less than 3% error. Using dynamic mode decomposition we are able to predict the temporal evolution of out-of-sample data as far as 500 time steps into the future with less than 5% error. The combination of these two techniques provides robust and reliable methods to analyze complex data sets.