Signal Representation and Modeling of Spatial Structures in Fluids

The analysis and modeling of time-varying spatially coherent physical phenomena using observations and numerical or experimental data are the key themes of this thesis. Nowadays due to the availability of low-cost computational power and efficient and cheap measurement techniques we can obtain a very precise description of phenomena in many physical, technical problems. However, due to the large amount of data, it is a non-trivial task to get insight in the properties of these phenomena and, so, specialist 'data-analysis-methods' are necessary. In addition, we would like to use the available data as a guide to construct a, preferably low dimensional, model for the observed phenomenon. Using such a model we can investigate the influence of parameters on the dynamics at low-cost. We are especially interested in physical, technical problems that show characteristic spatial structures that evolve in time. Examples are the formation, spiraling behavior and merging of vortices in the two-dimensional spatial mixing layer, the interaction of wave groups in two-dimensional surface flow and the coherent structures in the three-dimensional spatial mixing layer. In this thesis we will study these three examples in more detail. In this thesis we developed two 'data-analysis-methods' that use numerical or experimental data to obtain descriptions for spatial structures that evolve in time: the Principal Interval Decomposition method and the Phenomenological Model Manifold method. The former method is generally applicable and very eÆcient. The latter method is less generally applicable and needs some external input, but results in a more detailed description of the phenomenon. This method can also be used to construct a low-dimensional model. In both methods the data is described in an optimal way. To illustrate and quantify these methods they were mainly applied to data of the two-dimensional temporal mixing layer. The mixing layer shows spiraling and merging vortices and is an example of a flow in which the vortices can be clearly visualized as individual coherent structures.