Modal Visualization of Waves by Means of Linear Mapping Filtering

A method for generating bimodal decompositions of oscillating flow fields is presented, which readily generates the first dominant pure-tone modes by finding the reduced-order difference mappings that best represent the local oscillations. The formulae are simpler than the dynamic mode decomposition, introducing the novelty of local representative frequencies, which provides an indicator for spatial domain segmentation. A practical application of the present method is the rapid visualization of dominant fluctuating or traveling flow structures, such as waves or convected vortices, which are often concealed by the general chaotic character of the data. The bimodal decomposition is tested in a study case consisting of numerical data generated by means of the lattice Boltzmann method applied to the three-dimensional flow in a channel partially blocked by a permeable structure of wires. The case presents a linear instability resulting in the generation of a wave train with good periodicity. The method readily provides an outlook on the regions where fluctuations are dominated by this wave train and on the existence of harmonics or chaotic fluctuations.