Extracting energetically dominant flow features in a complicated fish wake using singular-value decomposition

We developed a method to extract the energetically dominant flow features in a complicated fish wake according to an energetic point of view, and applied singular-value decomposition (SVD) to two-dimensional instantaneous fluid velocity, vorticity and λ2 (vortex-detector) data. We demonstrate the effectiveness and merits of the use of SVD through an example regarding the wake of a fish executing a fast-start turn. The energy imparted into the water by a swimming fish is captured and portrayed through SVD. The analysis and interpretation of complicated data for the fish wake are greatly improved, and thus help to characterize more accurately a complicated fish wake. The velocity vectors and Galilean invariants (i.e., vorticity and λ2) resulting from SVD extraction are significantly helpful in recognizing the energetically dominant large-scale flow features. To obtain successful SVD extractions, we propose useful criteria based on the Froude propulsion efficiency, which is biologically and physically related. We also introduce a novel and useful method to deduce the topology of dominant flow motions in an instantaneous fish flow field, which is based on combined use of the topological critical-point theory and SVD. The concept and approach proposed in this work are useful and adaptable in biomimetic and biomechanical research concerning the fluid dynamics of a self-propelled body.