Seeing and Hearing the Eigenvectors of a Fluid

The intricate shapes and sounds that arise from vibrating Chladni plates are a well-known phenomenon. They are also quantitatively well understood, as the spatial patterns correspond to the eigenvectors of the underlying plate, and the audio frequencies arise from the plate’s eigenvalues. We explore a generalization of the phenomenon by computing analogous quantities for a computational fluid dynamics simulation. Unlike the Chladni plate case, direct analytic expressions are not available, so we instead compute a set of “empirical” eigenvectors and eigenvalues. We find that these vectors form abstract, turbulent patterns in space. In another departure from the Chladni plate case, the eigenvalues no longer have a natural sonic mapping, so we construct a sonification that allows us to “listen” to the eigenvectors of the fluid. The united visual and sonic forms comprise a multimodal compositional palette that has great artistic potential. Figure 1: Left: Chladni patterns realized through a physical experiment. Source: Wikimedia Commons. Right: Analytic 2D eigenvector of the Navier-Stokes equations using the method of de Witt et al. [1].