Scientific and artistic synergies on the complexity of geophysics

George F. Fitton, Ecole Nationale des Ponts et Chaussées, Champs-sur-Marne, France, Daniel J M Schertzer, Ecole Nationale des Ponts et Chaussées | Institut Polytechnique de Paris, Hydrology Meteorology and Complexity (HM&Co), Champs-sur-Marne, France and Ioulia Tchiguirinskaia, Ecole Nationale des Ponts et Chaussées | Institut Polytechnique de Paris, Hydrologie Météorologie et Complexité (HM&Co), Champs-sur-Marne, France
Abstract:
Surface wind dynamics, while of great theoretical and practical interest, are still poorly understood due to the amazing complexity of the process. In particular surface-wind dynamics break several symmetries (isotropy and homogeneity) that are mathematically convenient when studying turbulence thus further complicating the situation. Studying these phenomena requires large amounts of data. And, although many interesting developments in measuring devices have happened, there is always the need for more observations and visual representations.

Art pieces, such as Charles Sower’s WindSwept installation outside of the Randall Museum in San Francisco may radically help to change this situation. The installation was developed to help a large part of the public understand the complexity of the environment near the surface of the Earth. Its 612 light wind direction indicators reveal intermittent bursts of the wind while displaying also strong coherent structures that are characteristic of intermittent processes. Simulations of continuous in-scale universal multifractal velocity fields reveal identical characteristics to the WindSwept installation; velocity fields that until recently were thought could only be generated with brute force numerical methods of either the Navier-Stokes equations or approximations thereof.

With the advent of big data and their now more accessible visualisations (by artists akin to Charles Sower’s) hundreds of previously believed unthinkably complex processes are now seen to exhibit the same coherent patterns and intermittent yet repeating behaviour. Although these kinds of artwork are visually pleasing and important for public communication their link to stochastic processes has real application.

With fractals and multifractals we are able to connect these visually complex phenomena with meaningful mathematical models: models that allow us to not only reproduce these wonderful phenomena but give insight into the processes behind them which in turn allows for their prediction, forecasting and most importantly their understanding.

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