E-mail: edward.bolton@yale.edu

Research Philosophy

The natural world exhibits complexity at scales ranging from mineral grains to galactic structures. Many systems involve fluid flows, typically governed by nonlinear processes. I have taken the basic philosophy that the deepest insight into the dynamics of fluids can be gained by following flow regimes through their initial bifurcations. Analytical, numerical, and experimental work complement each other well in this approach. For thermal convection, as the control parameter (Rayleigh number) increases, the fluid layer goes through a sequence of bifurcations: from a static layer, to steady rolls, to time dependence via various instabilities. Stability analysis plays an important role in understanding these events. In addition to indicating the region of parameter space at which a solution branch may become unstable, an analysis of stability may provide the geometric form of the instability in the associated eigenvector.

Fluid and granular flows may be classified by their geometric forms. Some flows exhibit a preferred scale (e.g. convection rolls, sand ripples, beach sand cusps), while others exhibit scale independence (e.g. turbulent flows, clouds, land surfaces, each with fractal or multifractal characteristics). Flows with a preferred scale may be understood by following the initial bifurcations. Even chaotic flows retain structures remnant from primary instabilities. Turbulent flows are also strongly influenced by spatially inhomogeneous forcing. As an example, atmospheric flow responds to the strong equatorial solar forcing and inhomogeneous land/sea distribution to yield temporal and spatial means dominated by low wavenumber structure.

In my research, I concentrate on nonlinear flows and their bifurcations. Recently, I have expanded my research interests into the domain of fluid flow in the Earth's crust, modeling kinetically governed precipitation and dissolution of minerals for porous media flows in heterogeneous permeability fields, along with chemically reacting species. I have also begun modeling landform evolution via hydraulic erosion.