Complex fluid dynamics: From laminar to geophysical flows

In this dissertation, we present analytical, experimental, and numerical work relating to two problems in fluid flow.; We first treat the oldest, hardest, and arguably one of the most important problems in boundary layer theory: determining the drag on a sphere and an infinite cylinder moving at a fixed speed in a highly viscous fluid. We necessarily extensively review previous experimental and theoretical work, and then apply techniques based on the perturbative renormalization group to produce optimal "coarse-grained" approximations. These approximations lead to a new prediction for the drag coefficient, one which both reproduces and surpasses the results of matched asymptotics.; We next present investigations into the biocomplex system at Yellowstone National Park. This research, which includes field work, experimental measurements, and numerical modelling, has shown that microbes do not play an important role in the formation of large scale carbonate terraces. Although we found that microbial communities are highly correlated with depositional facies, we demonstrated that this is a consequence of tight correlations between aqueous chemistry and the underlying travertine. We show how these correlations can be used to reconstruct ancient depositional environments.; We also present highly successful minimal models which explain the formation of depositional facies and large scale travertine motifs, including the characteristic terrace architecture found at carbonate hot springs. Our numerical model predicts dynamical phenomena which are seen at real hot springs. It also produces patterns which have the same static statistical properties as those seen at real hot springs, and indicates that hot spring terraces are indeed scale invariant; we show that the distribution of pond areas in both simulated landscapes and real hot springs obeys the same power law. By analogy with studies of vicinal surfaces, we identify another universal statistical characterization, the terrace width distribution. We present evidence from both simulated landscapes and experimental data that this distribution is a universal property of carbonate terraces, applying regardless of the details of local chemistry and biology.