Using theoretical physics to address complex dynamical problems in turbulence, geosciences and biology

Abstract

Real-world systems are generally nonlinear, exhibiting complexity across a range of physical and temporal scales. In this thesis I tackle a series of real-world problems and questions which span the breadth of these different scales, from the microbiological to interplanetary. This is possible when each system is viewed from the perspective of theoretical physics as being reducible to the level of a dynamical system. Early on in my research, I realised that these approaches could be applied across many fields and chose to work in three of them. Turbulence remains one of the greatest challenges remaining in classical physics, and arises in our first dynamical system, the Navier-Stokes equations (NSEs). I investigate higher-dimensional versions of these equations using Direct Numerical Simulation studies to search for evidence of critical phenomena, using chaos as a measure. Using this together with a closure-approximated model, I investigate how increasing spatial dimensions appears to lead to a reduction in chaos, which might tentatively suggest a critical dimension of six for these equations. From the problem of turbulence, I turn to a related problem in ensemble numerical weather prediction, the signal-to-noise paradox. The paradox is that current ensemble systems seem to predict reality better than they predict themselves. By applying ergodic theory to ensemble forecasting, I show that using the ensemble mean as our best forecast of observations amounts to interpreting it as the most likely phase-space trajectory, which relies on the ergodic theorem. I argue that this fails in certain cases due to evidence of multi-modality, which can break the ergodic theorem, creating the paradox. Moving up a scale, the next problem I address is the practical challenge of contamination when trying to detect microbiology in Earth's upper atmosphere. Leveraging advances in aerospace technology, such as CubeSats and rocket-borne samplers, this research proposes a new technique called relative-velocity sampling, for capturing large particles in the understudied mesosphere and lower thermosphere. This technique reduces the contamination challenge to a simple one-dimensional dynamical system, obeying the NSEs. My ultimate problem lies on the largest scales where I apply the theory of island biogeography to interplanetary scales for planetary protection. This theory models population dynamics for inter-island populations and has been suggested as applicable to interplanetary systems. This is used to show that although such an equilibrium theory generally breaks down when applied to interplanetary scales, the mean-time to extinction resulting from the combined effects of growth and death rates can be quantified. This is used to challenge the probabilistic model of planetary protection and suggest how the mean-time to extinction can instead be used to assess colonisation risk. The broader applicability of island biogeography to considering biotic transfer at the interplanetary scale is considered. This thesis concludes with a synthesis of the problems tackled, illustrating the capability of theoretical physics to advance understanding in different fields underpinned by dynamical systems, and the role of interdisciplinary research