| dc.description.abstract | Turbulent flows are ubiquitous in natural and engineering applications. For example, stellar formation rates are an order magnitude larger due to turbulence effects and quarter of all energy expended in transport and commercial applications is used to move fluids or move objects through fluids, which are largely turbulent in nature. Prediction and control of turbulent flows, especially their extreme fluctuations, is an important challenge in diverse practical applications such supersonic and hypersonic flows, both in terms of flight performance and materials needed to build these vehicles. Turbulent flows have thus far been studied in the limit of high-Reynolds numbers (Rλ > 10³), largely due to their prevalence in applications. In this regime, turbulence has a wide-range of excited scales, with the largest scales often dictated by non-universal features such as the geometry of the object generating turbulence. Small scales are known to exhibit non-trivial statistics characterized by extreme fluctuations, a phenomenon collectively called intermittency. Higher-order statistics of velocity fluctuations, those describing the extreme events, are however exceedingly challenging to measure and compute. Computations have been carried out with over 163843 grid-points to measure them accurately. The observed scaling of extreme event statistics is known to be anomalous i.e. it differs greatly from classical predictions. The prediction of this anomalous behavior from first principles is still an open problem. Furthermore, the parameter range where the scaling behavior must be observed is also not well defined by classical theories. It is therefore important to understand and characterize the fundamental aspects of turbulent flows. In particular how turbulent behavior emerges, what its characteristics are, and how they relate to conditions found in realistic flows. This is the main thrust of this dissertation. This work provides a novel approach to address these open questions. We use highly resolved direct numerical simulations at low to moderate Rλ ∼ O(1 − 100), which are easily realizable on current generation of supercomputers, to measure high-order statistics and establish their scaling. The simulations in this dissertation have the finest small-scale and temporal resolution in literature. Anomalous scaling of high-order moments, assumed to be a high-Rλ feature, is shown to emerge at Rλ ∼ O(10) and we directly test its universality with respect to large scale production mechanisms. The observed scaling exponents are compared to recently developed theory. In contrast to classical theories, we also show that most extreme fluctuations develop turbulent character first. Therefore, high-Rλ features can be reliably computed by studying highly resolved low-Rλ turbulent flows. The classical concept of small-scale independence, a widely made assumption in modelling approaches, is also studied using the energy spectrum of turbulent fluctuations. We also extend the new formalism to compressible turbulence and show that the vortical modes behave similar to their incompressible counterpart. Compressible modes are shown to scale differently. Based on our results and a survey of the literature, we speculate that the asymptotic scaling at large parameter values in spatio-temporal chaotic systems can be understood by careful study of transition to this scaling at much lower parameter values. Within computing, this means that well-resolved simulations at low parameter values, X (e.g. X = Rλ etc.), which are order magnitudes cheaper than high-X, can reveal important and relevant physics at high-X. | |
