Turbulence is ubiquitous in both natural and engineered systems with examples extending in scale from the planetary turbulence of cyclones in the Earth's midlatitude atmosphere and the turbulent banded winds of Jupiter to the small scale turbulence responsible for mixing pollution from sources near the Earth's surface and droplets inside clouds.  The role of turbulence in transporting material substances and mechanical properties such as momentum is central to atmospheric dynamics at all scales.  Turbulence is also a primary component of drag in pipes, channels, airframes and wings as well as ship hulls and machinery such as turbines.  Control of turbulence is important in such diverse applications as preventing loss of lift in aircraft wings and maintaining confinement of reactants in fusion devices.  Despite the practical importance of and the challenge posed to physics by the turbulence problem a comprehensive understanding of the mechanism of turbulence has remained elusive.  The equations governing the dynamics of turbulence have been known since the middle of the nineteenth century and it is not in doubt that the secret of understanding the nature of turbulence lies in solving these equations.   The contribution of this work is to solve the turbulence problem at the level of fundamental mechanism by making a paradigm shift from viewing turbulence as a single vast interacting system to viewing turbulence as a cooperative interaction between a set of large scale coherent structures and the relatively small in scale remaining motions which, despite being largely incoherent,  are still systematically influenced by the coherent structures in a way that the equations governing the turbulence dictate.  The analytical reflection of this change in perspective is obtained by casting the same equations governing turbulence that have long been known in a different form so that the mechanistically crucial separation of the coherent and incoherent components is made explicit.   This switch in viewpoint from studying individual manifestations of turbulence as defined by the velocity at every point in the flow in all its complexity to studying the cooperative dynamics of interaction between statistical quantities defined by averaging the velocities in the turbulence uncovers an underlying far simpler and more easily understood form of the turbulence dynamics.   The power and theoretical insight gained through this change in perspective is validated by the fact that the turbulent state has analytical solution in this new formulation whereas it has no analytical solution in the traditional formulation, as has long been recognized.  In the work supported by this grant analytical and numerical methods have been developed and applied to exploit this change in perspective in order to solve the problem of large scale jet formation and equilibration in planetary atmospheres, the formation and equilibration of horizontal layers in velocity and density in the Earth's atmosphere and oceans and the transition to and maintenance of turbulence in pipes and channels as well as in the turbulence near the Earth's surface.  Taking a wider view, the insight gained and the methods developed in this work to study the dynamics of turbulence in the systems mentioned are now available to be used to solve many other problems the dynamics of which are fundamentally the result  of cooperative interaction among statistical entities.   This wide class of problems has heretofore been inaccessible to comprehensive solution using traditional techniques based on simulations of individual manifestations of what are in terms of their role in  the dynamics at the fundamental level statistical entities.

Last Modified: 05/13/2018
Modified by: Brian F Farrell