| Abstract: | Turbulence is hard to avoid in nature, from astrophysical flows to water flowing from a tap. Turbulent flow is also an example of a system driven far from equilibrium, sustained by a flux of energy between disparate scales. It is usually viewed as a large-scale flow which breaks down into smaller and smaller vortices. On the contrary, flows which are effectively two-dimensional exhibit the opposite process of self-organization, which can be traced to the presence of an additional conservation law. A key question is what principles determine the emergent flow, and what forms can it take. I will first describe a two-dimensional flow where the self-organized state satisfies a novel constraint, due to the competition between the two conservation laws. This gives rise to a surprisingly rich phase diagram of states, including a phase with spontaneously broken symmetry. I will then discuss three-dimensional rotating turbulence, which is known to self-organize into a large-scale two-dimensional flow, though the process is poorly understood. I will show that wave modes play a crucial role, restricting the possible interactions in the system, and giving birth to a new conservation law. This conservation law then leads to a directional transfer of energy from three-dimensional waves to the large-scale two-dimensional flow, sustaining the self-organized state. |