Highly turbulent Taylor-Couette flow: direct numerical simulations

Turbulence is all around us. Even if we are familiar with every day instances of turbulence, like the smoke coming out of a chimney, it remains a not-well-understood phenomenum. As it is impossible to fully simulate turbulence to precisely take into account its effect, models must be used. These rely on a series of assumptions about the characteristics of turbulence, which have been checked in diverse canonical flows. One of the flows which remains relatively unexplored is Taylor-Couette (TC) flow. TC flow is the flow in a fluid layer between two coaxial and independently rotating cylinders. In this thesis, we numerically simulate TC flow to explore the behaviour of TC flow at high Reynolds numbers (high turbulence). The thesis starts with the development of a highly parallel computer code, which is demonstrated to have adequate performance up to sixty-four thousand cores. Other new numerical strategies to deal with the effect of temperature, or salinity on the flow are also detailed in the thesis. After this, the thesis focuses on the physics of TC flow. Three things are explored: First, the behaviour of highly turbulent TC flow, and how it transitions to this “ultimate" regime, which is expected to be similar to that found in astro- and geo-physical flows is studied. The nature of turbulence in accretion disks is also explored in this context. Second, the existence of an optimal transport, i.e. a maxima in the torque required to rotate the cylinders for a given shear rate as a function of the ratio between the rotation rates of both cylinders is also analysed. This phenomena was earlier observed in experiments, but remained unexplained. Simulations have allowed us to unravel the physics behind this process in more detail. Last, the universality of turbulence was explored. Earlier experiments provided indication that the turbulence in TC flow appeared to be of a slightly different nature to that seen in pipes and channels. In the thesis, this is further explored, and the reasons behind these discrepancies are elucidated.