Taylor-Couette flows and Shear Flows

Starting with my PhD thesis, and continued thereafter, I have studied some canonical turbulent systems through direct numerical simulations: Taylor-Couette flow, Rayleigh-Bénard convection and double diffusive convection.

These systems are used as basic models when trying to understand the behaviour of more complicated natural or man-made flows. For example, Rayleigh-Bénard convection is useful to understand what is happening inside the Earth’s mantle, why the oceanic currents behave like they do, or how heat is transported inside the sun. Likewise, Taylor-Couette flow can be used as a basic model for many shear flows, going from the astrophysical scale (accretion disks around protostars) to the flow around a jetski’s hull. Double diffusive convection is commonly used to model the convection in the ocean. So even if these are easy systems to construct experimentally or perform direct numerical simulations of, they find applicability in many places and not all is known about them.

My PhD thesis mainly focused on investigating the boundary layer transitions in the Taylor-Couette system, and its relation to the analogous Rayleigh-Bénard problem. Later work developed some unanswered questions, especially regarding the nature of the large scale structures which form, such as the Taylor rolls in this video. Even for very large Reynolds numbers, and in very large computational boxes, these structures seem to be pinned in the same location over time.

A breakthrough came by using and further developing a rotating-frame formulation of Taylor-Couette flow. This allowed us to understand the fixing of these rolls as part of a self-sustaining process, and analogs to the rolls were found in other shear flows like Waleffe flow. Other variations on the canonical Taylor-Couette problem allowed us to better understand some features of turbulence decay and turbulence modulation in shear flows.

While there are a few minor points I would like to study further in Taylor-Couette and plane Couette flow, I feel like I do not have much mental energy left to devote to this system after many years.