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The aim in the dynamical systems approach to transitional turbulence is to construct a scaffold in phase space for the dynamics using simple invariant sets (exact solutions) and their stable and unstable manifolds. In large (realistic) domains where turbulence can co-exist with laminar flow, this requires identifying exact localized solutions. In wall-bounded shear flows the first of these has recently been found in pipe flow, but questions remain as to how they are connected to the many known streamwise-periodic solutions. Here we demonstrate the origin of the first localized solution in a modulational symmetry-breaking Hopf bifurcation from a known global travelling wave that has 2-fold rotational symmetry about the pipe axis. Similar behaviour is found for a global wave of 3-fold rotational symmetry, this time leading to two localized relative periodic orbits. The clear implication is that all global solutions should be expected to lead to more realistic localised counterparts through such bifurcations, which provides a constructive route for their generation.
The spectral model of Perry, Henbest & Chong (1986) predicts that the integral length-scale varies very slowly with distance to the wall in the intermediate layer. The only way for the integral length scales variation to be more realistic while keepi
Direct numerical simulations of turbulent pipe flow subjected to streamwise-varying wall rotation are performed. This control method is observed to be able to significantly reduce the friction drag and even laminarize the flow under certain control p
We demonstrate the existence of a large number of exact solutions of plane Couette flow, which share the topology of known periodic solutions but are localized in space. Solutions of different size are organized in a snakes-and-ladders structure stri
Turbulence is the major cause of friction losses in transport processes and it is responsible for a drastic drag increase in flows over bounding surfaces. While much effort is invested into developing ways to control and reduce turbulence intensities
The impact of wall roughness on fully developed laminar pipe flow is investigated numerically. The roughness is comprised of square bars of varying size and pitch. Results show that the inverse relation between the friction factor and the Reynolds nu