O. R. Tutty | Searcharxiv

arXiv2010

A Simple Redistribution Vortex Method (with Accurate Body Forces)

A circulation redistribution scheme for viscous flow is presented. Unlike other redistribution methods, it operates by transferring the circulation to a set of fixed nodes rather than neighbouring vortex elements. A new distribution of vortex elements can then be constructed from the circulation on the nodes. The solution to the redistribution problem can be written explicitly as a set of algebraic formulae, producing a method which is simple and efficient. The scheme works with the circulation contained in the vortex elements only, and does not require overlap of vortex cores. With a body fitted redistribution mesh, smooth and accurate estimates of the pointwise surface forces can be obtained. The ability of the scheme to produce high resolution solution is demonstrated using a series of test problems.

physics.flu-dyn↗

arXiv2006

Recurrence of Travelling Waves in Transitional Pipe Flow

The recent theoretical discovery of families of travelling wave solutions in pipe flow at Reynolds numbers lower than the transitional range naturally raises the question of their relevance to the turbulent transition process. Here a series of numerical experiments are conducted in which we look for the spatial signature of these travelling waves in transitionary flows. Working within a periodic pipe of 5D (diameters) length, we find that travelling waves with low wall shear stresses (lower branch solutions) are on a surface which separates initial conditions which uneventfully relaminarise and those which lead to a turbulent evolution. Evidence for recurrent travelling wave visits is found in both 5D and 10D long periodic pipes but only for those travelling waves with low-to-intermediate wall shear stress and for less than about 10% of the time in turbulent flow. Given this, it seems unlikely that the mean turbulent properties such as wall shear stress can be predicted as an expansion over the travelling waves in which their individual properties are appropriately weighted. Rather, further dynamical structures such as periodic orbits need to be isolated and included in any such expansion.

physics.flu-dyn↗