Richard R Kerswell

Exact coherent structures in pipe flow: travelling wave solutions

Three-dimensional travelling wave solutions are found for pressure-driven fluid flow through a circular pipe. They consist of three well-defined flow features – streamwise rolls and streaks which dominate and streamwise-dependent wavy structures. The travelling waves can be classified by the

The instability of precessing flow

m

Dam break with Coulomb friction: A model for granular slumping?

-fold rotational symmetry they possess about the pipe axis with

Recurrence of travelling waves in transitional pipe flow

m\,{=}\,1,2,3,4,5

On the internal shear layers spawned by the critical regions in oscillatory Ekman boundary layers

and

Tidal excitation of hydromagnetic waves and their damping in the Earth

6

Minimal seeds for shear flow turbulence: using nonlinear transient growth to touch the edge of chaos

solutions identified. All are born out of saddle-node bifurcations with the lowest corresponding to

Improved upper bound on the energy dissipation rate in plane Couette flow: the full solution to Busse's problem and the Constantin–Doering–Hopf problem with one-dimensional background field

m\,{=}\,3

Unification of variational principles for turbulent shear flows: the background method of Doering-Constantin and the mean-fluctuation formulation of Howard-Busse

and traceable down to a Reynolds number (based on the mean velocity) of 1251. The new solutions are found using a constructive continuation procedure based upon key physical mechanisms thought generic to wall-bounded shear flows. It is believed that the appearance of these new alternative solutions to the governing equations as the Reynolds number is increased is a necessary precursor to the turbulent transition observed in experiments.

An optimization approach for analysing nonlinear stability with transition to turbulence in fluids as an exemplar

Abstract An explanation is put forward for the instability observed within a precessing, rotating spheroidal container. The constant vorticity solution for the flow suggested by Poincare is found to be inertially unstable through the parametric coupling of two inertial waves by the underlying constant strain field. Such resonant couplings are due either to the elliptical or shearing strains present which elliptically distort the circular streamlines and shear their centres respectively. For the precessing Earths outer core, the shearing of the streamlines and the ensuing shearing instability are the dominant features. The instability of some exact, linear solutions for finite precessional rates is established and used to corroborate the asymptotic analysis. A complementary unbounded analysis of a precessing, rotating fluid is also presented and used to deduce a likely upperbound on the growth rate of a small disturbance. Connection is made with past experimental studies.