Neil J. Balmforth

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We study advection–diffusion of a passive scalar, T , by an incompressible fluid in a closed vessel bounded by walls impermeable to the fluid. Variations in T are produced by prescribing a steady non-uniform distribution of T at the boundary. Because there is no flow through the walls, molecular diffusion, κ, is essential in 'lifting' T off the boundary and(More)
Since the seminal remark by Pecora and Carroll that one can synchronize chaotic systems, the main example in the related literature has been the Lorenz equations. Yet this literature contains a mixture of true and false, and of justiied and unsubstantiated claims about the synchronization properties of the Lorenz equations. In this note we clarify some of(More)
The stability of a viscoplastic fluid film falling down an inclined plane is explored, with the aim of determining the critical Reynolds number for the onset of roll waves. The Herschel–Bulkley constitutive law is adopted and the fluid is assumed two-dimensional and incompressible. The linear stability problem is described for an equilibrium in the form of(More)