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(More)
Shallow-water equations with bottom drag and viscosity are used to study the dynamics of roll waves. First, we explore the effect of bottom topography on linear stability of turbulent flow over uneven surfaces. Low-amplitude topography is found to destabilize turbulent roll waves and lower the critical Froude number required for instability. At higher(More)
We present estimates of the amplitudes of intrinsically stable stochastically excited radial oscillations in stars near the main sequence. The amplitudes are determined by the balance between acoustical energy generation by turbulent convection (the Lighthill mechanism) and linear damping. Convection is treated with a time-dependent, nonlocal, mixing-length(More)
A nonlinear continuum model is considered that describes the dynamics of two-dimensional aeolian sand ripples. This integro-differential model is based on a phenomenological approach due to Anderson. Linear stability analysis using this model shows that a flat sand bed exposed to the action of wind is linearly unstable to long-wavelength perturbations. As(More)
We consider double-diffusive convection between two parallel plates and compute bounds on the flux of the unstably stratified species using the background method. The bound on the heat flux for Rayleigh–Bénard convection also serves as a bound on the double-diffusive problem (with the thermal Rayleigh number equal to that of the unstably stratified(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)
Microorganisms such as sperm routinely swim close to solid boundaries and within nonNewtonian fluids. In this paper, we exploit the lubrication approximation to model the motion of a flexible sheet near a rigid wall and immersed in a complex fluid. This allows us to specify an internally generated force density on the sheet and allow its shape and velocity(More)