We present an analysis of the primary bifurcations that occur in a mathematical model that uses the (three-dimensional) Navier-Stokes equations in the Boussinesq approximation to describe the flow of a near unity Prandtl number fluid (i.e. air) in the differentially heated rotating annulus. In particular, we investigate the double Hopf (Hopf-Hopf) bifurcations that occur along the axisymmetric ...

In a composite fluid system of two gravitationally coupled barotropic scale-free discs bearing a rotation curve v ∝ r and a power-law surface mass density Σ0 ∝ r −α with α = 1 + 2β, we construct coplanar stationary aligned and spiral perturbation configurations in the two discs. Due to the mutual gravitational interaction, there are two independent classes of perturbation modes with surface mas...

We investigate the large time behavior of an axisymmetric model for the 3D Euler equations. In [22], Hou and Lei proposed a 3D model for the axisymmetric incompressible Euler and Navier-Stokes equations with swirl. This model shares many properties of the 3D incompressible Euler and Navier-Stokes equations. The main difference between the 3D model of Hou and Lei and the reformulated 3D Euler an...

This paper reformulates the axisymmetric form of the material point method (MPM) using generalized interpolation material point (GIMP) methods. The reformulation led to a need for new shape functions and gradients specific for axisymmetry that were not available before. The new shape functions differ most from planar shape functions near the origin where r = 0. A second purpose for this paper w...

We consider torsional flow of a viscoelastic fluid in a cone-and-plate device. This flow is known to undergo a purely elastic instability when the Deborah number reaches a critical value. Beyond this critical value a Hopf bifurcation to spiral vortices occurs. In this paper we consider the stability of the flow to non-axisymmetric disturbances when the Reynolds number is non-zero. We examine th...

The linear impulse response of axisymmetric jets is examined for a family of variable-temperature profiles typical of the potential core. The influence of jet heating, shear layer thickness, Reynolds and Mach number on the spatio-temporal stability of both axisymmetric and helical modes is investigated. The linear impulse response is retrieved from a numerical solution of the spatial eigenvalue...

Rapid progress toward the understanding of tropical cyclones has been made during the past 10 years, largely as a result of the development of numerical models. The dynamics and energetics of the mature tropical cyclone are reviewed in this article. First, the pressure, wind, temperature, and moisture structures of the hurricane are summarized. Then a scale analysis is applied over four separat...

We consider the equilibrium and stability of rotating axisymmetric fluid drops by appealing to a variational principle that characterizes the equilibria as stationary states of a functional containing surface energy and rotational energy contributions, augmented by a volume constraint. The linear stability of a drop is determined by solving the eigenvalue problem associated with the second vari...

Most of the field problems in geotechnical engineering are in three dimensional state or close to a plane strain condition. Strength and deformation properties of soils in plane strain condition are considerably different from those in an axisymmetric condition. Many researchers have investigated the behaviour of soils under a plane strain condition. However, most of the previous studies have c...

We present an efficient method for computing numerically the solution to the time-dependent Maxwell equations in an axisymmetric domain, with arbitrary (not necessarily axisymmetric) data. The method is an extension of those introduced in [20] for Poisson’s equation, and in [4] for Maxwell’s equations in the fully axisymmetric setting (i.e., when the data is also axisymmetric). It is based on a...