We build corotational symmetric solutions to the harmonic map flow from the unit disc into the unit sphere which have constant degree. First, we prove the existence of such solutions, using a time semi-discrete scheme based on the idea that the harmonic map flow is the L-gradient of the relaxed Dirichlet energy. We prove a partial uniqueness result concerning these solutions. Then, we compute n...

Steady non-isothermal parallel-plate flow of a Newtonian fluid with a temperature dependent viscosity is considered. The viscosity is modelled by a Nahme type law. We apply axisymmetric Q finite elements to the coupled nonlinear system to obtain numerical solutions for a wide range of parameters.

The method of contour dynamics, developed for two-dimensional vortex patches by Zabusky, Hughes, and Roberts [34] is extended to vortex rings in which the vorticity distribution varies linearly with normal distance from the symmetry axis. The method tracks the motion of the boundaries of the vorticity regions and hence reduces the dimensionality of the problem by one. We discuss the formulation...

Axisymmetric vortices with high level of axial vorticity are considered. Consistency conditions result in so-called compensating regime of the vortical flow. The power laws associated with this regime are applied to a series of vortices of different scales: bathtub vortex, tornadoes and tropical cyclones. Key–Words: vortical flows, bathtub vortex, tornado, tropical cyclone

As part of ASHRAE Research Project 1185, field data from the constant flow rate charging of a stratified chilled water storage tank with double-ring octagonal slotted-pipe diffusers serving a university chilled water system were compared with results of a transient axisymmetric computational fluid dynamics (CFD) model. Charge processes at flows near design flow rate and 50% of design were model...

A stochastic simulation (Monte-Carlo-) method for the dynamics and rheological behaviour of small Brownian axisymmetric particles or fibres in a Newtonian solvent is tested and verified. The stress field due to the presence of the particles in a sheared or strained flow field is related to the conformation of the particles via the second and fourth moments of the conformation distribution funct...

Three-dimensional instability and patterns of an axisymmetric flow of electrically conducting liquid in a cylindrical enclosure driven by an axial traveling magnetic field (TMF) is studied. The attention is focused on the TMF of a large axial wavenumber or large frequency, which leads to a formation of the skin layer near the sidewall. It is shown that the flow intensity grows with the increase...

A mathematical model for the description of biomagnetic fluid flow exposed to a magnetic field that accounts for both electric and magnetic properties of the biofluid is presented. This is achieved by adding the Lorentz and magnetization forces in the Navier-Stokes equations. To demonstrate the effects of magnetic fields, we consider the case of laminar, incompressible, viscous, the steady flow...

The emergence of coherent vortical structures is a hallmark of the evolution of two-dimensional turbulence. Two fundamental processes of this evolution have been identified in vortex merging and vortex axisymmetrization. The question of whether axisymmetrization is a universal process has recently been answered in the negative. In the linear approximation, vortices indeed become axisymmetric, d...

We describe a three-dimensional (3D) cell culture system using monodisperse peptide hydrogel beads. We utilized a self-assembling peptide hydrogel to provide cells in vivo-like microenvironment. We succeeded in encapsulating endothelial cells within the hydrogels by using a 3D microfluidic axisymmetric flow-focusing device (AFFD), and showed the encapsulated endothelial cells were viable and we...