The present work uses a reducedorder model to study the motion of a buoyant vortex ring with nonnegligible core size. Buoyancy is considered in both nonBoussinesq and Boussinesq situations using an axisymmetric contour dynamics formulation. The density of the vortex ring differs from that of the ambient fluid, and both densities are constant and conserved. The motion of the ring is calculated by following the boundary of the vortex core, which is also the interface between the two densities. The velocity of the contour comes from a combination of a specific continuous vorticity distribution within its core and a vortex sheet on the core boundary. An evolution equation for the vortex sheet is derived from the Euler equation, which simplifies considerably in the Boussinesq limit. Numerical solutions for the coupled integrodifferential equations are obtained. The dynamics of the vortex sheet and the formation of two possible singularities, including singularities in the curvature and the shocklike profile of the vortex sheet strength, are discussed. Three dimensionless groups, the Atwood, Froude and Weber numbers, are introduced to measure the importance of physical effects acting on the motion of a buoyant vortex ring.
Phasefield model for a weakly compressible soft layered material: morphological transitions on smectic–isotropic interfaces
A coupled phasefield and hydrodynamic model is introduced to describe a twophase, weakly compressible smectic (layered phase) in contact with an isotropic fluid of different density. A nonconserved smectic order parameter is coupled to a conserved mass density in order to accommodate nonsolenoidal flows near the smectic–isotropic boundary arising from density contrast between the two phases. The model aims to describe morphological transitions in smectic thin films under heat treatment, in which arrays of focal conic defects evolve into conical pyramids and concentric rings through curvature dependent evaporation of smectic layers. The model leads to an extended thermodynamic relation at a curved surface that includes its Gaussian curvature, nonclassical stresses at the boundary and flows arising from density gradients. The temporal evolution given by the model conserves the overall mass of the liquid crystal while still allowing for the modulated smectic structure to grow or shrink. A numerical solution of the governing equations reveals that pyramidal domains are sculpted at the center of focal conics upon a temperature increase, which display tangential flows at their surface. Other cases investigated include the possible coalescence of two cylindrical stacks of smectic layers, formation of droplets, and the interactions between focal conic domains more »
 Award ID(s):
 1838977
 Publication Date:
 NSFPAR ID:
 10293559
 Journal Name:
 Soft Matter
 Volume:
 17
 Issue:
 25
 Page Range or eLocationID:
 6140 to 6159
 ISSN:
 1744683X
 Sponsoring Org:
 National Science Foundation
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