Author:
BECKERS M.,VERZICCO R.,CLERCX H. J. H.,VAN HEIJST G. J. F.
Abstract
The dynamics and the three-dimensional structure of vortices in a linearly stratified,
non-rotating fluid are investigated by means of laboratory experiments, an analytical
model and through numerical simulations. The laboratory experiments show that such
vortices have a thin pancake-like appearance. Due to vertical diffusion of momentum
the strength of these vortices decreases rapidly and their thickness increases in time.
Also it is found that inside a vortex the linear ambient density profile becomes
perturbed, resulting in a local steepening of the density gradient. Based on the
assumption of a quasi-two-dimensional axisymmetric flow (i.e. with zero vertical
velocity) a model is derived from the Boussinesq equations that illustrates that the
velocity field of the vortex decays due to diffusion and that the vortex is in so-called cyclostrophic balance. This means that the centrifugal force inside the vortex
is balanced by a pressure gradient force that is provided by a perturbation of the
density profile in a way that is observed in the experiments. Numerical simulations
are performed, using a finite difference method in a cylindrical coordinate system. As
an initial condition the three-dimensional vorticity and density structure of the vortex,
found with the diffusion model, are used. The influence of the Froude number, Schmidt
number and Reynolds number, as well as the initial thickness of the vortex, on the
evolution of the flow are investigated. For a specific combination of flow parameters
it is found that during the decay of the vortex the relaxation of the isopycnals back to
their undisturbed positions can result in a stretching of the vortex. Potential energy of
the perturbed isopycnals is then converted into kinetic energy of the vortex. However,
when the stratification is strong enough (i.e. for small Froude numbers), the evolution
of the vortex can be described almost perfectly by the diffusion model alone.
Publisher
Cambridge University Press (CUP)
Subject
Mechanical Engineering,Mechanics of Materials,Condensed Matter Physics
Cited by
35 articles.
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