1,557 research outputs found
Whirling skirts and rotating cones
Steady, dihedrally symmetric patterns with sharp peaks may be observed on a
spinning skirt, lagging behind the material flow of the fabric. These
qualitative features are captured with a minimal model of traveling waves on an
inextensible, flexible, generalized-conical sheet rotating about a fixed axis.
Conservation laws are used to reduce the dynamics to a quadrature describing a
particle in a three-parameter family of potentials. One parameter is associated
with the stress in the sheet, aNoether is the current associated with
rotational invariance, and the third is a Rossby number which indicates the
relative strength of Coriolis forces. Solutions are quantized by enforcing a
topology appropriate to a skirt and a particular choice of dihedral symmetry. A
perturbative analysis of nearly axisymmetric cones shows that Coriolis effects
are essential in establishing skirt-like solutions. Fully non-linear solutions
with three-fold symmetry are presented which bear a suggestive resemblance to
the observed patterns.Comment: two additional figures, changes to text throughout. journal version
will have a wordier abstrac
Waves in Newton's bucket
The motion of a liquid in an open cylindrical tank rotating at a constant rate around its vertical axis of symmetry, a configuration called Newton’s bucket, is investigated using a linear stability approach. This flow is shown to be affected by several families of waves, all weakly damped by viscosity. The wave families encountered correspond to: surface waves which can be driven either by gravity or centrifugal acceleration, inertial waves due to Coriolis acceleration which are singular in the inviscid limit, and Rossby waves due to height variations of the fluid layer. These waves are described in the inviscid and viscous cases by means of mathematical considerations, global stability analysis and various asymptotic methods; and their properties are investigated over a large range of parameters (a, Fr), with a the aspect ratio and Fr the Froude number
Waves and instabilities in rotating free surface flows
The stability properties of the rotating free surface flow in a cylindrical container is studied using a global stability approach, considering succesively three models. For the case of solid body rotation (Newton’s bucket), all eigenmodes are found to be stable, and are classified into three families : gravity waves, singular inertial modes, and Rossby waves. For the case of a potential flow, an instability is found. The mechanism is explained as a resonance between gravity waves and centrifugal waves, and is thought to be at the origin of the ”rotating polygon instability” observed in experiments where the flow is driven by rotation of the bottom plate (see [9]). Finally, we give some preliminary results concerning a third model : the Rankine vortex
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