Nonstationary vortices in a water glass

¿Quién no ha experimentado la formación de un vórtice o de un remolino en un vaso cuando disuelve el cacao en la leche y le da vueltas con una cuchara? En este artículo, se analizan los aspectos mecánicos de los vórtices no estacionarios formados cuando se agita agua con una cuchara alrededor de un eje central en un vaso de precipitados cilíndrico. Se mostrará que el vórtice no estacionario formado después de agitar el agua con la cuchara es de tipo forzado y se comparará la dinámica del fluido de este vórtice no estacionario con los conocidos vórtices libres estacionarios y forzados y con el de la dinámica del vórtice aislado libre (también conocido como el vórtice de Oseen-Lamb). Mostraremos que la observación de la generación y del decaimiento del vórtice no estacionario en el recipiente cilíndrico del agua en rotación es un simple experimento que puede constituir una experiencia muy fructífera para el entendimiento de los aspectos cinemáticos, dinámicos, y estáticos de la rotación axisimétrica, radial, o torsional de un fluido homogéneo e incompresible.Who has not experienced the formation of a vortex or a whirlpool in a glass of milk when trying to dissolve cocoa in it by stirring the liquid with a spoon? In this paper, we analyse the mechanical aspects of the unsteady vortex formed in swirling water that was stirred with a spoon around a central axis in a cylindrical glass. We show that the formed unsteady vortex is of forced type and we compare the fluid dynamics of this unsteady vortex to that of the well-known steady free and forced vortices and with the dynamics of the unsteady free isolated vortex (also known as Oseen-Lamb’s vortex). We show that the observation of the generation and decay of the unsteady vortex in a cylindrical glass of rotating water is a simple experiment that may constitute a very fruitful experience for understanding the kinematics, dynamics, and static aspects of the axisymmetric, rotational, or torsional flow of an homogeneous and incompressible fluid.F.J.M. y J.A.M. agradecen al Instituto de Ciencias de la Educación de la Universitat Politècnica de València por su ayuda a los Equipos Innovación y Calidad Educativa e-MACAFI y MoMa. A.B. agradece el apoyo del Vicerrectorado de Tecnologías de la Información de la Universidad de Alicante a través del proyecto GITE-09006-UA. E.A, A.N. y J.M.V. agradecen a Cajasol-La Caixa la financiación parcial de este trabajo

Surface instabilities of ferrofluids

We report on recent progress in understanding the formation of surface protuberances on a planar layer of ferrofluid in a magnetic field oriented normally to the surface. This normal field or Rosensweig instability can be tackled by a linear and a nonlinear description. In the linear regime of small amplitudes we focus on the wave number of maximal growth, its corresponding growth rate and the oscillatory decay of metastable pattern, accessible via a pulse technique. A quantitative comparison of measurements with predictions of the linear stability analysis is performed, whereby the viscosity and the finite depth of the liquid layer are taken into account. In the nonlinear regime the fully developed peak pattern can be predicted by a minimization of the free energy and by numerics employing the finite element method. For a comparison with the results of both methods, the three-dimensional surface profile is recorded by a radioscopic measurement technique. In the bistable regime of the flat and patterned state we generate localized states (ferrosolitons) which are recovered in analytical and numerical model descriptions. For higher fields an inverse hysteretic transition from hexagonal to square planforms is measured. % Via a horizontal field component the symmetry can be broken in the experiment, resulting in liquid ridges and distorted hexagons, as predicted by theory. Replacing ferrofluid by ferrogel also an elastic energy contribution has to be taken into account for a proper model description, yielding a linear shift of the threshold and an increased bistability range. Parametric excitation in combination with magnetic fields is widening the horizon of pattern formation even further. For the mono-spike oscillator harmonic and subharmonic response as well as deterministic chaos is observed and modeled. In a ring of spikes the formation of domains of different wavelengths and spatio-temporal intermittency is quantitatively studied. For an extended layer of ferrofluid we predict that a stabilizing horizontal field counteracted by vertical vibrations will result in oblique rolls with preselected orientation