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Papers by maria higuera

Research paper thumbnail of Faraday waves, streaming flow, and relaxation oscillations in nearly circular containers

Chaos, 2008

Faraday waves near onset in an elliptical container are described by a third-order system of ordi... more Faraday waves near onset in an elliptical container are described by a third-order system of ordinary differential equations with characteristic slow-fast structure. These equations describe the interaction of standing waves with a weakly damped streaming flow driven by Reynolds stresses in boundary layers at the free surface and the rigid walls, and capture the proliferation with decreasing damping of periodic and nonperiodic relaxation oscillations observed near onset in previous simulations. These structures are the result of slow drift through symmetry-related Hopf bifurcations.

Research paper thumbnail of Coupled Amplitude-Streaming Flow Equations for Nearly Inviscid Faraday Waves in Small Aspect Ratio Containers

Journal of Nonlinear Science, 2008

We derive a set of asymptotically exact coupled amplitude-streaming flow ({CASF}) equations gover... more We derive a set of asymptotically exact coupled amplitude-streaming flow ({CASF}) equations governing the evolution of weakly nonlinear nearly inviscid multimode Faraday waves and the associated streaming flow in finite geometries. The streaming flow is found to play a particularly important role near mode interactions. Such interactions come about either through a suitable choice of parameters or through breaking of degeneracy among modes related by symmetry. An example of the first case is provided by the interaction of two nonaxisymmetric modes in a circular container with different azimuthal wavenumbers. The second case arises when the shape of the container is changed from square to slightly rectangular, or from circular to slightly noncircular but with a plane of symmetry. The generation of streaming flow in each of these cases is discussed in detail and the properties of the resulting CASF equations are described. A preliminary analysis suggests that these equations can resolve discrepancies between existing theory and experimental results in the first two of the above cases.

Research paper thumbnail of Dynamics of nearly inviscid Faraday waves in almost circular containers

Physica D-nonlinear Phenomena, 2005

Parametrically driven surface gravity-capillary waves in an elliptically distorted circular cylin... more Parametrically driven surface gravity-capillary waves in an elliptically distorted circular cylinder are studied. In the nearly inviscid regime, the waves couple to a streaming flow driven in oscillatory viscous boundary layers. In a cylindrical container, the streaming flow couples to the spatial phase of the waves, but in a distorted cylinder, it couples to their amplitudes as well. This coupling may destabilize pure standing oscillations, and lead to complex time-dependent dynamics at onset. Among the new dynamical behavior that results are relaxation oscillations involving abrupt transitions between standing and quasiperiodic oscillations, and exhibiting 'canards'.

Research paper thumbnail of Weakly nonlinear nonaxisymmetric oscillations of capillary bridges at small viscosity

Physics of Fluids, 2002

Weakly nonlinear nonaxisymmetric oscillations of a capillary bridge are considered in the limit o... more Weakly nonlinear nonaxisymmetric oscillations of a capillary bridge are considered in the limit of small viscosity. The supporting disks of the liquid bridge are subjected to small amplitude mechanical vibrations with a frequency that is close to a natural frequency. A set of equations is derived for accounting the slow dynamics of the capillary bridge. These equations describe the coupled evolution of two counter-rotating capillary waves and an associated streaming flow. Our derivation shows that the effect of the streaming flow on the capillary waves cannot be a priori ignored because it arises at the same order as the leading (cubic) nonlinearity. The system obtained is simplified, then analyzed both analytically and numerically to provide qualitative predictions of both the relevant large time dynamics and the role of the streaming flow. The case of parametric forcing at a frequency near twice a natural frequency is also considered.

Research paper thumbnail of REFRACTOMETRÍA INTRODUCCIÓN

La Refractometría tiene variadas aplicaciones Medir la concentración de un alimento, resultaría m... more La Refractometría tiene variadas aplicaciones Medir la concentración de un alimento, resultaría muy complejo de no ser por la gran ayuda proporcionada por la Refractometría.

Research paper thumbnail of Faraday waves, streaming flow, and relaxation oscillations in nearly circular containers

Chaos, 2008

Faraday waves near onset in an elliptical container are described by a third-order system of ordi... more Faraday waves near onset in an elliptical container are described by a third-order system of ordinary differential equations with characteristic slow-fast structure. These equations describe the interaction of standing waves with a weakly damped streaming flow driven by Reynolds stresses in boundary layers at the free surface and the rigid walls, and capture the proliferation with decreasing damping of periodic and nonperiodic relaxation oscillations observed near onset in previous simulations. These structures are the result of slow drift through symmetry-related Hopf bifurcations.

Research paper thumbnail of Coupled Amplitude-Streaming Flow Equations for Nearly Inviscid Faraday Waves in Small Aspect Ratio Containers

Journal of Nonlinear Science, 2008

We derive a set of asymptotically exact coupled amplitude-streaming flow ({CASF}) equations gover... more We derive a set of asymptotically exact coupled amplitude-streaming flow ({CASF}) equations governing the evolution of weakly nonlinear nearly inviscid multimode Faraday waves and the associated streaming flow in finite geometries. The streaming flow is found to play a particularly important role near mode interactions. Such interactions come about either through a suitable choice of parameters or through breaking of degeneracy among modes related by symmetry. An example of the first case is provided by the interaction of two nonaxisymmetric modes in a circular container with different azimuthal wavenumbers. The second case arises when the shape of the container is changed from square to slightly rectangular, or from circular to slightly noncircular but with a plane of symmetry. The generation of streaming flow in each of these cases is discussed in detail and the properties of the resulting CASF equations are described. A preliminary analysis suggests that these equations can resolve discrepancies between existing theory and experimental results in the first two of the above cases.

Research paper thumbnail of Dynamics of nearly inviscid Faraday waves in almost circular containers

Physica D-nonlinear Phenomena, 2005

Parametrically driven surface gravity-capillary waves in an elliptically distorted circular cylin... more Parametrically driven surface gravity-capillary waves in an elliptically distorted circular cylinder are studied. In the nearly inviscid regime, the waves couple to a streaming flow driven in oscillatory viscous boundary layers. In a cylindrical container, the streaming flow couples to the spatial phase of the waves, but in a distorted cylinder, it couples to their amplitudes as well. This coupling may destabilize pure standing oscillations, and lead to complex time-dependent dynamics at onset. Among the new dynamical behavior that results are relaxation oscillations involving abrupt transitions between standing and quasiperiodic oscillations, and exhibiting 'canards'.

Research paper thumbnail of Weakly nonlinear nonaxisymmetric oscillations of capillary bridges at small viscosity

Physics of Fluids, 2002

Weakly nonlinear nonaxisymmetric oscillations of a capillary bridge are considered in the limit o... more Weakly nonlinear nonaxisymmetric oscillations of a capillary bridge are considered in the limit of small viscosity. The supporting disks of the liquid bridge are subjected to small amplitude mechanical vibrations with a frequency that is close to a natural frequency. A set of equations is derived for accounting the slow dynamics of the capillary bridge. These equations describe the coupled evolution of two counter-rotating capillary waves and an associated streaming flow. Our derivation shows that the effect of the streaming flow on the capillary waves cannot be a priori ignored because it arises at the same order as the leading (cubic) nonlinearity. The system obtained is simplified, then analyzed both analytically and numerically to provide qualitative predictions of both the relevant large time dynamics and the role of the streaming flow. The case of parametric forcing at a frequency near twice a natural frequency is also considered.

Research paper thumbnail of REFRACTOMETRÍA INTRODUCCIÓN

La Refractometría tiene variadas aplicaciones Medir la concentración de un alimento, resultaría m... more La Refractometría tiene variadas aplicaciones Medir la concentración de un alimento, resultaría muy complejo de no ser por la gran ayuda proporcionada por la Refractometría.

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