Comment on "Selection of the Saffman-Taylor finger width in the absence of surface tension: an exact result"

A Comment on the Letter by Mark Mineev-Weinstein, Phys. Rev. Lett. 80, 2113 (1998). The authors of the Letter offer a Reply.

Nonlinear Saffman-Taylor instability

We show, both theoretically and experimentally, that the interface between two viscous fluids in a Hele-Shaw cell can be nonlinearly unstable before the Saffman-Taylor linear instability point is reached. We identify the family of exact elastica solutions [Nye et al., Eur. J. Phys. 5, 73 (1984)] as the unstable branch of the corresponding subcritical bifurcation which ends up at a topological singularity defined by interface pinchoff. We devise an experimental procedure to prepare arbitrary initial conditions in a Hele-Shaw cell. This is used to test the proposed bifurcation scenario and quantitatively asses its practical relevance.

Reply to Comment on 'Two-finger selection theory in the Saffman-Taylor problem

We clarify the meaning of the results of Phys. Rev. E 60, R5013 (1999). We discuss the use and implications of periodic boundary conditions, as opposed to rigid-wall ones. We briefly argue that the solutions of the paper above are physically relevant as part of a more general issue, namely the possible generalization to dynamics, of the microscopic solvability scenario of selection.

Experiments of periodic forcing of Saffman-Taylor fingers

We report on an experimental study of long normal Saffman-Taylor fingers subject to periodic forcing. The sides of the finger develop a low amplitude, long wavelength instability. We discuss the finger response in stationary and nonstationary situations, as well as the dynamics towards the stationary states. The response frequency of the instability increases with forcing frequency at low forcing frequencies, while, remarkably, it becomes independent of forcing frequency at large forcing frequencies. This implies a process of wavelength selection. These observations are in good agreement with previous numerical results reported in [Ledesma-Aguilar et al., Phys. Rev. E 71, 016312 (2005)]. We also study the average value of the finger width, and its fluctuations, as a function of forcing frequency. The average finger width is always smaller than the width of the steady-state finger. Fluctuations have a nonmonotonic behavior with a maximum at a particular frequency.

Phase-field approach to spatial perturbations in normal Saffman-Taylor fingers

We make a numerical study of the effect that spatial perturbations have in normal Saffman-Taylor fingers driven at constant pressure gradients. We use a phase field model that allows for spatial variations in the Hele-Shaw cell. We find that, regardless of the specific way in which spatial perturbations are introduced, a lateral instability develops on the sides of the propagating Saffman-Taylor finger. Moreover, the instability exists regardless of the intensity of spatial perturbations in the cell as long as the perturbations are felt by the finger tip. If, as the finger propagates, the spatial perturbations felt by the tip change, the instability is nonperiodic. If, as the finger propagates, the spatial perturbations felt by the tip are persistent, the instability developed is periodic. In the later case, the instability is symmetrical or asymmetrical depending on the intensity of the perturbation.

Dynamical Systems approach to Saffman-Taylor fingering. A Dynamical Solvability Scenario

A dynamical systems approach to competition of Saffman-Taylor fingers in a Hele-Shaw channel is developed. This is based on global analysis of the phase space flow of the low-dimensional ordinary-differential-equation sets associated with the classes of exact solutions of the problem without surface tension. Some simple examples are studied in detail. A general proof of the existence of finite-time singularities for broad classes of solutions is given. Solutions leading to finite-time interface pinchoff are also identified. The existence of a continuum of multifinger fixed points and its dynamical implications are discussed. We conclude that exact zero-surface tension solutions taken in a global sense as families of trajectories in phase space are unphysical because the multifinger fixed points are nonhyperbolic, and an unfolding does not exist within the same class of solutions. Hyperbolicity (saddle-point structure) of the multifinger fixed points is argued to be essential to the physically correct qualitative description of finger competition. The restoring of hyperbolicity by surface tension is proposed as the key point to formulate a generic dynamical solvability scenario for interfacial pattern selection.

Fluctuations in Saffman-Taylor fingers with quenched disorder

We make an experimental characterization of the effect that static disorder has on the shape of a normal Saffman-Taylor finger. We find that static noise induces a small amplitude and long wavelength instability on the sides of the finger. Fluctuations on the finger sides have a dominant wavelength, indicating that the system acts as a selective amplifier of static noise. The dominant wavelength does not seem to be very sensitive to the intensity of static noise present in the system. On the other hand, at a given flow rate, rms fluctuations of the finger width, decrease with decreasing intensity of static noise. This might explain why the sides of the fingers are flat for typical Saffman-Taylor experiments. Comparison with previous numerical studies of the effect that temporal noise has on the Saffman-Taylor finger, leads to conclude that the effect of temporal noise and static noise are similar. The behavior of fluctuations of the finger width found in our experiments, is qualitatively similar to one recently reported, in the sense that, the magnitude of the width fluctuations decays as a power law of the capillary number, at low flow rates, and increases with capillary number for larger flow rates.

"Maurice" de James Ivory . ¿Traïció a la Tradició Clàssica en adaptar la novel·la d'E. M. Forster?

D'acord amb els estudis sobre literatura i cinema i des del punt de vista de la influència de la Tradició Clàssica -Tradició Grega Clàssica, en aquest cas-, aquest article és una anàlisi acurada de les traïcions inevitables -fins a un cert punt- dels guionistes respecte dels textos literaris que adapten. Tanmateix, malgrat ser pràcticament inevitable, el Dr. Pau Gilabert Barberà indica quins són en opinió seva els límits que Ivory/Hesketh-Harvey no haurien d'haver ultrapassat a fir de no diluir el temperament hel·lènic de "Maurice" d'E. M. Forster.

Grècia i amor platònic a Maurice d'E. M. Forster, o la grandesa i els límits de l'Antiguitat com a inspiració.

L'objectiu d¿aquest article és mostrar com, malgrat la idealització evident de Grècia i l'amor platònic en diferents autors de l'Anglaterra Victoriano-Eduardina, ambdós tenen els seus límits. Per explicar-ho, doncs, l'autor presenta una anàlisi minuciosa del text anglès i, alhora, fa constants referències al textos grecs implícits, com ara el Simposi i el Fedre de Plató i tal vegada fins i tot l'Eròtic de Plutarc en cerca d'una tradició clàssica que és cabdal per entendre l'Anglaterra de principis del segle XX.

Grecia y amor platónico en Maurice de E.M. Forster, o la grandeza y los límites de la Antigüedad como inspiración

El objetivo de este artículo es mostrar cómo, pese a la evidente idealización de Grecia y el amor platónico en la Inglaterra Victoriano-Eduardina, ambos tienen sus límites. Para explicarlo, pues, el autor presenta un análisis minucioso del texto inglés y, a la vez, se refiere constantemente a los textos griegos implícitos como el Simposio y el Fedro de Platón y tal vez incluso el Erótico de Plutarco en busca de una tradición clásica que es capital para entender la Inglaterra de principios del siglo XX

Greece and Platonic Love in E. M. Forster's Maurice, or the greatness and limits of Antiquity as a source of inspiration.

The aim of this article is to show how, although the evident idealization of Greece and Platonic love throughout the Victorian-Edwardian England, both also show their limits. In order to make it clear the author refers constantly to the implicit Greek texts such as Plato's Symposium and Phaedrus and perhaps even to Plutarch¿s Eroticus in search of a Classical Tradition which is highly significant in order to understand that England at the beginning of the twentieth century.

Audit report on Taylor County, Iowa for the year ended June 30, 2011

Audit report on Taylor County, Iowa for the year ended June 30, 2011

"Maurice" de James Ivory . ¿Traición a la Tradición Clásica al adaptar la novela de E. M. Forster?

De acuerdo con los estudios sobre literatura y cine y desde el punto de vista de la influencia de la Tradición Clásica -Tradición Griega Clásica, en este caso-, este artículo es un análisis minucioso de las traiciones inevitables ¿hasta un cierto punto- de los guionistas a los textos literarios que adaptan. Sin embargo, a pesar de ser prácticamente inevitable, el Dr. Pau Gilabert Barberà indica cuáles son en su opinión los límites más allá de los cuales Ivory/Hesketh-Harvey no deberían haber ido a fin de no diluir el temperamento helénico de "Maurice" de E. M. Forster.