Descripción: With the aim of describing the mountain building process, we have previously applied the lubrication approximation to obtain the evolution equations of the problem of two stacked layers of viscous fluids with different densities and different viscosities. The lubrication approximation is a perturbation method where the small parameter is the aspect ratio (thickness/lenght) of the current. This approximation is widely used to study the slow flow of one layer of a viscous fluid, but it is not well known under which conditions it can be applied in more general settings. Here we analyze in detail the assumptions needed to apply the lubrication theory to study the flow of two stacked viscous fluid layers. We employ the same perturbation method and we found that, besides the usual conditions (low Reynolds number and gentle slope), we must require that the viscosity and density ratios are of the order of unity. These requirements determine the range of validity of the equations of our model of the mountain building.

Descripción: We numerically and theoretically investigate the evolution of the ridges and rifts produced by the convergent and divergent motions of two substrates over which an initially uniform layer of a Newtonian liquid rests. We put particular emphasis on the various asymptotic self-similar and quasi-self-similar regimes that occur in these processes. During the growth of a ridge, two self-similar stages occur; the first takes place in the initial linear phase, and the second is obtained for a large time. Initially, the width and the height of the ridge increase as t 1/2. For a very large time, the width grows as t 3/4, while the height increases as t 1/4. On the other hand, in the process of formation of a rift, there are three self-similar asymptotics. The initial linear phase is similar to that for ridges. The second stage corresponds to the separation of the current in two parts, leaving a dry region in between. Last, for a very large t, each of the two parts in which the current has separated approaches the self-similar viscous dam break solution. © 2008 American Institute of Physics.

Descripción: The spatial stability of similarity solutions for an incompressible fluid flowing along a channel with porous walls and driven by constant uniform suction along the walls is analyzed. This work extends the results of Durlofsky and Brady [Phys. Fluids 27, 1068 (1984)] to a wider class of similarity solutions, and examines the spatial stability of small amplitude perturbations of arbitrary shape, generated at the entrance of the channel. It is found that antisymmetric perturbations are the best candidates to destabilize the solutions. Temporally stable asymmetric solutions with flow reversal presented by Zaturska, Drazin, and Banks [Fluid Dyn. Res. 4, 151 (1988)] are found to be spatially unstable. The perturbed similarity solutions are also compared with fully bidimensional ones obtained with a finite difference code. The results confirm the importance of similarity solutions and the validity of the stability analysis in a region whose distance to the center of the channel is more than three times the channel half-width. © 2000 American Institute of Physics.

Descripción: The Ischigualasto-Villa Union basin developed as a consequence of processes taking place at the transition between Sierras Pampeanas and Precordillera, together with the Gondwana extension and ultimate break-up since the Upper Palaeozoic-Triassic (Lower Jurassic ?). In the Ischigualasto region the basin is characterized by accumulations of continental sediments and contemporaneous mafic magmatic rocks. This paper presents data on the basalts and trachytes, which are alkaline rocks of the basalt-trachybasalt-trachyte series. Petrology indicates high pressure and temperature involving the fractionation of olivine, magnetite (Ti-magnetite), ilmenite, cpx, Ca feldspar and apatite. Flows were extruded through fracture-related vents and/or monogenetic volcanoes constructed of piles of thick and viscous lavas. These rocks seem to correspond and are interpreted as being the product of fast magmatic ascent and subsequent intrusion or flow. Temporary storage in smaller chambers at intermediate depth could have been the mechanism for the differentiation process.

Descripción: We investigate an unsteady plane viscous gravity current of silicone oil on a horizontal glass substrate. Within the lubrication approximation with gravity as the dominant force, this current is described by the nonlinear diffusion equation [Formula Presented]=([Formula Presented][Formula Presented][Formula Presented] (φ is proportional to the liquid thickness h and m=3>0), which is of interest in many other physical processes. The solutions of this equation display a fine example of the competition between diffusive smoothening and nonlinear steepening. This work concerns the so-called waiting-time solutions, whose distinctive character is the presence of an interface or front, separating regions with h≠/0 and h=0, that remains motionless for a finite time interval [Formula Presented] meanwhile a redistribution of h takes place behind the interface. We start the experiments from an initial wedge-shape configuration [h(x)≊[Formula Presented]([Formula Presented]-x)] with a small angle ([Formula Presented]⩽0.12 rad). In this situation, the tip of the wedge, situated at [Formula Presented] from the rear wall (15 cm⩽[Formula Presented]⩽75 cm), waits at least several seconds before moving. During this waiting stage, a region characterized by a strong variation of the free surface slope (corner layer) develops and propagates toward the front while it gradually narrows and [Formula Presented]h/∂[Formula Presented] peaks. The stage ends when the corner layer overtakes the front. At this point, the liquid begins to spread over the uncovered substrate. We measure the slope of the free surface in a range ≊10 cm around [Formula Presented], and, by integration, we determine the fluid thickness h(x) there. We find that the flow tends to a self-similar behavior when the corner layer position tends to [Formula Presented]; however, near the end of the waiting stage, it is perturbed by capillarity. Even if some significant effects are not included in the above equation, the main properties of its solutions are well displayed in the experiments © 1996 The American Physical Society.