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: We investigate the evolution of the ridge produced by the non-symmetrical convergent motion of two substrates over which an initially uniform layer of a Newtonian liquid rests. The lack of symmetry of the flow arises because the substrates move with different velocities. We focus on the self-similar regimes that occur in this process. For short times, within the linear regime, the height and the width increase as t1/2 and the profile is symmetric, independently of degree of asymmetry of the motion of the substrates. In the self-similar regime for large time, the height and the width of the ridge follow the same power laws as in the symmetric case, but the profiles are asymmetric. © 2009 IOP Publishing Ltd.

Descripción: We investigate the evolution of the ridge produced by the convergent motion of two substrates, on which a layer of a non-Newtonian power-law liquid rests. We focus on the self-similar regimes that occur in this process. For short times, within the linear regime, the height and the width increase as t 1/2, independently of the rheology of the liquid. In the self- similar regime for large time, the height and the width of the ridge follow power laws whose exponents depend on the rheological index. © 2009 IOP Publishing Ltd.

Descripción: With the purpose of modeling the process of mountain building, we investigate the evolution of the ridge produced by the convergent motion of a system consisting of two layers of liquids that differ in density and viscosity to simulate the crust and the upper mantle that form a lithospheric plate. We assume that the motion is driven by basal traction. Assuming isostasy, we derive a nonlinear differential equation for the evolution of the thickness of the crust. We solve this equation numerically to obtain the profile of the range. We find an approximate self-similar solution that describes reasonably well the process and predicts simple scaling laws for the height and width of the range as well as the shape of the transversal profile. We compare the theoretical results with the profiles of real mountain belts and find an excellent agreement. © 2010 American Institute of Physics.

Descripción: Context. A magnetic cloud (MC) is a magnetic flux rope in the solar wind (SW), which, at 1 AU, is observed ∼2-5 days after its expulsion from the Sun. The associated solar eruption is observed as a coronal mass ejection (CME).Aims. Both the in situ observations of plasma velocity distribution and the increase in their size with solar distance demonstrate that MCs are strongly expanding structures. The aim of this work is to find the main causes of this expansion and to derive a model to explain the plasma velocity profiles typically observed inside MCs.Methods. We model the flux rope evolution as a series of force-free field states with two extreme limits: (a) ideal magneto-hydrodynamics (MHD) and (b) minimization of the magnetic energy with conserved magnetic helicity. We consider cylindrical flux ropes to reduce the problem to the integration of ordinary differential equations. This allows us to explore a wide variety of magnetic fields at a broad range of distances to the Sun.Results. We demonstrate that the rapid decrease in the total SW pressure with solar distance is the main driver of the flux-rope radial expansion. Other effects, such as the internal over-pressure, the radial distribution, and the amount of twist within the flux rope have a much weaker influence on the expansion. We demonstrate that any force-free flux rope will have a self-similar expansion if its total boundary pressure evolves as the inverse of its length to the fourth power. With the total pressure gradient observed in the SW, the radial expansion of flux ropes is close to self-similar with a nearly linear radial velocity profile across the flux rope, as observed. Moreover, we show that the expansion rate is proportional to the radius and to the global velocity away from the Sun.Conclusions. The simple and universal law found for the radial expansion of flux ropes in the SW predicts the typical size, magnetic structure, and radial velocity of MCs at various solar distances. © 2009 ESO.

Descripción: We study in this paper the time evolution of the spreading process of a small drop in contact with a flat dry surface, using asymptotic techniques. We reduced the problem by solving a quasisteady self-similar macroscopic problem and matched with the precursor region solution, where the van der Waals forces are important. A final nonlinear third-order ordinary differential equation has been solved numerically using shooting methods based on the fourth-order Runge-Kutta techniques. We obtained how the capillary number changes when the drop size decreases with time. The evolution process then diverges slightly from that obtained using the spherical cap approximation. The influence of gravity is also considered for both hanging and sitting drops. © 1998 The American Physical Society.

Descripción: Invariance properties of physical systems govern their behaviour: energy conservation in turbulence drives a wide distribution of energy among modes, as observed in geophysical or astrophysical flows. In ideal hydrodynamics, the role of the invariance of helicity (correlation between velocity and its curl, measuring departures from mirror symmetry) remains unclear since it does not alter the energy spectrum. However, in the presence of rotation, significant differences emerge between helical and non-helical turbulent flows. We first briefly outline some of the issues such as the partition of energy and helicity among modes. Using massive numerical simulations, we then show that smallscale structures and their intermittency properties differ according to whether helicity is present or not, in particular with respect to the emergence of Beltrami core vortices that are laminar helical vertical updraft vortices. These results point to the discovery of a small parameter besides the Rossby number, a fact that would relate the problem of rotating helical turbulence to that of critical phenomena, through the renormalization group and weak-turbulence theory. This parameter can be associated with the adimensionalized ratio of the energy to helicity flux to small scales, the three-dimensional energy cascade being weak and self-similar. copy; 2010 The Royal Society.

Descripción: Context. A large amount of magnetized plasma is frequently ejected from the Sun as coronal mass ejections (CMEs). Some of these ejections are detected in the solar wind as magnetic clouds (MCs) that have flux rope signatures. Aims. Magnetic clouds are structures that typically expand in the inner heliosphere. We derive the expansion properties of MCs in the outer heliosphere from one to five astronomical units to compare them with those in the inner heliosphere. Methods. We analyze MCs observed by the Ulysses spacecraft using in situ magnetic field and plasma measurements. The MC boundaries are defined in the MC frame after defining the MC axis with a minimum variance method applied only to the flux rope structure. As in the inner heliosphere, a large fraction of the velocity profile within MCs is close to a linear function of time. This is indicative of a self-similar expansion and a MC size that locally follows a power-law of the solar distance with an exponent called ζ. We derive the value of ζ from the in situ velocity data. Results. We analyze separately the non-perturbed MCs (cases showing a linear velocity profile almost for the full event), and perturbed MCs (cases showing a strongly distorted velocity profile). We find that non-perturbed MCs expand with a similar non-dimensional expansion rate (ζ = 1.05 ± 0.34), i.e. slightly faster than at the solar distance and in the inner heliosphere (ζ = 0.91 ± 0.23). The subset of perturbed MCs expands, as in the inner heliosphere, at a significantly lower rate and with a larger dispersion (ζ = 0.28 ± 0.52) as expected from the temporal evolution found in numerical simulations. This local measure of the expansion also agrees with the distribution with distance of MC size, mean magnetic field, and plasma parameters. The MCs interacting with a strong field region, e.g. another MC, have the most variable expansion rate (ranging from compression to over-expansion). © 2012 ESO.

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.