Capillary jet instability under the influence of gravity

The focus of this paper is on the effect of gravity stretching on disturbed capillary jet instability. Break-up and droplet formation under low flows are simulated using finite difference solution of a one-dimensional approximation of disturbed capillary jet instability chosen from the work by Eggers and Dupont (J. Fluid Mech. 155 (1994) 289). Experiments were conducted using water and aqueous glycerol solutions to compare with simulations. We use a gravity parameter, G, which quantifies gravity stretching by relating flow velocity, orifice size and acceleration and is the reciprocal of the Fronde number. The optimum disturbance frequency Omega(opt) was found to be inversely proportional to G. However, this relationship appears to be complex for the range of G's investigated. At low G, the relationship between Omega(opt) and G appears to be linear but takes on a weakly decaying like trend as G increases. As flows are lowered, the satellite-free regime decreases, although experimental observation found that merging of main and satellite drops sometimes offset this effect to result in monodispersed droplet trains post break-up. Viscosity did not significantly affect the relationship between the disturbance frequency and G, although satellite drops could be seen more clearly close to the upper limit for instability at high G's. It is possible to define regimes of satellite formation under low flows by considering local wavenumbers at the point of instability. (C) 2004 Elsevier Ltd. All rights reserved.

Efficient accommodation of local minima in watershed model calibration

The Gauss-Marquardt-Levenberg (GML) method of computer-based parameter estimation, in common with other gradient-based approaches, suffers from the drawback that it may become trapped in local objective function minima, and thus report optimized parameter values that are not, in fact, optimized at all. This can seriously degrade its utility in the calibration of watershed models where local optima abound. Nevertheless, the method also has advantages, chief among these being its model-run efficiency, and its ability to report useful information on parameter sensitivities and covariances as a by-product of its use. It is also easily adapted to maintain this efficiency in the face of potential numerical problems (that adversely affect all parameter estimation methodologies) caused by parameter insensitivity and/or parameter correlation. The present paper presents two algorithmic enhancements to the GML method that retain its strengths, but which overcome its weaknesses in the face of local optima. Using the first of these methods an intelligent search for better parameter sets is conducted in parameter subspaces of decreasing dimensionality when progress of the parameter estimation process is slowed either by numerical instability incurred through problem ill-posedness, or when a local objective function minimum is encountered. The second methodology minimizes the chance of successive GML parameter estimation runs finding the same objective function minimum by starting successive runs at points that are maximally removed from previous parameter trajectories. As well as enhancing the ability of a GML-based method to find the global objective function minimum, the latter technique can also be used to find the locations of many non-global optima (should they exist) in parameter space. This can provide a useful means of inquiring into the well-posedness of a parameter estimation problem, and for detecting the presence of bimodal parameter and predictive probability distributions. The new methodologies are demonstrated by calibrating a Hydrological Simulation Program-FORTRAN (HSPF) model against a time series of daily flows. Comparison with the SCE-UA method in this calibration context demonstrates a high level of comparative model run efficiency for the new method. (c) 2006 Elsevier B.V. All rights reserved.

A unified friction description and its application to the simulation of frictional instability using the finite element method

This article first summarizes some available experimental results on the frictional behaviour of contact interfaces, and briefly recalls typical frictional experiments and relationships, which are applicable for rock mechanics, and then a unified description is obtained to describe the entire frictional behaviour. It is formulated based on the experimental results and applied with a stick and slip decomposition algorithm to describe the stick-slip instability phenomena, which can describe the effects observed in rock experiments without using the so-called state variable, thus avoiding related numerical difficulties. This has been implemented to our finite element code, which uses the node-to-point contact element strategy proposed by the authors to handle the frictional contact between multiple finite-deformation bodies with stick and finite frictional slip, and applied here to simulate the frictional behaviour of rocks to show its usefulness and efficiency.