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In this paper, we propose a new hydrodynamic model for gas–liquid two-phase flows in undulant pipelines based on the gas tracking method. The motion of three main forms of gas phase, including elongated bubbles, small bubbles, and gas pockets, is modeled by respective momentum equations. The mass transfer behaviors among the three gas forms, including interior mass transfer of single gas form, are considered. Therefore, the flow patterns along the pipeline can be predicted based on the gas tracking method. Afterward, the integrated pressure gradient of the gas–liquid two-phase flow in undulant pipelines can be obtained with the updated flow patterns. The model validation using the field data of a real pipeline in China shows that the accuracy of this model is within acceptable range. According to the simulation results, how the pipe terrain affects the gas transport and flow patterns is revealed, and sensitive analysis is carried out. These findings are of great practical value to obtain a deeper understanding of gas–liquid two-phase flows in undulant pipelines. [ABSTRACT FROM AUTHOR]

In order to describe the development of plateaus such as the Tibet and the Altiplano we extend the two-layer model used in a previous paper [C. A. Perazzo and J. Gratton, Phys. Fluids 22, 056603 (2010)] to reproduce the evolution of mountain ranges. As before, we consider the convergent motion of a system of two liquid layers to simulate the crust and the upper mantle that form a lithospheric plate, but now we assume that the viscosity of the crust falls off abruptly at a specified depth. We derive a nonlinear differential equation for the evolution of the thickness of the crust. The solution of this equation shows that the process consists of a first stage in which a peaked range is formed and grows until its root reaches the depth where its viscosity drops. After that the range ceases to grow in height and a flat plateau appears at its top. In this second stage the plateau width increases linearly with time as its sides move outward as traveling waves. We derive simple approximate formulas for various properties of the plateau and its evolution. [ABSTRACT FROM AUTHOR]