Showing papers by "Chiang C. Mei published in 1989"

Slow spreading of a sheet of Bingham fluid on an inclined plane

Abstract: To study the dynamics of fluid mud with a high concentration of cohesive clay particles, we present a theory for a thin sheet of Bingham-plastic fluid flowing slowly on an inclined plane. The physics is discussed on the approximate basis of the lubrication theory. Because of the yield stress, the free surface need not be horizontal when the Bingham fluid is in static equilibrium, nor parallel to the plane bed when in steady flow. We then show that there is a variety of gravity currents that can advance at a constant speed and with the same profile. Experimental confirmation of one type is presented. By solving a nonlinear partial differential equation, transient flows due either to a steady upstream discharge or to the sudden release of a finite fluid mass on another fluid layer are studied. In the first case there is a mud front which ultimately propagates as a constant speed as a steady gravity current. In the second case, when the ambient layer is sufficiently shallow that there is no initial motion, the flow induced by the new fluid can terminate after the disturbance has travelled a finite distance. The extent of the final spread is examined. Disturbances due to an external pressure travelling parallel to the free surface are also examined. It is found in particular that a travelling localized pulse of pressure gradient not only generates a localized mud disturbance which travels along with the forcing pressure, but further leaves behind a permanent footprint.

Mechanics of Heterogeneous Porous Media With Several Spatial Scales

Abstract: By extending the theory of homogenization, we consider a heterogeneous porous medium whose material structure is characterized by multiple periodicity over several disparate length scales. Because for geological and engineering applications the driving force (e. g. the pressure gradient) and the global motion of primary interest is usually at a scale much larger than the largest of structural periodicity, we derive the phenomenological equations of motion by using the perturbation technique of multiple scales. All the effective coefficients are defined by boundary-value problems on unit cells in smaller scales and no constitutive assumptions are added aside from the basic equations governing the mechanics of the pore fluid and the solid matrix. In Part I the porous matrix is assumed to be rigid; the case of three scales is treated first. Symmetry and positiveness of the effective Darcy permeability tensor are proven. Extensions to four and more scales are then discussed. In Part II we allow the solid matrix to be deformable and deduce the equations of consolidation of a two-phase medium. The coupling of fluid flow and the quasi-static elastic deformation of the matrix is considered when there are three disparate length scales. Effective coefficients of various kinds are deduced in terms of cell problems on the scale of the pores. Several general symmetry relations as well as specific properties of a medium composed of layers of porous matrix are discussed.

Long-period oscillations in a harbour induced by incident short waves

Abstract: Progressive short waves with a narrow frequency band are known to be accompanied by long set-down waves travelling with the groups. In finite depth, scattering of short waves by a large structure or a varying coastline can radiate free long waves which propagate faster than the incident set-down. In a partially enclosed harbour attacked by short waves through the entrance, such free long waves can further resonate the natural modes of the harbour basin. In this paper an asymptotic theory is presented for a harbour whose horizontal dimensions are much greater than the entrance width, which is in turn much wider than the short wavelength.

Effects of Wave-Induced Friction on a Muddy Seabed Modelled as a Bingham-Plastic Fluid

Abstract: Fluid mud found at the bottom of some estuaries and coastlines contains a high concentration of clay particles. The rheological properties of this cohesive material is very complex and there have been vastly different models for predicting the mutual effects of mud and waves. In this paper we focus on the Bingham-plastic behavior known to exist in estuary and river mud with high concentration. By including interfacial friction, motion in a thin mud layer Induced by a solitary wave propagating in a much thicker layer of overlaying water is analyzed. Effects of the mud motion on wave damping is then calculated for both horizontal and sloping sea beds.