Showing papers by "Chiang C. Mei published in 1990"

Approximate equations for the slow spreading of a thin sheet of Bingham plastic fluid

Abstract: A model that can approximately describe a non‐Newtonian fluid such as paint and fluid mud is a Bingham plastic with a yield stress. To facilitate the study of slow but transient spreading of a thin sheet of fluid mud, we need the approximate equations governing the nonlinear motion. Beginning with a modified Bingham model with two viscosities, the approximate equations are derived by a systematic perturbation analysis. The controlling parameters are found to be the Reynolds number R, the shallowness ratio h/L=δ1/2, and the ratio of viscosities β=ν/ν1 [as defined in (45)]. Results valid for R,β,δ≪1 but δ/β2≤O(1) are obtained. In the special case when δ/β2≪1, the limits can also be obtained by heuristic arguments similar to those in the lubrication theory. Two examples are discussed.

Centrifugal instability of an oscillatory flow over periodic ripples

Abstract: An oscillating flow over a sandy beach can initiate and enhance the formation of bed ripples, with crests perpendicular to the direction of the ambient oscillation. Under certain circumstances, bridges may develop to span adjacent ripple crests, resulting in a brick pattern. It has been suggested that the onset of this transition is due to a three-dimensional centrifugal instability of an otherwise two-dimensional flow over periodic long-crested ripples. Here we analyse theoretically such an instability by assuming that the ripples are rigid and smooth. Two complementary cases are studied. We first consider a weak ambient oscillation over ripples of finite slope in Case (i). The three-dimensional disturbance is found to be localized in a small region either along the crests or along the troughs. In Case (ii) we analyse finite oscillations over ripples of mild slope. The region influenced by the instability is now comparable with a ripple wavelength and the unstable disturbance along adjacent ripples may interact with each other. Four types of harmonic and subharmonic instabilities are found. The associated steady streaming close to the ripple surface shows various tendencies of possible sand accumulations, some of which appear to be qualitatively relevant to the initiation of brick-patterned ripples.

Oscillating flows over periodic ripples

Abstract: Oscillating flows over periodic ripples are of practical as well as scientific interest because of their relevance to beach processes. When either the ripples are sufficiently steep or the amplitude of ambient oscillations large, streamlines of a viscous flow are no longer parallel to the ripple surface. Circulation cells are formed which can help redistribute suspended sediments. Here we study theoretically these cells for a low-viscosity fluid such as pure water over rigid ripples. In particular we have calculated cells whose dimensions are as large as the ripple wavelength and therefore represent viscous effects far above the usual Stokes boundary layer. An idea of Stuart which was originated for stationary mean circulations around a cylinder is extended here. For large ambient amplitude, large oscillating vortices drifting with the ambient flow are found by seeking the stationary cells in a moving coordinate system.

Slow Modulation of Weakly Nonlinear Waves

Abstract: In oceans, surface waves are not only irregular and of finite amplitude, but also nonstationary, in that their average features change with space and time. The nonstationarity is inherently due to nonlinear interactions among waves of different frequencies. Here we discuss two examples. The first is the evolution of unidirectional waves in deep water. Group splitting is shown to develop in both two and three dimensional cases. Individual crests in the transient groups may exceed the threshold of breaking. The second example is the excitation of trapped long waves on a submarine ridge by incident short wave groups. Such long waves may be important to moored ships of semisubmercibles.