Theoretical Monochromatic Wave Induced Currents In Intermediate Water With Viscosity And Nonzero Mass Transport

Author : Chiang C. Mei
Publisher :
ISBN 13 :
Total Pages : 310 pages
Book Rating : 4.:/5 (318 download)

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Download or read book Mass Transport in Water Waves written by Chiang C. Mei and published by . This book was released on 1972 with total page 310 pages. Available in PDF, EPUB and Kindle. Book excerpt: When a fluid is in periodic wave motion, a fluid particle is carried by a velocity field varying from place to place. At different instants the location of the particle differs and so does the velocity field in its immediate neighborhood. As a result the time-averaged velocity of a particle may be different from the local velocity field. In particular, a fluid particle may have a net mean drift even if the local velocity field has zero mean; this is indeed the case in irrotational gravity waves. In a viscous fluid, the wave-induced Reynolds stress imparts a steady momentum to the fluid; a steady shear is set up to balance it and hence a further mean velocity field results. The sum of these two steady currents provides the total drift by which a fluid particle migrates, and is termed the mass transport velocity. It is of importance to the study of sediment motion in coastal waters. The present report describes a coordinated inquiry into both theoretical and experimental aspects of mass transport by waves. In accordance with the division of effort, it is separated into two parts. However, nearly all ideas expressed and actions taken in both parts have been influenced by extensive mutual discussions. Part I (Theory) begins with a review of the basic assumptions underlying existing theories. General formulas of mass transport velocity components throughout the Stokes boundary layer near a solid body are then derived; details of two examples are calculated. The three-dimensional mass transport distribution throughout the cross section of a wave tank is worked out for progressive waves of very small amplitudes. The effects of finite width is studied with the assumption that vorticity is diffused by molecular viscosity throughout the entire cross section. For a wave obliquely incident and reflected from a vertical sea wall, the structure in the second boundary layer between the Stokes layer and the inviscid core is investigated. This is appropriate for amplitudes much greater than the Stokes layer thickness. Part II (Experiments), were intended in part to check and to evaluate the theoretical deductions in Part I. In particular, extensive measurements were made for the longitudinal mass transport velocity in a progressive wave in a long tank with a smooth bottom. For standing waves and partially standing waves, possible features of erosion and deposition were observed by spreading (1) a small amount of sand on a smooth bottom and (2) a thick layer of sand on the bottom. The relevance of mass transport very near the bottom to the bed load transport is discussed in the light of the real beach environment.