This book treats the subject of sediment transport in the marine environment, covering transport of noncohesive sediment by waves and currents in- and outside the surf zone. It can be read independently, but a background in hydraulics and basic wave mechanics is required.
The primary aim of the book is to describe the physical processes of sediment transport and how to represent them in mathematical models. The book can be divided in two main parts; in the first, the relevant hydrodynamic theory is described. This part contains a review of elementary theory for water waves, chapters on the turbulent wave boundary layer and the turbulent interaction between waves and currents, and finally, surf zone hydrodynamics and wave driven currents.
The second part covers sediment transport and morphological development.The part on sediment transport introduces the basic concepts (critical bed shear stress, bed load, suspended load and sheet layer, near-bed concentration, effect of sloping bed); it treats suspended sediment in waves and current and in the surf zone, and current and wave-generated bed forms. Finally, the modelling of cross-shore and long-shore sediment transport is described together with the development of coastal profiles and coastlines.
Contents:
Basic Concepts of Potential Wave Theory
Wave Boundary Layers
Bed Friction and Turbulence in Wave-Current Motion
Waves in the Surf Zone
Wave-Driven Currents
Current Velocity Distribution in the Surf Zone
Basic Concepts of Sediment Transport
Vertical Distribution of Suspended Sediment in Waves and Current Over a Plane Bed
Current-Generated Bed Waves
Wave-Generated Bed Forms
Cross-Shore Sediment Transport and Coastal Profile Development
Longshore Sediment Transport and Coastline Development
Readership: Ocean and electronics engineers, geologists, mathematical physicists and graduate students.
Chapter 1. Basic concepts of potential wave theory
This introductory chapter is mainly a summary of the basic concepts for wave mechanics which are necessary for the further developments presented later in this book. For this reason, nearly all derivations axe omitted, and readers are instead referred to standard texts in wave hydrodynamics, (e.g. Dean and Dalrymple, 1990; Svendsen and Jonsson, 1976; Mei, 1990; Phillips, 1966; Wiegel, 1964).
1.1 Waves propagating over a horizontal bottom
Wave kinematics are usually described by potential theory requiring the fluid to be inviscid and irrotational. In this case, a potential
can be introduced, which is related to the velocity field by
where x and y are horizontal coordinates, and z is the vertical coordinate (Fig. 1.1). Origin of the coordinate system is located on the seabed, u, v and w are the velocity components in the x-, y- and z-directions. By inserting Eq. 1.1 into the continuity equation
the Laplace equation is obtained
Figure 1.1 Definition of the coordinate-system.
The boundary conditions are
1. At the seabed, the flow velocity perpendicular to the bed is zero. For a plane horizontal bed this gives
2. A fluid particle located at the free surface must remain at the free surface giving
in which D is the mean water depth, and η is the surface elevation, see Fig. 1.2.
3. The pressure at the water surface must be equal to the atmospheric pressure and can be set to zero, where by the Bernoulli equation gives
in which C is a function of t only.
Figure 1.2 Definition sketch of D and η.
If the wave is two-dimensional and periodic with a wave period
and a direction of propagation in the x-direction, Eqs. 1.3 - 1.6 can be solved as a boundary value problem.
As the maximum surface elevation is assumed to be small compared to a typical dimension, for instance the wave length L, the problem can be linearized and solved analytically. As all higher order terms in ηmax/L are neglected, the solution to the boundary value problem becomes
This solution is the linear wave solution, also called the Airy wave or a Stokes first order wave. In Eq. 1.8H is the wave height (from trough to crest), k the wave number, and Ï the cyclic frequency, k and Ï being defined as
If second order terms in H/L are also included in the solution of Eqs. 1.3 - 1.6, then the Stokes second order solution is obtained, which is given by
and
where
(1) is given by Eq. 1.7 and
where the constant C1, which must be of the order (H/L)2, represents a steady, uniform flow. If the mean value over a wave period of the mass flux through a vertical section is zero, then C1 must have the value
The last term in Eq. 1.15 does not affect the velocity profile, but appears from the Bernoulli equation 1.6.
The horizontal flow velocity in Stokes second order theory is found from Eqs. 1.1 and 1.14 to be
where u(1) is given by Eq. 1.10 and
Similarly, the vertical velocity can be found to be
in which w(1) is given by Eq. 1.11 and
Example 1.1: Group velocity
Considering the superposition of two linear waves with same wave height but with slightly different wave numbers ...
