Mechanics of Coastal Sediment Transport

Jørgen Fredsøe, Rolf Deigaard

• Publisher: WSPC
• Year: 1992
• ISBN:
  9789814365680
• Topic: Ciencias físicas
• Subtopic: Oceanografía

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 η_max/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. 1.8 H is the wave height (from trough to crest), k the wave number, and ω the cyclic frequency, k and ω 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

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Example 1.1: Group velocity

Considering the superposition of two linear waves with same wave height but with slightly different wave numbers ...