海岸动力学英文课件CoastalHydrodynamics22

1、Coastal Hydrodynamics 海 岸 动 力 学,Chapter 2 WAVE THEORY,Stating description of wave motion,Stating basic equations of wave motion,Stating the small amplitude wave theory,Stating the finite amplitude wave theory,Stating wave theory limits of applicability,1/21,Chapter 2,Water is treated as a uniform,As

2、sumptions,continuity equation,The fluid viscosity is normally,velocity potential,The surface tension and,gravity only,The bottom is impermeable.,zero velocity,ignored.,Coriolis force are ignored.,and incompressible fluid.,Waves travel in the x-z plane.,2/21,Chapter 2,G.D.E.,B.B.C.,on z= -h,L.B.C.,D.

3、F.S.B.C.,K.F.S.B.C.,on z=,on z=,Boundary Value Problem of Wave Motion,3/21,1. Linearization of basic equations,Chapter 2,2.3 Small Amplitude Wave Theory,2. Solution of the linearized equations,3. Dynamic thus any products of these variables are small enough to be ignored. This process is called line

4、arization. Linear in the sense that variables are only raised to the first power.,7/21,Chapter 2,A small amplitude wave is also called a linear wave. It is a wave which travels very slowly, the wave height is far smaller than the wave length and the water depth is much greater than its wave height.,

5、What is a small amplitude wave ?,8/21,Chapter 2,Suppose that the wave is a small amplitude wave, namely HL or Hh.,How to linearize DFSBC & KFSBC ?,Use the Taylor series expansion to relate the boundary conditions at the unknown elevation to the still water level.,Take the pressure on the free surfac

6、e to be zero.,9/21,Chapter 2,If a continuous function f(x,y) of two independent variables x and y is known at the position where x is equal to x0, then it can be approximated at another location on the x axis, by using the Taylor series.,What is the Taylor series ?,10/21,Chapter 2,The linear DFSBC c

7、an be written as follows.,What is the linear DFSBC ?,It relates the instantaneous displacement of the free surface to the time rate of change of the velocity potential.,11/21,Chapter 2,Retaining only the terms that are linear in our small parameters,u, v, and w, and recalling that is not a function

8、of z, the linear KFSBC can be written as follows.,What is the linear KFSBC ?,12/21,Chapter 2,G.D.E.,Summary,B.B.C.,L.B.C.,D.F.S.B.C.,K.F.S.B.C.,13/21,Chapter 2,Coordinates System,2. Solution,14/21,Chapter 2,How to obtain the solution ?,Velocity Potential,15/21,Chapter 2,Assuming that the wave slope

9、is small (H/L1), the solution of velocity potential is:,While the elevation of the water surface is,16/21,Chapter 2,Substituting the velocity potential and the surface elevation into the K.F.S.B.C yields the dispersion relationship.,Dispersion relationship,17/21,Chapter 2,This relationship shows tha

10、t the wave length continually decreases with decreasing depth for a constant wave period. That is to say, waves of constant period slow down as they enter shallow water.,Dispersion relationship,A field of propagating waves consisting of many frequencies would separate due to the different celerities

11、 of the various frequency components.,18/21,Chapter 2,Case study of “wave dispersion”,19/21,Chapter 2,Had we used the surface elevation instead of , how would the velocity potential be changed?,MINI-EXAMINATION (1),Homework,Chapter 2,A wave with the period of 5s travels in water of 5m, what is its c

12、elerity and what is its length? You are on a ship( 100m in length) on the deep ocean traveling north. The regular waves are propagating north also and you note two items of information:(1)when the ship bow is positioned at a crest, the stern is at a trough, and (2) a different crest is positioned at the bow every 2