Applicability of Wave Models in Shallow Coastal Waters

APPLICABILITY OF WAVE MODELS IN SHALLOW COASTAL WATERS

by

Stephan Mai1+ , Nino Ohle2+ and Claus Zimmermann3+

ABSTRACT

The wave propagation within coastal areas is strongly influenced by the coastal morphology withits islands, bars, shoals and channels. Predominant processes in this zone are shoaling, bottomfriction, breaking, refraction, wind generation and to some extent diffraction of waves. Thesimulation results with measurements in a wave tank and on site measurements at the NorthFrisian Coast of Germany. The numerical and experimental data measured in the wave flume arein very good agreement for all applied wave models proving the numerical formulation quality ofbottom friction, shoaling and breaking. A comparison of numerical simulations results withSWAN and field data shows also a quite good agreement but revealed in some cases largerdifferences which may be contributed to the interaction of tidal currents and waves.1. INTRODUCTION

Due to the complexity of wave propagation in coastal areas the estimation of wave parameters forengineering purposes is based on numerical simulations. In contrast to the ray tracing technique ofconventional wave models which often lead to chaotic wave ray patterns and therefore to adifficult interpretation the numerical formulation of basic wave equations on a regular gridbecomes more common (Ris et al., 1994). Examples for wave models with regular grids are thestandard models HISWA (Booij et al., 1985), SWAN (Ris, 1997) and MIKE 21 EMS (Madsenand Larsen, 1987). These wave models differ in the set of basic equations and the mathematicalformulation employed to describe e.g. bottom friction, wave breaking and wind generation.Experiments in the large wave tank of FORSCHUNGSZENTRUM KÜSTE, Hannover, Germany,on the wave propagation along a foreland with submerged dike are used to test the applicability ofthese wave models in shallow waters putting emphasis on the adjustment of the parameter ofbottom friction and wave breaking. Similar model tests are described for HISWA by Booij et al.(1985), by Mai et al. (1998) or by Kaiser and Niemeyer (1998) and for SWAN by Ris (1997).Based on field measurements of the public department ALR Husum, Germany, at the NorthFrisian wadden sea coast additional tests of SWAN are presented using the standard setting ofmodel parameters. Analogous comparisons are given by Ris (1997) or by Kaiser and Niemeyer(1998).

12

Stephan.Mai@fi.uni-hannover.de Nino.Ohle@fi.uni-hannover.de3

Claus.Zimmermann@fi.uni-hannover.de+

University of Hannover, Franzius-Institut, Nienburger Str. 4, 30167 Hannover, Germany

2. WAVE MODELS2.1 Basic Model Equations

The wave model HISWA and the advanced model SWAN are based on the following actionbalance equation:

S(x,y,σ,θ)

+cN+cN++cN=NcN

t(x,y,σ,θ) xx(x,y,σ,θ) yy(x,y,σ,θ) σσ(x,y,σ,θ) θθ(x,y,σ,θ)σ

(1)

where the geographical coordinates are x and y, the propagation direction is θ, the relative

vvvv

frequency is σ=ω k u, the wave number is k, the depth-averaged underlying current is u, theaction density spectrum is N(x,y,σ,θ)=E(x,y,σ,θ)/σ, the propagation velocities are c x, c y, c σ, c θ ofwave energy in geographical and spectral space and the energy source term is S (x,y,σ,θ) (Ris, 1997,Holthuijsen and Booij, 1987).

The processes of shoaling and refraction are implied in the left hand side of equation 1 by the

vv

definition of propagation velocities c=(cx,cy) as the sum of group velocity cg and underlyingcurrent:

v

2 k d σ kvvvv1

c=cg+u= 1++u2 sinh(2 k d) k2

(2)

in which d is the water depth.

The influence of currents on wave propagation is not taken into consideration within our model

v

tests, i.e. u=0.

The processes of dissipation of wave energy due to water-depth induced breaking Sds,br or wavebottom interactions Sds,b and the generation of wave energy by wind Sin are included in the energysource term:

S(x,y,σ,θ)=Sds,br+Sds,b+Sin+......

(3)

Diffraction is not described by the action balance equation and therefore not included in HISWAand SWAN. The time-dependence of the action balance equation is neglected in our model test ofHISWA and SWAN although SWAN contains a non-stationary mode.

The action balance equation is solved in SWAN with a full discrete two-dimensional wave-spectrum N(x,y,σ,θ) using an iterative four-sweep technique allowing wave-propagation in alldirections in the entire geographical domain. In contrast to this the wave spectrum in HISWA isdiscrete only in directions but parametric in frequency, i.e. the shape of the frequency spectrum isprescribed. This prescription of shape is especially problematic in case of double-peaked ing the parametric frequency spectrum the action balance equation (eq. 1) is separated intoevolution equations for the zero-order moment and the first-order moment of action-densityspectrum. The evolution equations in HISWA are solved using a forward stepping procedure inthe numerical scheme allowing wave propagation in forward direction only.

The wave model MIKE 21 EMS is based on the elliptic mild slope equation:

cg 2ζ

(c cg ζ) =0

c t2

(4)

where the phase velocity is c=ω k and the surface elevation is ζ (Madsen and Larsen, 1987).Equation 4 includes the processes of refraction, shoaling and diffraction.

In order to include energy dissipation due to bed friction, wave breaking and energy loss insideporous structures in MIKE 21 EMS, the equation 4 is rewritten by introducing complex harmonicpseudo-fluxes P, Q (DHI, 1996):

cg S cg P Q

+ i ω+fs S++=SSc t c x y

cg P cg 2 S+ (i ω+ω fp)+fs+ef+eb P+cg=0c t c x cg Q cg 2 S+ (i ω+ω fp)+fs+ef+eb Q+cg=0c t c y

where S is the wave amplitude, i is the imaginary unit, f s and f p are linear friction …… 此处隐藏：5648字，全部文档内容请下载后查看。喜欢就下载吧 ……