About Us  | Abstract  | Background | Simple Cases and Results | Complex Case: Sheboygan Harbor | Conclusion | References
Background

 To fully understand what the STWAVE program was calculating, we first examined some fairly simple examples taken from lecture and our homework.  We solved these first by hand, and then created a mesh for each case in SMS and analyzed them using STWAVE.  

Important Concepts Used

The main concepts used to solve the simple examples by hand are refraction, reflection, and diffraction.  Wave refraction is a shallow water phenomena that occurs when the topography of the bottom varies (as waves approach shore).  The wave crest will bend to conform to the present topography.  Wave reflection is a process in which incident waves rebound or reflect off of a structure or sloping bed.  Finally, wave diffraction is the transmission of energy laterally across a wave crest when a train of waves approach a barrier.  An underlying theory for all three of these concepts is that of dispersion.  The dispersion relationship relates a wave's frequency, number, and depth where:
ω2 = g*k* tanh (k*d)
and
ω = (2*pi)/T      k = (2*pi)/L     

The first of the simple scenarios investigated consisted of a semi-infinite breakwater in an area of uniform depth.  In this approach, only diffraction has an effect on the passing waves.  The second approach consisted of a finite-length breakwater with varying topography.  In this scenario, all three concepts came into play.  Please refer to the Simple Cases and Results portion of this web page for images and further discussion.

STWAVE Basics

This model inherently contains six assumptions: 
  1. Mild bottom slope and negligible wave reflection
  2. Spatially homogeneous offshore wave conditions
  3. Steady-state waves, currents, and winds
  4. Linear refraction and shoaling
  5. Depth-uniform current
  6. Bottom friction is neglected
  7. Linear radiation stress
STWAVE also uses some governing equations such as the dispersion relation, those for wave celerities, those for refraction and shoaling, and those for diffraction.  It incorporates an equation for surf-zone wave breaking, however, this leads to the first criticism of the program.  It does not consider wave overtopping. Overtopping occurs when the wave height is greater than the breakwater height. This is something that did not come into play in our analysis, so the results in this regard should be accurate.

One other flaw inherent in this program is the numerical method it uses to calculate diffraction.  The model uses the following formula to smooth energy in a given frequency and direction:
E j (ω a ,α ) = 0.55E j (ω a ,α ) + 0.225[E j+1 (ω a ,α ) + E j−1(ω a ,α )]

The problem with this formula is that it is dependent on the spacing of the grid STWAVE uses when the SMS mesh is converted.  Therefore, the larger the grid spacing, the less accurate diffraction is estimated.