Date of Award

Fall 1981

Document Type


Degree Name

Doctor of Philosophy (PhD)


Ocean/Earth/Atmos Sciences



Committee Director

Chester E. Grosch

Committee Member

William D. Lakin

Committee Member

John C. Ludwick

Committee Member

Carvel Blair


Two different kinds of wave refraction models are formulated in the present study using Stokes' third order wave theory. One type of model is utilized in a parametric study employing several different topographies. Wave trajectories obtained from this model, when obtained by using first and third order wave theory with and without the consideration of energy dissipation, show considerable differences. These differences are examined in more detail for a bottom of constant slope: (1) An approximate 10% difference occurs between the refraction coefficients obtained using the first and the third order wave theory. (2) Considerably different ray trajectories are detected for a high wave steepness, and for a large incident angle due to intensive energy dissipation. (3) The refraction coefficient is found to decrease as the sea floor gets steeper. (4) The wave propagation directions, occurring near the wave breaking point, are found to be sensitive to both the wave steepness and incident angle. (5) Changes in wave breaking depth due to wave refraction and energy dissipation show that the waves of large incident angle and of higher frequencies break in shallower water.

The second type of model uses power refraction theory; this provides a new approach for spectral transformation in shallow water. For this model, the deep water spectrum is supplied as an initial condition. This spectrum is then dissasembled to component waves of individual wave height. The power transmitting line at a given water depth is determined by taking a vector sum of the powers of all the component waves, which have been exposed to refraction and energy dissipation. The spectra along this line of power flow are back calculated using these wave components. The spectra obtained from the above method are then compared to spectra from Hasselmann and Collins' model and remote sensing data. The model gives a reasonable result for relatively deeper water, but it does not reproduce the real conditions encountered by the irregular ocean floor region in which the water depth is very shallow. This disagreement seems to be caused mainly by the dissipation rate functions used in this model. Development of a new dissipation rate function is necessary for a better application of this model to shallow water region.