INTRODUCTION

The statistical analysis of ocean waves discussed in previous chapters assumes that waves are a Gaussian random process; namely, waves are a steady-state, ergodic random process and displacement from the mean obeys the normal probability law. Verification that deep ocean waves are a Gaussian process was given in Section 1.1 through the central limit theorem. It has also been verified through observations at sea as well as in laboratory tests that waves can be considered a Gaussian random process even in very severe seas if the water depth is sufficiently deep.

The above statement, however, is no longer true for waves in finite water depth. Time histories of waves in shallow water show a definite excess of high crests and shallow troughs as demonstrated in the example shown in Figure 1.1(b), and thereby the histogram of wave displacement is not symmetric with respect to its mean value, as shown in Figure 1.2(b). Thus, waves in shallow water are considered to be a non-Gaussian random process. This implies that ocean waves transform from Gaussian to non-Gaussian as they propagate from deep to shallow water.

Figure 9.1 shows a portion of wave records measured simultaneously at various water depths during the ARSLOE Project carried out by the Coastal Engineering Research Center at Duck, North Carolina.