GRAVIT-INDUCED WATER WAVES HAVE AN IMPORTANT ON MANY OF MAN'S ACTIVITIES IN THE SHALLOW WATERS OF OUR COASTAL REGIONS, INCLUDING SHIP NAVIGATION, DESIGN OF OFFSHORE STRUCTURES, SEDIMENT TRANSPORT, ETC.

GRAVIT-INDUCED WATER WAVES HAVE AN IMPORTANT ON MANY OF MAN'S ACTIVITIES IN THE SHALLOW WATERS OF OUR COASTAL REGIONS, INCLUDING SHIP NAVIGATION, DESIGN OF OFFSHORE STRUCTURES, SEDIMENT TRANSPORT, ETC. WAVES IN SHALLOW WATERSEDIMENT TRANSPORT ARE OBSERVED TO BE NONLINEAR, AND THE SURFACE WAVE PATTERNS ARE FULLY TWO-DIMENSIONAL. WE PROPOSEHERE TO CONSTRUCT AN EXPLICIT, ANALYTICAL MODEL OF PERIODIC WAVES OF FINITE AMPLITUDE IN SHALLOW WATER, BY DEVELOPING A CERTAIN CLASS OF EXACT SOLUTIONS OF THE KADOMTSEV-PETVIASHVILI (OR "TWO-DIMENSIONAL KORTEWEG-DEVRIES") EQUATION. THE WAVES PRODUCED BY THIS MODEL WOULD HAVE TWO INDEPENDENT SPATIAL PERIODS IN TWO INDEPENDENT HORIZONTAL DIRECTIONS. BOTH LONG-CRESTED AND SHORT-CRESTED WAVES WOULD BE AVAILABLE. THESE BI-PERIODIC WAVES WOULD BE DIRECT GENERALIZATIONS OF THE WELL-KNOWN (SIMPLY PERIODIC) CNOIDAL WAVES. JUST AS CNOIDAL WAVES ARE OFTEN USED AS ONE-DIMENSIONAL MODELS OF "TYPICAL" NONLINEAR PERIODIC WAVES IN SHALLOW WATER, THESE BI-PERIODIC WAVES WOULD REPRESENT "TYPICAL" NONLINEAR PERIODIC WAVES IN SHALLOW WATER WITHOUT THE ASSUMPTION OF ONE-DIMENSIONALITY. THE COMPLETE MODEL WOULD BE ENCODED IN A SIMPLE SOFTWARE PACKAGE.