WATER WAVES ON A BILINEAR SHEAR CURRENT

A WATER WAVE THEORY IS PRESENTED TO DESCRIBE WAVES PROPAGATING ON A BILINEAR SHEAR CURRENT FLOWING IN THE DIRECTION OF THE WAVES.THE THEORY IS DERIVED ASSUMING AN IDEAL FLUID IN WHICH A CURRENT EXISTS, HAVING A VERTICAL VELOCITY PROFILE WHICH VARIES LINEARLY FROM A MEAN WATER LEVEL VELOCITY OF U/SUB S/, AN INTERFACIAL VELOCITY U/SUB I/ AT DEPTH, D, AND A BOTTOM VELOCITY U/SUB B/.THE THEORY IS DEVELOPED FIRST FOR SMALL AMPLITUDE WAVES AND THEN EXTENDED TO ANY ARBITRARY ORDER BY A NUMERICAL PERTURBATION TECHNIQUE FOR SYMMETRIC WAVES.FOR MEASURED WAVES, AN IRREGULAR FORM OF THE THEORY IS PRESENTED TO PROVIDE A REPRESENTATION OF THESE WAVES FOR ANALYSIS.(A)