EFFECTS OF CURRENTS ON WAVES 



by 



Barry E. Hershenroder 



I. INTRODUCTION 



A horizontal current can modify surface gravity waves in several ways. 

 One modification is to the wavelength. A current can locally stretch or 

 shrink features in a wave train. This wave-train distortion produces a "Dop- 

 pler shift" in the wave period. As a result, a stationary observer measures a 

 different wave period than an observer moving with the local current velocity. 

 To a good approximation, the period of a monochromatic wave is fixed in the 

 stationary coordinate system. To an observer moving with the local current 

 velocity, the measured period of this wave changes in time and at each point 

 in response to the changing current. 



The wave orthogonal, crest, and ray directions are also modified. An 

 orthogonal is a line perpendicular to the local wave crest direction. A ray 

 is a line parallel to the local group velocity vector, i.e., tangent to the 

 local direction of wave energy flow. In the absence of a current, rays are 

 parallel to orthogonals. When a current is present, orthogonals (by defini- 

 tion) are still perpendicular to the local crest orientation but rays are not 

 parallel to the orthogonals unless the wave is propagating in the same direc- 

 tion as the current. 



Another way a current modifies surface waves is to change the wave energy 

 by causing an exchange of energy between wave and current. Energy per unit 

 length of wave crest is no longer approximately conserved between rays, but 

 rather a quantity called "wave action" is conserved. This new quantity, a 

 generalization of wave energy, is given by the energy per unit length of wave 

 crest divided by the "intrinsic angular frequency" of the wave, the latter 

 being the Doppler-shif ted angular frequency seen by an observer moving with 

 the local current velocity. Since wave action rather than energy is conserved 

 between rays, enough wave energy is gained from the current or lost to the 

 current to keep the wave action the same as the wave propagates. 



A modification also occurs in the pressure field accompanying the wave. 

 This change can be an appreciable source of error in measuring wave character- 

 istics if an existing current is not accounted for. In particular, a signifi- 

 cant error can sometimes arise if bottom pressure measurements are used to 

 determine surface wave heights and lengths. 



Prediction of current-modified wave energy, heights, directions, and 

 pressures usually involves the use of complex numerical models and computer 

 programs. Such models and programs are under development and will be avail- 

 able over the next few years. However, relatively easy but useful calcula- 

 tions can be done without a computer. This report presents some of these 

 simpler calculations, such as methods to determine (a) the wavelength modifi- 

 cation due to a current, (b) whether a current can stop a wave from reaching 

 a particular location, (c) a correction for the presence of a current when 

 bottom pressure measurements are used to determine wave heights, and (d) the 

 range of periods (if any) for which currents can be neglected when these 

 pressure measurements are used to determine wave heights. 



