Wave Force on an Ocean Current

Abstract

Linear momentum of surface gravity waves changes with time during refraction by a horizontally variable current, as is predicted by ray theory; the momentum change per unit time requires a force by the current on the waves. According to Newton?s third law, the waves apply an equal but opposite force back on the current. The wave force of linear waves on the current is calculated for a steady horizontal shear current and it is found to be directly proportional to the wave momentum times the shear in the current. For a current like the Gulf Stream it is theoretically possible for the wave force on the current to be as large as the Coriolis force on the current to the depth of wave influence; the effect on equatorial surface currents is likely to be even more significant. Considering the reasonable conjecture that the orbital angular momentum of the waves cannot be exchanged with the current, the growth or decay of the wave amplitude in the shear current is computed as well. An exponential growth or decay of the amplitude is obtained with the e-folding scale being proportional to the current shear. A comparison between the calculated wave force and the Coriolis force for reported data describing the reflection of waves by the Gulf Stream is presented. The potential effects of the wave force on the surface extent of such currents and their observations by remote sensing, including possible bias in estimation of their transport capacity, are discussed. Instances of potential positive and negative feedback acting during the interaction between the waves and the current are outlined.