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Real world water waves often propagate on current. And, the measurement ofwaves and current is an important task for coastal and marine engineers. Modernmarine measurement technologies (i.e. unmanned autonomous vehicles, drones)often propagate with different velocities relative to the current and waves. Ithas been shown that, due to a loss of Galilean invariance, viewer velocity hasa non-trivial effect on the mathematical form of the wave and uniform currentproblem. It is demonstrated herein that similar complexities arise for shearingcurrents. The work provides a generalized formulation of the wave and shearingcurrent boundary value problem for an arbitrary inertial viewer. The movingviewer dispersion relation for the special case of a constant current shear isalso derived.

Waves on shearing current for an arbitrary inertial viewer