Instruments for measuring ocean waves often propagate in different directions with varying velocities, and the relationship between current velocity and viewer velocity is an important factor to consider when interpreting data from these instruments. Although these measurements are often assumed to be Galilean invariant, David Kouskoulas and Yaron Toledo revisited this problem.

According to the researchers, Galilean invariance only exists for surface water waves in a restricted sense. This has large consequences on data interpretation. Counterintuitively and contrary to common assumption, an observer moving with the current is not equivalent to a fixed observer of still water – there is a crucial distinction between current and viewer motion, and the two cannot be conflated.

“There are unexpected discrepancies when comparing different descriptions of surface water waves on current between different viewers,” Kouskoulas said.

If one uses an incorrect dispersion relation, the wave information reconstructed from the data will be wrong.

“The implications are important to various measurement instrumentation. These include not only wave buoys, but also acoustic Doppler current profilers, radars and other wave measurement technologies,” Toledo said. “These measurement instrumentations often move with different velocities. An intuitive relationship between these different measurements is lost with the loss of Galilean invariance,” Kouskoulas added.

Luckily, the authors noted that the data can be corrected at both the collection and interpretation level, allowing one to construct a complete and consistent picture of the waves. The improved dispersion relation is a step towards seeing the full picture of waves on current for all current and viewer velocities.

Source: “Linear surface gravity waves on current for a general inertial viewer,” by David M. Kouskoulas and Yaron Toledo, Physics of Fluids (2020). The article can be accessed at