 Additive freedom of a velocity potential

Adding a spatially constant function of time to a velocity potential leaves its velocity $\mathbf{u}=\nabla \varphi$ unchanged. When integrating the Euler equations in space, this freedom can absorb the time-only integration term in the potential form of momentum balance. A spatially constant zero-frequency potential represents no acoustic velocity and must not be counted as a propagating normal mode merely because a frequency determinant vanishes at zero. Pressure conventions and time dependence must still be fixed consistently when the potential is used to recover physical fields.