= Additive freedom of a velocity potential
{title2=$\widetilde\phi(\mathbf x,t)=\phi(\mathbf x,t)+C(t)$}
Adding a spatially constant function of time to a <velocity potential> leaves its <velocity> $\mathbf u=\nabla\phi$ 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.
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