= Pressure projection in a displaced stratified blob
{title2=$\omega^2=N^2k_h^2/(k_h^2+m^2)$}
Incompressibility makes pressure adjust throughout the surrounding fluid. Projecting the linear <Boussinesq equations> perpendicular to a Fourier wavevector gives $w_t=[k_h^2/(k_h^2+m^2)]b$ and $b_t=-N^2w$. A localized spherical disturbance contains many wavevector directions and therefore many <internal gravity wave> frequencies, rather than one oscillator at $N$. Its shape evolves and energy radiates into the surroundings; a rigid-sphere <added mass> analogy illustrates extra inertia but does not give an exact coherent frequency for a free material blob.
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