= Small-body loading-noise threshold
{title2=$a/\ell\sim M^{1/3}$}
For a nonseparating small body in a smooth nearly inviscid eddy of speed $U$ and length $\ell$, the fluctuating resultant is an <added mass> or pressure-gradient force $F\sim\rho_0a^3U^2/\ell$. A uniform pressure integrates to zero over a closed surface. With time $\ell/U$, its <acoustic dipole> power divided by the eddy's <acoustic quadrupole> power is $(a/\ell)^6/M^2$, where $M=U/c_0$ is the <Mach number>. Equal powers therefore give the displayed threshold. An area-scaled separated drag force with the same eddy time instead gives $a/\ell\sim\sqrt M$; a body-scale time gives a different criterion. The threshold depends on the specified loading and time models.
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