  A series of numerical experiments is suggested for the three-dimensional
Navier-Stokes and Euler equations on a periodic domain based on a set of
$L^{2m}$-norms of vorticity $\Omega_{m}$ for $m\geq 1$. These are scaled to
form the dimensionless sequence $D_{m}=
(\varpi_{0}^{-1}\Omega_{m})^{\alpha_{m}}$ where $\varpi_{0}$ is a constant
frequency and $\alpha_{m} = 2m/(4m-3)$. A numerically testable Navier-Stokes
regularity criterion comes from comparing the relative magnitudes of $D_{m}$
and $D_{m+1}$ while another is furnished by imposing a critical lower bound on
$\int_{0}^{t}D_{m}\,d\tau$. The behaviour of the $D_{m}$ is also important in
the Euler case in suggesting a method by which possible singular behaviour
might also be tested.
