  The old idea that an infinite dimensional dynamical system may have its high
modes or frequencies slaved to low modes or frequencies is re-visited in the
context of the $3D$ Navier-Stokes equations. A set of dimensionless frequencies
$\{\tilde{\Omega}_{m}(t)\}$ are used which are based on $L^{2m}$-norms of the
vorticity. To avoid using derivatives a closure is assumed that suggests that
the $\tilde{\Omega}_{m}$ ($m>1$) are slaved to $\tilde{\Omega}_{1}$ (the global
enstrophy) in the form $\tilde{\Omega}_{m} =
\tilde{\Omega}_{1}\mathcal{F}_{m}(\tilde{\Omega}_{1})$. This is shaped by the
constraint of two H\"older inequalities and a time average from which emerges a
form for $\mathcal{F}_{m}$ which has been observed in previous numerical
Navier-Stokes and MHD simulations. When written as a phase plane in a scaled
form, this relation is parametrized by a set of functions $1 \leq
\lambda_{m}(\tau) \leq 4$, where curves of constant $\lambda_{m}$ form the
boundaries between tongue-shaped regions. In regions where $2.5 \leq
\lambda_{m} \leq 4$ and $1 \leq \lambda_{m} \leq 2$ the Navier-Stokes equations
are shown to be regular\,: numerical simulations appear to lie in the latter
region. Only in the central region $2 < \lambda_{m} < 2.5$ has no proof of
regularity been found.
