  We set up the scaling theory for stably stratified turbulent fluids. For a
system having infinite extent in the horizontal directions, but with a finite
width in the vertical direction, this theory predicts that the inertial range
can display three possible scaling behaviour, which are essentially
parametrised by the buoyancy frequency $N$, or dimensionless horizontal Froude
number $F_h$, and the vertical length scale $l_v$ that sets the scale of
variation of the velocity field in the vertical direction, for a fixed Reynolds
number. For very low $N$ or very high $Re_b$ or $F_h$, and with $l_v$ being of
the same order as $l_h$, the typical horizontal length scale, buoyancy forces
are irrelevant and hence, unsurprisingly, the kinetic energy spectra shows the
well-known K41 scaling in the inertial range. In this regime, the local
temperature behaves as a passively advected scalar, without any effect on the
flow fields. For intermediate ranges of values of $N,\,F_h\sim {\cal O}(1)$,
corresponding to moderate stratification, buoyancy forces are important enough
to affect the scaling. This leads to the Bolgiano-Obukhov scaling which is
isotropic, when $l_v\sim l_h$. Finally, for very large $N$ or equivalently for
vanishingly small $F_h,\,L_o$, corresponding to strong stratification, together
with a very small $l_v$, the system effectively two-dimensionalise; the kinetic
energy spectrum is predicted to be anisotropic with only the horizontal part of
the kinetic energy spectra follows the K41 scaling, suggesting an intriguing
{\em re-entrant} K41 scaling, as a function of stratification, for ${\bf
v}_\perp$ in this regime. The scaling theory further predicts the scaling of
the thermal energy in each of these three scaling regimes. Our theory can be
tested in large scale simulations and appropriate laboratory-based experiments.
