  We study the statistics of the vertical motion of inertial particles in
strongly stratified turbulence. We use Kinematic Simulation (KS) and Rapid
Distortion Theory (RDT) to study the mean position and the root mean square
(rms) of the position fluctuation in the vertical direction. We vary the
strength of the stratification and the particle inertial characteristic time.
The stratification is modelled using the Boussinesq equation and solved in the
limit of RDT. The validity of the approximations used here requires
that$\sqrt{{L}/{g}}<{2\pi}/{\mathcal{N}}<\tau\_{\eta}$,where $\tau\_{\eta}$ is
the Kolmogorov time scale, $g$ the gravitational acceleration, $L$ the
turbulence integral length scale and $\mathcal{N}$ the Brunt-V\"ais\"al\"a
frequency. We introduce a drift Froude number$Fr\_{d} = \tau\_p g / \mathcal{N}
L$. When $Fr\_{d} < 1$, the rms of the inertial particle displacement
fluctuation is the same as for fluid elements, i.e.$\langle(\zeta\_3 - \langle
\zeta\_3 \rangle)^2\rangle^{1/2} = 1.22\, u'/\mathcal{N} +
\mbox{oscillations}$. However, when $Fr\_{d} > 1$,$\langle(\zeta\_3 - \langle
\zeta\_3 \rangle)^2\rangle^{1/2} = 267 \, u' \tau\_p$. That is the level of the
fluctuation is controlled by the particle inertia $\tau\_p$ andnot by the
buoyancy frequency $\mathcal{N}$. In other words it seems possible for inertial
particles to retain the vertical capping while loosing the memory of
theBrunt-V\"ais\"al\"a frequency.
