  The Lagrangian (LA) and Eulerian Acceleration (EA) properties of fluid
particles in homogeneous turbulence with uniform shear and uniform stable
stratification are studied using direct numerical simulations. The Richardson
number is varied from $Ri=0$, corresponding to unstratified shear flow, to
$Ri=1$, corresponding to strongly stratified shear flow. The probability
density functions (pdfs) of both LA and EA have a stretched-exponential shape
and they show a strong and similar influence on the Richardson number. The
extreme values of the EA are stronger than those observed for the LA.
Geometrical statistics explain that the magnitude of the EA is larger than its
Lagrangian counterpart due to the mutual cancellation of the Eulerian and
convective acceleration, as both vectors statistically show an anti-parallel
preference. A wavelet-based scale-dependent decomposition of the LA and EA is
performed. The tails of the acceleration pdfs grow heavier for smaller scales
of turbulent motion. Hence the flatness increases with decreasing scale,
indicating stronger intermittency at smaller scales. The joint pdfs of the LA
and EA indicate a trend to stronger correlations with increasing Richardson
number and at larger scales of the turbulent motion. A consideration of the
terms in the Navier--Stokes equation shows that the LA is mainly determined by
the pressure-gradient term, while the EA is dominated by the nonlinear
convection term.
