# Laboratoire de Mécanique des Fluides et d’Acoustique - UMR 5509

LMFA - UMR 5509
Laboratoire de Mécanique des Fluides et d’Acoustique
Lyon
France

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Article dans Phys. Rev. Fluids (2020)

## Single-particle Lagrangian statistics from direct numerical simulations of rotating-stratified turbulence

Dhawal Buaria, Alain Pumir, Fabio Feraco, Raffaele Marino, Annick Pouquet, Duane Rosenberg & Leonardo Primavera

Geophysical fluid flows are predominantly turbulent and often strongly affected by the Earth’s rotation, as well as by stable density stratification. Using direct numerical simulations of forced Boussinesq equations, we study the influence of these effects on the motion of fluid particles. We perform a detailed study of Lagrangian statistics of acceleration, velocity, and related quantities, focusing on cases where the frequencies associated with rotation and stratification ($\mathrm{Ra}S$), $f$ and $N$, respectively, are held at a fixed ratio $N/f=5$. The simulations are performed in a periodic domain, at Reynolds number $\mathrm{Re}\approx4000$, and Froude number $\mathrm{Fr}$ in the range $0.03\lesssim\mathrm{Fr}\lesssim0.2$ (with Rossby number $\mathrm{Ro}=5\mathrm{Fr}$). As the intensity of $\mathrm{Ra}S$ increases, a sharp transition is observed between a regime dominated by eddies to a regime dominated by waves, which corresponds to $\mathrm{Fr}\lesssim0.07$. For the given runs, this transition to a wave-dominated regime can also be seemingly described by simply comparing the timescales $1/N$ and $\tau\eta$, the latter being the Kolmogorov timescale based on the mean kinetic energy dissipation. Due to the known anisotropy induced by $\mathrm{Ra}S$, we consider separately the motion in the horizontal and vertical directions. In the regime $N\tau\eta<1$, acceleration statistics exhibit well known characteristics of isotropic turbulence in both directions, such as probability density functions with wide tails and acceleration variance approximately scaling as per Kolmogorov’s theory. In contrast for $N\tau\eta>1$, they behave very differently, experiencing the direct influence of the imposed rotation and stratification. On the other hand, the Lagrangian velocity statistics exhibit visible anisotropy for all runs ; nevertheless the degree of anisotropy becomes very strong in the regime $N\tau\eta>1$. We observe that in the regime $N\tau\eta<1$, rotation enhances the mean-square displacements in horizontal planes in the ballistic regime at short times but suppresses them in the diffusive regime at longer times. This suppression of the horizontal displacements becomes stronger in the regime $N\tau\eta>1$, with no clear diffusive behavior. In contrast, the displacements in the vertical direction are always reduced. This inhibition is extremely strong in the $N\tau\eta>1$ regime, leading to a scenario where particles almost appear to be trapped in horizontal planes.