Abstract
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 (RaS), and , respectively, are held at a fixed ratio . The simulations are performed in a periodic domain, at Reynolds number , and Froude number Fr in the range (with Rossby number ). As the intensity of RaS increases, a sharp transition is observed between a regime dominated by eddies to a regime dominated by waves, which corresponds to . For the given runs, this transition to a wave-dominated regime can also be seemingly described by simply comparing the timescales and , the latter being the Kolmogorov timescale based on the mean kinetic energy dissipation. Due to the known anisotropy induced by RaS, we consider separately the motion in the horizontal and vertical directions. In the regime , 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 , 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 . We observe that in the regime , 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 , with no clear diffusive behavior. In contrast, the displacements in the vertical direction are always reduced. This inhibition is extremely strong in the regime, leading to a scenario where particles almost appear to be trapped in horizontal planes.
3 More- Received 26 September 2019
- Accepted 11 May 2020
DOI:https://doi.org/10.1103/PhysRevFluids.5.064801
Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI. Open access publication funded by the Max Planck Society.
Published by the American Physical Society