Abstract
Surface semi-geostrophic turbulence is examined in this study. In our
simulations, the strength of the ageostrophic component of the flows is
controlled by the Rossby number ε, varying from 0.01 to 0.2. The flows
manifest a cyclone-anticyclone asymmetry with a cyclonic preference for
cold vortices and an anticyclonic preference for warm filaments. This
asymmetry becomes especially pronounced in the flows with large ε, where
an abundance of warm filaments is observed.
Strong vertical motions concentrate in the small-scale filaments and at
the periphery of the vortices. There, the lateral divergence becomes
significant. A negative correlation between the divergence and the
relative vorticity is identified using joint probability density
functions.
Slopes of the kinetic and potential energy spectra vary between -2.2 and
-1.7 at intermediate scales. Analyses of spectral fluxes demonstrate an
inverse kinetic energy cascade and a forward cascade of potential
energy. As ε increases, the filaments become more numerous in the flows.
They wrap around cyclones, weakening their interactions and subsequent
mergers, thus suppressing the inverse cascade of kinetic energy.
We characterize lateral dispersion in the SSG flows using the
finite-scale Lyapunov exponents (FSLEs). They are used to identify
Lagrangian coherent structures, such as those created by the interaction
of vortices. The FSLEs are also used to investigate the regimes of
dispersion at different scales. The results show a smooth transition
from hyper-ballistic diffusion at small scales to normal diffusion at
large scales.