  Three dimensional (3D) Finite Time Lyapunov Exponents (FTLEs) are computed
from numerical simulations of a freely evolving mixed layer (ML) front in a
zonal channel undergoing baroclinic instability. The 3D FTLEs show a complex
structure, with features that are less defined than the two-dimensional (2D)
FTLEs, suggesting that stirring is not confined to the edges of vortices and
along filaments and posing significant consequences on mixing. The magnitude of
the FTLEs is observed to be strongly determined by the vertical shear. A
scaling law relating the local FTLEs and the nonlocal density contrast used to
initialize the ML front is derived assuming thermal wind balance. The scaling
law only converges to the values found from the simulations within the
pycnocline, while it displays differences within the ML, where the
instabilities show a large ageostrophic component. The probability distribution
functions of 2D and 3D FTLEs are found to be non Gaussian at all depths. In the
ML, the FTLEs wavenumber spectra display -1 slopes, while in the pycnocline,
the FTLEs wavenumber spectra display -2 slopes, corresponding to frontal
dynamics. Close to the surface, the geodesic Lagrangian Coherent Structures
(LCSs) reveal a complex stirring structure, with elliptic structures detaching
from the frontal region. In the pycnocline, LCSs are able to detect filamentary
structures that are not captured by the Eulerian fields.
