The present study aims to improve the calculus of finite-time Lyapunov
exponents (FTLEs) applied to describe the transport of inertial particles in
a fluid flow. To this aim, the deformation tensor is modified to take into
account that the stretching rate between particles separated by a certain
distance is influenced by the initial velocity of the particles. Thus, the
inertial FTLEs (iFTLEs) are defined in terms of the maximum stretching
between infinitesimally close trajectories that have different initial
velocities. The advantages of this improvement, if compared to the standard
method

The advection of finite-size or inertial particles in open, unsteady flows
was initially assessed independently by

During the last years, the dynamics of inertial particles have been studied
in many research fields such as sedimentation processes

Although the transport of Lagrangian particles as described by finite-time
Lyapunov exponents (FTLEs) has been extensively studied to date, to our
knowledge only a few studies have been performed with inertial particles

For the dynamical system described above (Eq.

In order to characterize the transport of inertial particles, we introduce
the iFTLEs

For the computation of the iFTLE field, the integration time

Finite-time Lyapunov exponents

The results obtained from using the improved iFTLE calculation method will be
compared to those obtained from the standard method

We investigate the effect of initial velocity

Finite-time Lyapunov exponents

The (

Spatial average FTLE as a function of the initial velocity
parameters

Contribution to the eigenvector

A comparison between Figs.

Figure

The mean FTLEs are larger for the heavier particles (

Next, the iFTLE-field response to changes in the initial conditions is
assessed by means of the eigenvector, decomposed into the factors “initial
position” and “initial velocity”. To this end, we calculate the ratio
between both,

In the present study, a new method for calculating iFTLEs used to describe
the motion of inertial particles in a fluid flow was suggested, which, in
contrast to the standard method

More importantly, our method does not only hold for particle motions
described by the Maxey–Riley equation (Eq.

The periodically varying

The

This flow can be divided into three distinct regimes: a central meandering
eastward jet, several closed circulation cells located above the meander
troughs and below the meander crests, and an exterior retrograde westward
motion

For both flows, their advective velocities

This work was supported by the Ministerio de Economía y Competitividad under research grant CGL2013-45932-R. Edited by: A. M. Mancho Reviewed by: two anonymous referees