Geoscience Reference
In-Depth Information
15
Lagrangian Methods in Experimental Fluid Mechanics
Mickael Bourgoin
1
, Jean-François Pinton
2
, and Romain Volk
2
15.1. INTRODUCTION
directly related to the Reynolds number of the flow, Re:
L/η
Re
3
/
4
[
Tennekes and Lumley
, 1992]. Reynolds num-
bers of the order 10
6
are usual in geophysical flows,
implying that at least four decades of spatial dynamics are
typically involved. Similarly in the time domain, the ratio
between the eddy turnover time
T
L
at injection scale and at
dissipation scales
τ
η
goes as
T
L
/τ
η
∝
∝
Atmospheric and oceanographic flows are character-
ized by a strong complexity: Stratification, anisotropy,
global rotation, inhomogeneity, turbulence, etc., are just
a few of the main features involved. This chapter reviews
some of the most recent advances in metrology relevant to
investigate such complex flows in model laboratory exper-
iments. We focus on high-resolution techniques which give
access to the hierarchy of multiple spatial and tempo-
ral scales involved in this type of highly turbulent flows.
As described below, among these techniques, Lagrangian
approaches (where tracer particles are tracked in the
flow) have undergone significant developments in the past
decade. Lagrangian metrology has become one of the
most versatile and accurate tools for the investigation of
complex flows, particularly suited in regard to geophysical
motivations, where transport issues are paramount.
In the last decades, the increase of performance in
numerical simulations of fluid dynamics processes (CFD)
has motivated an increasing demand in the accuracy
of models and, naturally, experimental measurements.
A particular challenge in the context of atmospheric
and oceanographic research concerns the improvement
of the multiscale description of flows and of energy cas-
cade mechanisms. Geophysical flows are indeed charac-
terized by a high turbulence intensity which results in
an important hierarchy of relevant scales, with struc-
tures ranging from kilometers down to millimeters. In
turbulent flows, the range of relevant scales (called the
inertial range
) between the energy injection scale
L
and
the dissipative scale (also called Kolmogorov scale)
η
is
Re
1
/
2
, covering three
decades of temporal dynamics. These dynamical ranges
can be even further extended toward the largest scales
due to inverse cascade mechanisms, which may become
important in the atmosphere or the ocean, at scales where
dynamics exhibits 2D properties, where flow structures
can extend over hundreds of kilometers. To investigate
related physics in laboratory experiments, with a typical
dimension of the order of 1 m and typical correlation
time scale of the order of 1 s, the investigation of a com-
parable hierarchy of scales pushes the smallest involved
structures down to tens to hundreds of micrometers (or
even smaller) in space with a typical time scale of fractions
of milliseconds. This stimulates a permanent effort in the
experimental community to develop measurements with
increasing degrees of accuracy and resolution. Technolog-
ical advances in high-speed digital imaging with the ability
to record pictures with millions of pixels at rates exceed-
ing thousands of frames per second have opened up a new
era in experimental fluid dynamics and laboratory models
of geophysical flows. In parallel, several innovative devel-
opments of scattering techniques (sound or light) have
emerged. More recently, progress in embedded sensor and
radio transmission technologies have led to the develop-
ment of instrumented particles which probe the flow as
they are entrained by the local motions.
Let us briefly recall that flow measurements are done
using two approaches: the Eulerian description and the
Lagrangian one (see Figure 15.1). In Eulerian techniques,
the fluid velocity
1
Laboratoire des Écoulements Géophysiques et Industriels,
Université de Grenoble & CNRS, Grenoble, France.
2
Laboratoire de Physique, École Normale Supérieure de
Lyon, Lyon, France.
v
E
(
r
,
t)
is studied as a field varying in
space
r
at time
t
. Although this field also experiences in
