Geoscience Reference
In-Depth Information
5
Altimetry in a GFD Laboratory and Flows on the Polar
β
-Plane
Yakov D. Afanasyev
5.1. INTRODUCTION
spatial resolution, or rather the range of scales that PIV
can resolve at the same time.
In this chapter we describe a different technique for
global measurements of dynamic fields. This technique is
based on optical altimetry and allows one to measure the
slope of the surface elevation in every pixel of the image
of the flow. With modern megapixel cameras this makes
the problem of spatial (and temporal) resolution a thing
of the past. The slope of the surface elevation can be con-
verted to barotropic velocity using relations suitable for a
rotating fluid. Laboratory altimetry is not unlike satellite
radar altimetry, which has provided global observations
of the sea surface elevation since the TOPEX/Poseidon
satellite was launched in 1992. The altimetry technique
is somewhat less versatile than PIV, but it is well suited
for rotating GFD experiments. Because of its high spa-
tial and temporal resolution, laboratory altimetry can be
used effectively for detailed comparison and testing of
numerical models [
Slavin and Afanasyev
, 2012].
In a two-layer fluid this technique can be used in com-
bination with a traditional optical density method that
allows one to measure the thickness of one of the layers
almost simultaneously with the surface elevation mea-
surements [
Afanasyev et al.
, 2009]. Thus the baroclinic
component of velocity can also be resolved. The combi-
nation of barotropic and baroclinic components provides
complete information about the system. The amount of
data obtained in such an experiment is comparable with
that in a numerical simulation such that one can think of
a laboratory tank as of an “analogue computer”for GFD
modeling.
This chapter is organized as follows. Section 5.2 gives
a brief review of the general features of a rotating
layer with a free surface, including the so-called polar
β
-plane approximation. We then proceed in Section 5.3
to the description of the experimental technique, includ-
ing the methods of conversion of the slope of the surface
Rotating table experiments are essential in the study of
geophysical fluid dynamics (GFD) where planetary rota-
tion is important. They are a valuable research tool that
allows one to gain insight into the dynamics of oceanic
and atmospheric flows. They can be especially useful for
studying three-dimensional (3D) flows with relatively high
Reynolds numbers. Indeed, at Reynolds numbers of the
order of 10
3
10
5
, laboratory experiments can be even
more time effective than current 3D numerical models.
Although numerical simulations provide more flexibility
in the choice of the physical setup, including initial and
boundary conditions, the range of control parameters,
and type of forcing, experiments are indispensable for
the purpose of testing and validating numerical models.
A numerical simulation run in parallel with the exper-
iment, especially with some form of data assimilation
from the experiment [e.g.,
Ravela et al.
, 2010], can be very
beneficial for supplementing the experimental data and
obtaining complete information about the flow.
One limiting factor of an experiment is a measurement
problem. It is often desirable to resolve all significant
scales from the viscous scale of an order of 1 mm up to
the scale of the experimental tank (typically 1-2 m). Parti-
cle image velocimetry (PIV) is widely used by researchers
for measurements of the velocity field in the entire flow
domain. PIV is a well-developed method applicable for
virtually all possible flows. However, there is a resolu-
tion problem with the PIV technique. By design, PIV uses
interrogation windows of size from 12
2
to 24
2
or more
pixels. Given the total size of the imaging array used in a
video camera, the window size ultimately determines the
−
Department of Physics and Physical Oceanography, Memo-
rial University of Newfoundland, St. John's, Newfoundland,
Canada.
