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of waves by vortices/eddies is discussed in the context
of emission of Rossby waves by vortex arrays on the
polar
β
-plane and emission of inertial waves by vor-
tices in quasi two-dimensional rotating turbulence on the
f
-plane. The Rhines scale, which was originally derived
using the idea of synchronization between waves and vor-
tices of matching wave number, is relevant in the former
case. A modification of the original Rhines scale to the
polar
β
-plane is discussed. It allows one to predict at
what scale the emission of Rossby waves becomes sig-
nificant and as a result a change in the regime of the
flow can occur. A similar consideration of synchroniza-
tion/matching between vortices on the
f
-plane gives a
prediction of when the most efficient emission of inertial
waves can occur.
1.0
24
22
0.8
20
0.6
18
0.4
16
0.2
Acknowledgments.
I would like to thank J. Craig for
his help with expriments on two-dimensional turbulence
and S. H. Curnoe for thorough proofreading of the draft
of this chapter. The support of the Natural Sciences and
Engineering Research Council of Canada is gratefully
acknowledged.
14
10
20
30
kD
/(2π)+1
40
50
Figure 5.12.
Energy spectrum of rotating turbulence shown
in frequency and wave number space. The gray scale shows
energy in logarithmic scale. The frequency is normalized by the
Coriolis parameter while the wave number is normalized by
the diameter of the container,
D
= 90 cm. The solid line shows
the dispersion relation (5.20) for the inertial waves.
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but at higher wave numbers (20-40). Thus it is quite clear
that inertial waves are detected in this flow, although their
energy is quite small compared to that of the vortices.
5.6. SUMMARY
This chapter has reviewed a new laboratory technique
of optical altimetry designed to visualize rotating flows
with a free surface and to measure their surface elevation
and velocity fields. An additional benefit of the rotating
system, where the depth of the layer varies quadratically
with the distance from the center, is that it models the
planetary polar
β
-plane. The theoretical background for
Rossby and inertial waves is given as well as the method
for calculating the velocity field from the slopes of the
surface elevation. This chapter gives several examples
of experiments that illustrate the advantages of labora-
tory altimetry in studying global patterns of GFD flows,
including Rossby and inertial waves and vortices. Typi-
cal features of the
β
-plane dynamics are demonstrated
in experiments with flows over a bottom topography
and around an obstacle where striking differences are
observed between the eastward and westward flows. The
interesting and geophysically relevant issue of emission
