Geoscience Reference
In-Depth Information
11
Frontal Instabilities at Density-Shear Interfaces in Rotating
Two-Layer Stratified Fluids
Hélène Scolan
1
, Roberto Verzicco
2
, and Jan-Bert Flór
3
11.1. INTRODUCTION
Phillips
[1954] and
Pedlosky
[1964, 1970] [see
Hart
, 1972]
predicts well the observed wavelengths of the baroclinic
instability. These flows depend on stratification, rotation,
and the flow aspect ratio as expressed by the Burger num-
ber. This number indicates the baroclinicity of the flow.
Strongly baroclinic flows have a small Burger number cor-
responding to a strongly inclined density field. This num-
ber serves as a control parameter for baroclinic instability
(see Section 11.2.1). Various aspects of baroclinic insta-
bility have been considered. For small Burger numbers,
periodic variations occur in the amplitude of the dom-
inant baroclinic mode of the system, a nonlinear effect
known as amplitude vacillation [
Hart
, 1980, 1985;
King
,
1979]. In considering the same forcing at the fluid surface
for an annular flow, also
Bradford et al.
[1981],
Appleby
[1982],
Lovegrove et al.
[2000], and
Williams et al.
[2003,
2004a, 2004b, 2005] showed cases of amplitude vacilla-
tion, whereas for even smaller Burger numbers the flow
is known to transit to chaos and turbulence [
Hide
, 2011;
Read et al.
, 1992;
Früh and Read
, 1997;
Eccles et al.
,
2009].
Other examples of fronts where the baroclinic insta-
bility is observed to develop are density intrusions in a
rotating fluid, such as gravity currents, coastal flows, and
vortex lenses created by the release of a fluid of a different
density in a homogeneous (or stratified) rotating ambi-
ent [
Chia et al.
, 1982;
Bouruet-Aubertot and Linden
, 2002].
These systems generally consist of two layers, and the
Phillips model for baroclinic instability shows good agree-
ment with the observed instability wavelengths [
[Griffiths
and Linden
, 1981;
Cenedese and Linden
, 2002]. Interac-
tions of the front with the Ekman boundary layer do
not seem to influence the instability wavelength of these
close to laminar fronts in small-scale laboratory experi-
ments. Also the complex dynamics of critical layers at the
interface do not significantly modify observations of the
Fronts in Earth oceans and atmosphere separate
different temperature fluids or masses of air and therefore
play a major role for the transport of heat and chemi-
cal or biological tracers in large-scale geophysical flows.
Their dynamics and instability are crucial for weather
forecasting, whereas their variability is a key element for
understanding climate. First experiments that showed the
occurrence of baroclinic modes were conducted in annu-
lar rotating tanks of which the exterior (or inner) cylinder
was heated (cooled) [
Hide
, 1953, 1958;
Fultz et al.
, 1959;
Fowlis and Hide
, 1965].
Baroclinic instability arises at a density field that is
inclined with respect to the horizontal. As mentioned, an
inclined density gradient may be created in a rotating fluid
by differential heating. In the quasi-geostrophic approxi-
mation, these flows are in thermal wind balance, i.e, the
tilting of the vorticity due to shear in the fluid equals the
baroclinic production of vorticity,
f
∂
u
∂z
=
g
ρ
o
× ∇
H
ρ
,
−
z
where
u
is the horizontal velocity,
g
the gravitational con-
stant, and
∇
H
ρ
the horizontal density gradient. Another
manner to create a baroclinic front in thermal wind bal-
ance is achieved by applying a vertical shear across the
density field. Such a shear can be obtained by using a
rotating disk at the fluid surface [
Hart
, 1972]. For this
type of flow the quasi-geostrophic two-layer model of
1
Atmospheric, Oceanic & Planetary Physics, University of
Oxford, Oxford, United Kingdom.
2
Department of Mechanical Engineering, Università di Roma
Tor Vergata, Rome, Italy.
3
Laboratoire des Ecoulements Géophysiques et Industriels
(LEGI), Grenoble, France.
