224
DYNAMICAL OCEANOGRAPHY
◭
To describe the mechanism of barotropic instability, we again consider the motion of three water columns on the β-plane (Fig. 10.4) similar to the description
used of the propagation of the Rossby wave in section 7.3. Assume that column
B initially moves northward then, through conservation of potential vorticity, it
acquires a negative rotation. For an eastward flow, the horizontal shear induces a
positive rotation (Fig. 10.4a) that will counteract the rotation of B. For a westward
flow, the horizontal shear amplifies the negative rotation of B (Fig. 10.4b), which
explains the asymmetry of the growth of perturbations. The growth of the perturbation itself is identical to that of plane shear instabilities where the Reynolds’
stress induces the energy transfer between the mean state and the perturbations.
(a)
(b)
Figure 10.4. Sketch to understand the mechanism of barotropic instability for (a) an eastward
flow and (b) a westward flow.
10.3. The Eady model
One of the simple situations in which baroclinic instability occurs is the flow
in a zonal channel with lateral walls at y = ± 1. Bottom friction is neglected,
DYNAMICAL OCEANOGRAPHY
◭
To describe the mechanism of barotropic instability, we again consider the motion of three water columns on the β-plane (Fig. 10.4) similar to the description
used of the propagation of the Rossby wave in section 7.3. Assume that column
B initially moves northward then, through conservation of potential vorticity, it
acquires a negative rotation. For an eastward flow, the horizontal shear induces a
positive rotation (Fig. 10.4a) that will counteract the rotation of B. For a westward
flow, the horizontal shear amplifies the negative rotation of B (Fig. 10.4b), which
explains the asymmetry of the growth of perturbations. The growth of the perturbation itself is identical to that of plane shear instabilities where the Reynolds’
stress induces the energy transfer between the mean state and the perturbations.
(a)
(b)
Figure 10.4. Sketch to understand the mechanism of barotropic instability for (a) an eastward
flow and (b) a westward flow.
10.3. The Eady model
One of the simple situations in which baroclinic instability occurs is the flow
in a zonal channel with lateral walls at y = ± 1. Bottom friction is neglected,