427
Resonance of the zonal mean flow with the wave field occurs when U
equals the baroclinic Rossby wave phase speed 'Y. This modification of the
linear theory (where the resonance is at U = 'Y) is due to the inclusion of
the nonlinear interaction with the mode (0,2). Notice that there is only a
resonant behavior in the baroclinic amplitude T
Expressing the interfacial and bottom form stresses as functions of U
and V by use of (42) to (46), the two momentum equations (40) and (41)
become implicit functions defining curves in (U, V)-space. Their intersection points determine the steady states. Figure 5 displays the two curves
for various values of the topography height. There are five straight lines
in these plots with a specific physical meaning. The upper horizontal line
reflects a balance between the wind input and interfacial friction in the
baroclinic momentum, i. e. 6702 - 2/-lV = O. On the lower horizontal line
we have V + 'Y = 0, hence the baroclinic wave amplitude 'T vanishes. In
addition, there is a change of sign in the interfacial form stress when this
line is crossed: below we have a source of eastward momentum and above
we have a sink. Thus for eastward windstress the steady states must lie
above. The right diagonal line characterizes the balance between wind input and bottom friction in the barotropic balance, i. e. 6702 - E(U - V) = O.
On the left diagonal line we have U = V so both wave amplitudes vanish.
The resonance U = 'Y of the mean zonal flow with the Rossby waves is on
the vertical line.
For vanishing topography both amplitudes P and 'T vanish by (44)
and (46) and only frictional processes can balance the momentum input.
The solution curves are both straight lines. With increasing topography
height the resonance near U - ' Y leads to high amplitudes of 'T and more
complicated curve forms appear: the curve associated with the barotropic
balance (40) bends with increasing height and at a certain height (which
depends on the other parameters) a closed second part of the curve appears near the resonance line U = 'Y. The extent of this isolated curve
increases with increasing topography until the two parts join. In parallel, with increasing height, the baroclinic momentum balance (41) develops a resonance reaching down on the line U = 'Y. In this way, there
is a succession from one to three to two steady states when the topography is increased. These properties are displayed in the Figures 5 and
6 for two sets of parameters. Figure 5, using the unrealistic parameters
70 = 3 X 1O-5m 2s -I,,8 = 2 x 1.471421 X 1O-llm-1s- 1 , makes the structure
more obvious and Figure 6 applies the standard ACC parameters.
Resonance of the zonal mean flow with the wave field occurs when U
equals the baroclinic Rossby wave phase speed 'Y. This modification of the
linear theory (where the resonance is at U = 'Y) is due to the inclusion of
the nonlinear interaction with the mode (0,2). Notice that there is only a
resonant behavior in the baroclinic amplitude T
Expressing the interfacial and bottom form stresses as functions of U
and V by use of (42) to (46), the two momentum equations (40) and (41)
become implicit functions defining curves in (U, V)-space. Their intersection points determine the steady states. Figure 5 displays the two curves
for various values of the topography height. There are five straight lines
in these plots with a specific physical meaning. The upper horizontal line
reflects a balance between the wind input and interfacial friction in the
baroclinic momentum, i. e. 6702 - 2/-lV = O. On the lower horizontal line
we have V + 'Y = 0, hence the baroclinic wave amplitude 'T vanishes. In
addition, there is a change of sign in the interfacial form stress when this
line is crossed: below we have a source of eastward momentum and above
we have a sink. Thus for eastward windstress the steady states must lie
above. The right diagonal line characterizes the balance between wind input and bottom friction in the barotropic balance, i. e. 6702 - E(U - V) = O.
On the left diagonal line we have U = V so both wave amplitudes vanish.
The resonance U = 'Y of the mean zonal flow with the Rossby waves is on
the vertical line.
For vanishing topography both amplitudes P and 'T vanish by (44)
and (46) and only frictional processes can balance the momentum input.
The solution curves are both straight lines. With increasing topography
height the resonance near U - ' Y leads to high amplitudes of 'T and more
complicated curve forms appear: the curve associated with the barotropic
balance (40) bends with increasing height and at a certain height (which
depends on the other parameters) a closed second part of the curve appears near the resonance line U = 'Y. The extent of this isolated curve
increases with increasing topography until the two parts join. In parallel, with increasing height, the baroclinic momentum balance (41) develops a resonance reaching down on the line U = 'Y. In this way, there
is a succession from one to three to two steady states when the topography is increased. These properties are displayed in the Figures 5 and
6 for two sets of parameters. Figure 5, using the unrealistic parameters
70 = 3 X 1O-5m 2s -I,,8 = 2 x 1.471421 X 1O-llm-1s- 1 , makes the structure
more obvious and Figure 6 applies the standard ACC parameters.