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DYNAMICAL OCEANOGRAPHY
example, exists at the eastern side of the warm pool.
a. Assume that there is a positive temperature anomaly that causes westely
wind anomalies. Describe the effect on the zonal currents in the ocean.
b. Consider in the SST-equation, the balance
∂ ˜
T ∗ /∂t ∗ ≈−˜ u ∗ ∂ ¯
T ∗ /∂x ∗
that describes the evolution of temperature anomalies ˜
T ∗ due to anomalies in
the zonal current ˜
u ∗ . Describe the mechanism of the zonal advection feedback.
(12.4) The two-strip model
From the two-strip model in section 12.3, the delayed oscillator equations
can be derived explicitly from the shallow-water model and the SST equation. Central in this derivation is the integration over characteristics defined by
Kelvin and Rossby waves.
a. Determine the characteristics of a free Kelvin wave along the equator and
sketch these in the x − t plane.
b. Determine the characteristics of a free j =1Rossby wave along the y max
value in Table 11.1 and also sketch these in the x − t plane.
c. Why can y n in the two-strip model be identified with y max as given in
Table 11.1?
d. Carry out the integration of the equations (12.19) along both characteristics
under a. and b. and derive the equations (12.28a-b).
(12.5) The delayed oscillator
Equation (12.30) forms the basic model for the delayed oscillator.
a. Scale time with 1/a and temperature by
a/c, derive the dimensionless
equation
dT
dt
= T (t) − αT (t − δ T ) − T
3 (t),
and determine α and δ T .
DYNAMICAL OCEANOGRAPHY
example, exists at the eastern side of the warm pool.
a. Assume that there is a positive temperature anomaly that causes westely
wind anomalies. Describe the effect on the zonal currents in the ocean.
b. Consider in the SST-equation, the balance
∂ ˜
T ∗ /∂t ∗ ≈−˜ u ∗ ∂ ¯
T ∗ /∂x ∗
that describes the evolution of temperature anomalies ˜
T ∗ due to anomalies in
the zonal current ˜
u ∗ . Describe the mechanism of the zonal advection feedback.
(12.4) The two-strip model
From the two-strip model in section 12.3, the delayed oscillator equations
can be derived explicitly from the shallow-water model and the SST equation. Central in this derivation is the integration over characteristics defined by
Kelvin and Rossby waves.
a. Determine the characteristics of a free Kelvin wave along the equator and
sketch these in the x − t plane.
b. Determine the characteristics of a free j =1Rossby wave along the y max
value in Table 11.1 and also sketch these in the x − t plane.
c. Why can y n in the two-strip model be identified with y max as given in
Table 11.1?
d. Carry out the integration of the equations (12.19) along both characteristics
under a. and b. and derive the equations (12.28a-b).
(12.5) The delayed oscillator
Equation (12.30) forms the basic model for the delayed oscillator.
a. Scale time with 1/a and temperature by
a/c, derive the dimensionless
equation
dT
dt
= T (t) − αT (t − δ T ) − T
3 (t),
and determine α and δ T .