X

Figure 8. Distribution of nondimensional average kinetic energy of the fluctuations for the case of a = 0.03.

value 0.11 vs 0.09). The exit region of each modified background jet, on the average, is therefore more diffluent than the corresponding jet in the reference state. There would be stronger local stretching deformation in the exit region of each jet, which contributes to a stabilizing influence on the eddies. The meridional shear on both sides of each jet is also reduced. Such feedback effect is comparable to the counterpart found in GCM simulations (Black and Dole, 2000). The modification is stronger for the Atlantic jet. The strength of modification itself is relatively mild. This is a posteriori verification that the form of forcing used in the model will yield relevant time mean jets.

4.2. Modal storm tracks with uniform friction

Now let us examine the model storm tracks. As a measure of the intensity of variability, we plot in Fig. 8 the distribution of the average kinetic energy of the equilibrated disturbance field in the control run using a = 0.03. There are two well-defined model storm tracks. The high degree of meridional symmetry of this statistical property about the central latitude of the domain is an indication that the integration is sufficiently long. The maximum intensities of the model Pacific and Atlantic storm tracks are 0.029 vs 0.032 respectively. A value of

Figure 9. Distribution of nondimensional average kinetic energy of the fluctuations in the experiment using a 0.015 in the oceanic sectors and a = 0.045 in the land sectors.

0.03 corresponds to a fluctuating wind speed of about 11 m/s. The storm track downstream of the stronger jet (model Pacific jet) is therefore weaker than the storm track downstream of the weaker jet (model Atlantic jet) by about 10%. This may be taken as evidence in support of the hypothesis concerning the role of seeding disturbances in determining the relative intensity of the two nonlinear storm tracks.

4.3. Modal storm tracks with differential friction

In the second set of experiments, we consider the impact of differential friction. Very little is really known empirically about the dependence of the frictional coefficient on the surface roughness. Therefore, we simply use two different plausible values of frictional coefficients for the land and ocean sectors in this model. Different combinations of them have been tried. The results obtained with the use of a = 0.045 for the land sectors in the model (North America, Euro-Asia) and a = 0.015 for the ocean sectors (Pacific and Atlantic) are representative of this set of experiments. While the drag coefficient over land is three times larger than that over the ocean in this experiment, the domain average value of the drag coefficient in the two experiments is about the same as in the control run. The time mean equilibrated departure stream function field also has dipole structure downstream of each jet similar to that for the case of a = 0.03 everywhere. One difference is that the time mean departure flow in the Atlantic sector is twice as strong as that in the Pacific sector (0.21 vs 0.09; plot not shown for brevity). There are also two equilibrated storm tracks in this case, arising from continual self-sustained transient growth of disturbances. Figure 9 shows the distribution of average kinetic energy of the fluctuating flow component in this experiment. The model storm track downstream of the model Atlantic jet is found to be about 38% more intense than that downstream of the model Pacific jet. Their maximum values are 0.08 vs 0.05 respectively. The key point is that differential friction over land versus over oceans can significantly accentuate the relative intensity of the two storm tracks in favor of the Atlantic storm track for the reason elaborated in the Introduction. This result is a further demonstration that seeding disturbances of the model Atlantic jet are statistically stronger than those of the model Pacific jet, leading to the relative intensity of the two storm tracks.

5. Concluding Remarks

It has been found that the set of inviscid normal modes of a two-localized-jet basic flow that broadly resembles the Pacific and Atlantic jets consists of three groups: single-jet modes, low-frequency modes and synoptic-frequency modes. The synoptic-frequency modes are most relevant to the disturbances in the model storm tracks jointly influenced by the two jets. The differential friction associated with the land and ocean sectors in the model is shown to have significant impact on the eigenvalues as well as the structure of the normal modes. It is noteworthy that some synoptic-frequency modes do not have a stronger localized magnitude downstream of the Atlantic jet. The relative intensity of the Pacific and Atlantic storm tracks therefore cannot be interpreted from the perspective of modal linear dynamics.

Nonlinear simulation of this forced flow produces a slightly more intense model Atlantic storm track with uniform friction. Seeding disturbances arise from wave-wave interactions among the major constituent wave components in a general flow field. Differential friction enhances the difference in the seeding disturbances, leading to an even greater difference in the relative intensity of the model storm tracks. We may conclude from this analysis that, given two pertinent localized jets as a proxy forcing, their locations and the related differential friction coefficients are the most important factors.

There are obvious limitations to the model results. For example, the model height variability has two regions of maximum values straddling each jet, with pronounced symmetric tilts against the shear of the background flow. Such features are intrinsic characteristics of barotropic unstable disturbances. This symmetry also reflects the constraint due to the use of ,3-plane approximation. In a spherical domain, wave disturbances would be dispersed preferentially toward the low latitudes. This study illustrates that the validity of the hypothesis for the relative intensity between the Pacific and Atlantic storm tracks can be demonstrated even in a barotropic model setting. While this is a significant contributing factor, it is unlikely to be the only important factor.

Renewable Energy Eco Friendly

Renewable Energy Eco Friendly

Renewable energy is energy that is generated from sunlight, rain, tides, geothermal heat and wind. These sources are naturally and constantly replenished, which is why they are deemed as renewable.

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