Rossby Wave Crossing Time Calculation

The time ($t$) for a wave to cross a region of width ($W$) depends on its speed ($v$), following the formula: $ t = \frac{W}{v} $ Atmospheric Rossby waves are considerably faster than oceanic ones.

Pacific Width Given

The width of the equatorial Pacific is given as $W = 17,760\text{ km}$.

Wave Speeds Analysis

We analyze the implied speeds based on typical crossing times for atmospheric and oceanic Rossby waves across this width.

Atmospheric Rossby Wave Speed

Atmospheric Rossby waves typically cross the equatorial Pacific in approximately $18\text{ days}$. The implied speed ($v_{atm}$) is calculated as:

$ v_{atm} = \frac{17,760\text{ km}}{18\text{ days}} \approx 987\text{ km/day} $

This speed, approximately $11.4\text{ m/s}$, is characteristic of atmospheric Rossby waves.

Oceanic Rossby Wave Speed

Oceanic Rossby waves travel much slower, taking approximately $210\text{ days}$ to cross.

The implied speed ($v_{oceanic}$) is calculated as:

$ v_{oceanic} = \frac{17,760\text{ km}}{210\text{ days}} \approx 84.6\text{ km/day} $

This speed, approximately $0.98\text{ m/s}$, is characteristic of slower oceanic Rossby waves.

Rossby Wave Conclusion

The calculated speeds are consistent with established values for atmospheric and oceanic Rossby waves, confirming that $18\text{ days}$ and $210\text{ days}$ are the respective crossing times for atmospheric and oceanic waves across the equatorial Pacific.