CLIMATE/EARTH 401�Geophysical Fluid Dynamics�Dynamical Meteorology

Richard B. Rood

rbrood@umich.edu

https://openclimate.org/

Practice the use of complex exponentials (Euler’s formula)

• This is a problem to practice the use of complex exponentials, which is called Euler’s formula. You might want to look this up.
• In words, to get Euler’s formula write out the Taylor series for e^ix, where i is the imaginary unit number. Then, recognize the resulting series as the Taylor series expansion of the cos and sin.

​

e^ix = cos(x) + isin(x)

The equation below is a wave equation. �The variables are according to the conventions used in class.

Dispersion relation. Relates frequency and wave number to flow. Must be true for waves.

What is the dispersion relationship for a stationary wave?

Wind must be positive, from the west, for a wave.