Find the dispersion* relationship associated with sinusoidal disturbances to the above background state: +' = A...

 

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Find the dispersion* relationship associated with sinusoidal disturbances to the above background state: +' = A exp(ikx +ily + imp - iwt) a. Calculate the phase velocity in the x-direction. b. Rearrange your answer and solve for m. For stationary Rossby waves (c = 0), for what range of values for u will m be positive? If m < 0, what structure does the disturbance given in #3 take in the vertical direction? (Note, qy > 0. You also know that the stratification must be positive in a stably stratified atmosphere.) Find the dispersion* relationship associated with sinusoidal disturbances to the above background state: +' = A exp(ikx +ily + imp - iwt) a. Calculate the phase velocity in the x-direction. b. Rearrange your answer and solve for m. For stationary Rossby waves (c = 0), for what range of values for u will m be positive? If m < 0, what structure does the disturbance given in #3 take in the vertical direction? (Note, qy > 0. You also know that the stratification must be positive in a stably stratified atmosphere.)