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October 15, 2021
The aim of this assignment is to study and understand waves that are gen- erated when D(y) and f(y) are sloping planes of the form D = D0 + αy and f = f0 + βy. For this assignment you should use a model with periodic and open (sponge) boundary conditions. The initial disturbance should be in geostrophic balance to avoid gravity waves.
Experiments and model setup Model setup
- Use an initial disturbance in geostrophic balance. (Tip: when you de- fine h, you also need to program u and v, so that they are in geostrophic balance.)
- Use periodic boundaries in x (East – West).
- Use open boundaries (Sponge) in y (South – North).
- Program a sloping plane D = D0 + αy using LOGICAL (or CASE) so that you can chose to have it on or off in the simulation.
- Program a new Coriolis parameter describing f = f0 +βy. In the same sense, use LOGICAL (or CASE) so that you can chose to turn it on or off. *Author: Sara Berglund, 2020; modified: Ezra Eisbrenner, 2021 1
DEPARTMENT OF METEOROLOGY
STOCKHOLMS UNIVERSITET MO8007
Experiment 1 – β plane
- Consider a rectangular basin with L = 7·106 m and H = 4000 m in the mid latitudes (e.g. North Pacific ). Run the model for at least 30 days.
- Start by deriving the phase speed and group velocity for Rossby waves in this linear system. (The derivation should not be included in the report, only the final solution).
- Run the model with a β-plane and constant topography (D).
- Describe and explain the evolution of the system.
- Connect the results to theory.
- What kind of waves develop?
- Do they have any distinguishing properties? Experiment 2 – Phase and group velocities
- Rerun the model as in Experiment 1, but with different wavenumbers. (Tip: To change wavenumber, change disturbance width).
- Compare the obtained phase speed and group velocity to the theoretical values.
- Repeat this exercise but keep f constant and vary the topography us- ing an α plane. Discuss the differences. Experiment 3 – β − α compensation
- Run the model using a varying topography and f-field ( D = D0 + αy and f = f0 + βy).
- Calculate the value of α that cancels the β effect. What happens to the initial disturbance under these circumstances?