MO8007
Laboration 3A:
Aim
The aim of this assignment is to study and understand waves that are generated 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 define 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.
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 using 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?
