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DYNAMICAL OCEANOGRAPHY
3.4. Exercises on chapter 3
(3.1) Vorticity
Consider a flow having a width of 200 km directed northward with a maximum
velocity of 2 ms −1 near the latitude 27 ◦ N.
a. Calculate the value of the Coriolis parameter f 0 of this flow.
b. Determine a typical value of the relative vorticity of the flow.
c. Provide estimates of the time scales τ f , τ a and the Rossby number ǫ.
(3.2) Properties of the Coriolis acceleration
a. Show, in the same way as in section 3.1.2, that the rotation of the (e 1 , e 3 )
plane induces an acceleration −2Ωw cos θ in the e 1 direction and an acceleration 2Ωu cos θ in the e 3 direction.
In section 3.1.2 we derived the expression for the Coriolis acceleration a c .
b. Show that a c ⊥ Ω and a c ⊥ v.
(3.3) Rossby deformation radius
Both the external (R D ) and internal (L D ) Rossby deformation radii are important length scales in the ocean.
a. Use typical values of ocean depth (Fig. 1.1) and buoyancy frequency
(Fig. 3.4) to estimate L D and R D in the Atlantic Ocean at a latitude of 5 ◦ N,
30 ◦ N and 55 ◦ N.
b. Provide a priori arguments whether effects of stratification are important
in (i) the ‘gyre’ circulation, (ii) the mean Gulf Stream, and (iii) rings which
develop from the Gulf Stream (see Fig. 2.10).
c. Same as b. but now for the effects of ocean-atmosphere deformation.
DYNAMICAL OCEANOGRAPHY
3.4. Exercises on chapter 3
(3.1) Vorticity
Consider a flow having a width of 200 km directed northward with a maximum
velocity of 2 ms −1 near the latitude 27 ◦ N.
a. Calculate the value of the Coriolis parameter f 0 of this flow.
b. Determine a typical value of the relative vorticity of the flow.
c. Provide estimates of the time scales τ f , τ a and the Rossby number ǫ.
(3.2) Properties of the Coriolis acceleration
a. Show, in the same way as in section 3.1.2, that the rotation of the (e 1 , e 3 )
plane induces an acceleration −2Ωw cos θ in the e 1 direction and an acceleration 2Ωu cos θ in the e 3 direction.
In section 3.1.2 we derived the expression for the Coriolis acceleration a c .
b. Show that a c ⊥ Ω and a c ⊥ v.
(3.3) Rossby deformation radius
Both the external (R D ) and internal (L D ) Rossby deformation radii are important length scales in the ocean.
a. Use typical values of ocean depth (Fig. 1.1) and buoyancy frequency
(Fig. 3.4) to estimate L D and R D in the Atlantic Ocean at a latitude of 5 ◦ N,
30 ◦ N and 55 ◦ N.
b. Provide a priori arguments whether effects of stratification are important
in (i) the ‘gyre’ circulation, (ii) the mean Gulf Stream, and (iii) rings which
develop from the Gulf Stream (see Fig. 2.10).
c. Same as b. but now for the effects of ocean-atmosphere deformation.