Fluid Dynamics of the Atmosphere and Ocean - Problem Set 9

ProЫem set 9 1) Assume that the atmospheric Ekman layer over the earth's surface at а latitude of 45 degrees north сап Ье approximated Ьу an eddy viscosity of vv = 1О m2/s. If the geostrophic velocity above the Ekman layer is 1О m/s, what is the Ekman transport across isobars? [КСО4: 14.3] 2) Between 15 degrees north and 45 degrees north, the winds over the North Pacific consist mostly of the easterly trades (15 degrees north to 30 degrees north) and the westerlies (30 degrees north to 45 degrees north). An adequate representation of the zonal wind stress is where тO = 0.15 N/m2 is the maximum wind stress and L = 1670 km. Taking р0 = 1028 kg/m3 and the value of the Coriolis parameter coпesponding to 30 degrees north, calculate the Ekman pumping. Which way is it directed (up or down)? Calculate the vertical volume flux over the entire 15 degree to 45 degree strip of the North Pacific (width = 8700 km). Express you answer in sverdrup units ( 1 sverdrup = 1 Sv = 106 m3 /s). [CR94: 5.6] 3) In class we derived DOJZ + fJv = о (1) Dt using Kelvin's Circulation Theorem for а rotating, inviscid, barotropic, fixed depth fluid. Previously, we derived а vorticity equation for а rotating fluid given Ьу 1 ? Dro (2) -=((ro+2.Q)-v')u+-2 v'pxv'p+vv-ro, Dt р and if the fluid is assumed to Ье inviscid, barotropic, and fixed depth, this equation appears to reduce to Dro = (3) О. Dt Explain why equation ( 1) is different from equation (3). Which is correct? 4) Derive expressions for the dispersion relation, phase speed, and group velocity of the Rossby wave solutions of equation (1) above. Include а plot of contours of OJ / /J as а function of zonal and meridional wave numbers.