Climate Physics and Chemistry Ocean and Climate: Problem Set Corrected Problem 2. 1. The pressure ﬁeld at depth } = 1000m in the ocean is found to follow the rule, ¢ ¡ ¢ ¡ s = s0 cos {@104 cos |@104 = The origin of | is taken to be 30 N and {> | are measured in meters. What are the northward and eastward components of geostrophic velocity at { = 104 @2> | = 0? If the ﬂuid density is approximated as uniform, = 0 = 1=03 × 103 kg/m3 > how much water (mass) is moving northward between the seasurface and 1000m, between { = 0 and { = 104 @2? For a numerical answer, let s0 = 238N/m2 = (Hint: Treat the seasurface as ﬂat, and note that the pressure gradient is independent of depth if the density is uniform.) 2. A ship measures the temperature and salinity in the ocean at { = 0> and { = 50km at a latitude of 45 N. When converted to density, the two proﬁles are found to be closely approximated as, ¡ ¢¢ ¡ ({ = 0> }) = 1=03 × 103 kg/m3 1 }@ 2 × 104 > ¡ £ ¢¤ ({ = 50km,}) = 1=03 × 103 kg/m3 1 (} + 1 × 1037 } 2 )@ 2 × 104 where } is in meters. Compute and plot the northward velocity as a function of } for 0 } 3000m under the assumption that } = 2000m is a level of no motion. What is dierent at 10 N? Take gravity, j = 10m/s2 = 3. A uniform wind blows towards the northeast such that the windstress on the ocean is = 0 (1> 1). Using the equations C2x C} 2 C2y ix = D 2 C} iy = D which govern the Ekman layer, ﬁnd x> y as a function of }= (Hint: multiply the second equation by l and add to the ﬁrst equation. Solve this equation for the complex quantity x + ly=) (In Problems 1 and 2, the numerical result is less important than telling me what you are doing.)