Chapter 10  Geostrophic Currents 10.7 Currents From Hydrographic Sections Lines of hydrographic data along ship tracks are often used to produce contour plots of density in a vertical section along the track. Crosssections of currents sometimes show sharply dipping density surfaces with a large contrast in density on either side of the current. The baroclinic currents in the section can be estimated using a technique first proposed by Margules (1906) and described by Defant (1961: Chapter 14). The technique allows oceanographers to estimate the speed and direction of currents perpendicular to the section by a quick look at the section.
To derive Margules’ equation, consider the slope ∂z/∂x of the stationary interface between two water masses with densities ρ_{1} and ρ_{2} (see Figure 10.11). To calculate the change in velocity across the interface we assume homogeneous layers of density ρ_{1} < ρ_{2} both of which are in geostrophic equilibrium. Although the ocean does not have an idealized interface that we assumed, and the water masses do not have uniform density, and the interface between the water masses is not sharp, the concept is still useful in practice. The change in pressure on the interface is:
and the vertical and horizontal pressure gradients are obtained from (10.6):
Therefore:
The boundary conditions require δp_{1} =δp_{2} on the interface if the boundary is not moving. Equating (10.20a) with (10.20b), dividing by δx, and solving for δz/δx gives:
where β is the slope of the sea surface, and γ is the slope of the boundary between the two water masses. Because the internal differences in density are small, the slope is approximately 1000 times larger than the slope of the constant pressure surfaces. For small values of β and γ, β is the slope of the sea surface, and γ is the slope of the interface. Consider the application of the technique to the Gulf Stream (Figure 10.8). From the figure: φ = 36°, ρ_{1} = 1026.7 kg/m^{3}, and ρ_{2} = 1027.5 kg/m^{3} at a depth of 500 decibars. If we use the σ_{t} = 27.1 surface to estimate the slope between the two water masses, we see that the surface changes from a depth of 350 m to a depth of 650 m over a distance of 70 km. Therefore, tan γ = 4300 × 10^{6} = 0.0043, and Δv = v_{2}  v_{1} = 0.38 m/s. Assuming v_{2} = 0, then v_{1} = 0.38 m/s. This rough estimate of the velocity of the Gulf Stream compares well with velocity at a depth of 500 m calculated from hydrographic data (Table 10.4) assuming a level of no motion at 2,000 decibars. The slope of the constantdensity surfaces are clearly seen in Figure 10.8. And plots of constantdensity surfaces can be used to quickly estimate current directions and a rough value for the speed. In contrast, the slope of the sea surface is 8.4 × 10^{6} or 0.84 m in 100 km if we use data from Table 10.4. Note that constantdensity surfaces in the Gulf Stream slope downward to the east, and that seasurface topography slopes upward to the east. Constant pressure and constant density surfaces have opposite slope. If the sharp interface between two water masses reaches the surface, it is an oceanic front. Such fronts have properties that are very similar to atmospheric fronts. Eddies in the vicinity of the Gulf Stream can have warm or cold cores (Figure 10.12). Application of Margules’ method these mesoscale eddies gives the direction of the flow. Anticyclonic eddies (clockwise rotation in the northern hemisphere) have warm cores (ρ_{1} is deeper in the center of the eddy than elsewhere) and the constantpressure surfaces bow upward. In particular, the sea surface is higher at the center of the ring. Cyclonic eddies are the reverse.


Department of Oceanography, Texas A&M University Robert H. Stewart, stewart@ocean.tamu.edu All contents copyright © 2005 Robert H. Stewart, All rights reserved Updated on October 13, 2006 