Other, less common models based on work by Mackay, divide the slick into thick and thin segments that spread separately (Garcia-Martinez et al., 1996). Elliot et al. (1986) develop a spreading formula based on the shear processes cited earlier. Many models combine processes when computing their oil spread rates (Plutchak and Kolpak, 1981). The impact of these approaches in terms of modeling spill trajectories is unclear.

Advection

Few studies have been conducted on the subsurface advection of oil (Spaulding, 1995). The potential for mixing petroleum with water due to evaporation and cooling of surface waters seems limited as the buoyant forces working on the droplet tends to overcome these mechanisms. Limited modeling and observation suggest that the dissolved and particulate oil move as the bulk water moves and that the water moves in concert with mass circulation including the influence of currents and tides (Spaulding, 1995). Additional influences in the subsurface movement include vertical mixing by Langmuir circulation (McWilliams and Sullivan, 2000).

Empirical studies in the 1960s established that oil slicks on a sea surface are transported with the surface current (top centimeter of water) at 2.5 to 4 percent of the wind speed (Fallah and Stark, 1976; Reed, 1992). Furthermore, it was established that a deflection angle was appropriate to account for the Coriolis effect during slick transport. The drift velocity has largely been taken as 3.5 percent, which is the mean of the range shown above but also is a result of several carefully measured experiments (Audunson et al., 1984; Youssef and Spaulding, 1993; Reed et al., 1994). The deflection angle has been sometimes taken as 3 percent; however, Youssef and Spaulding (1993) have provided calculated values that vary with wind speed.

Langmuir Circulation

Langmuir cells (LC), often expressed as windrows, are a common feature in the sea and are generated by a wind-driven shear instability in combination with the mean Lagrangian motion from surface waves (so-called Stokes drift) as depicted in Figure 4-4. The so-called cells that compose LC have time scales of minutes and length of tens of meters. LC creates convergence and divergence zones on the sea surface running parallel to the wind vector. In the vertical, LC cause local downwelling regions that can drag surface pollutants such as oil down into the water column.

LC can potentially have many effects on surface oil. First, it enhances movement of the slick. Second, LC can create convergence and divergence zones on the surface that affect oil thickness, which in turn can affect biota, weathering rates, and cleanup strategies. Finally, LC enhances vertical dispersion of oil droplets. By pushing the droplets down into the

FIGURE 4-4 Diagram of Langmuir Circulation (LC) showing (a) perspective sketch of some of the features of LC (Note regions of convergence on the surface and characteristic length scale of the cells is “L” in the vertical and horizontal); (b) longitudinal dispersion and advection of floating particles by Langmuir circulation. A rectangular cloud of particles is shown at the start of LC motion (t=0) and after some time but before LC breaks us (t=T); (c) advective dispersion of a plume of seed particles when the wind and current angles are inclined at angle, a; and, (d) dispersion of seed particles at LC break-up or instability. (Modified from Thorpe, 2001, Elsevier Science, Inc.)

water column, LC can indirectly affect horizontal advection and dispersion, and increase the amount of hydrocarbon that dissolves into the water column.

McWilliams and Sullivan (2001) compare the LC enhancement of vertical and horizontal dispersion and argue persuasively that vertical dispersion is the most important. They argue that since the characteristic mixing length of LC



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