Spirals and Sea Surface Dynamics

C.Y. Shen and T.E. Evans
Remote Sensing Division

Introduction: Space flights and satellite-borne sensors have enabled surface features of the ocean to be observed in their entirety, many for the first time. The "spiral" of ~10 km diameter is one such feature discovered from space (Fig. 4) and, by far, is perhaps the most intriguing. Not only is its presence widespread, but its rotation is surprisingly distinct- cyclonic in the northern hemisphere and anticyclonic in the southern hemisphere. Since the spiral feature is made visible by slick lines wound up by the surface current, its occurrence suggests that some previously unrecognized processes are active near the sea surface. One possibility that has been considered is that the slick lines arise from surfactants concentrated along a converging density front and that their spiral shape is induced by eddies formed through flow instability along this front, which typically contains excess cyclonic or anticyclonic vorticity in the northern or southern hemisphere, respectively.¹ Although this explanation is plausible, evidence such as that shown in Fig. 4 suggests that many slick lines and spirals may have formed in situ, unrelated to the frontal convergence process. This process would have compressed multiple slick lines and would have produced spirals aligned along the convergence, none of which is apparent in the figure. On the other hand, a different process, known as "inertial" instability, can arise naturally in near-surface currents, with horizontal shears varying on a 10-km or less scale. Through three-dimensional computer modeling, we have shown that this instability can lead directly to the formation of slick lines and spirals, without the restrictive frontal preconditioning. Thus, it potentially can be a significant process near the sea surface, given the widespread occurrence of slick lines and spirals.

FIGURE 4
Sun-glint photograph of the central Mediterranean Sea taken from the Space Shuttle in 1984. Area covered (cropped from the original published photo) is ~150 km on each side. The bright bands are naturally occurring slicks. Numbers 1, 2, and 3 identify three of the several spirals visible on the sea surface. Some ship wakes are also visible on the surface and are indicated by numbers 4 and 5. (Courtesy of National Aeronautics and Space Administration, Oceanography from Space, 1986)

Inertial Instability: For a parallel shear current, the condition for the onset of inertial instability requires the sum of the horizontal current shear V/ x and twice the Earth's rotational frequency 2ω to be negative, viz., V/ x + 2ω < 0; here, V is the rectilinear current velocity directed perpendicularly to the across-stream coordinate x in a right-handed rectangular coordinate system. The onset of this instability is akin to the centrifugal instability that occurs in a rotating fluid body when the balance between the internal centrifugal force and pressure gradient force is disrupted by a local change of fluid rotation, a role played by V/ x on the rotating Earth. Thus, in the northern hemisphere, the inertially unstable currents are those with V/ x < 0 and | V/ x|> 2ω, since ω > 0 with respect to a right-handed coordinate system in the northern hemisphere. The opposite holds in the southern hemisphere where ω < 0. Noting this sign difference, it suffices to describe the northern hemisphere case.

Vortex and Spiral Generation: Figure 5 shows the unfolding instability in the ocean surface mixed layer, assumed 30-m depth, calculated with a nonlinear hydrodynamic model, with V = (30 cm/s) sin(2πx/ 10 km) and ω = 3.5 X 10^-5/s, the local normal component around mid-latitudes. The instability acts normal to V in an across-current vertical section. In less than a day, the distortion of V in the inertially unstable region ( V/ x < 0) has become quite pronounced. As the instability continues, an increasingly larger portion of V including the inertially stable region (dV/dx > 0) is affected. By day 2.37, the unstable motion has filled the entire width of the current. By this time, it is significant to note that the anticyclonic shear has been greatly reduced by its conversion to across-stream motion and is no longer inertially unstable. Simultaneously, the stable cyclonic shear region has become narrow and the shear has been enhanced by the across-stream motion.² Thus, the process has led to the emergence of a current structure that is inertially stable overall but strongly asymmetrical, with cyclonic shear favored.

FIGURE 5
Vertical section of current velocity V. Positive V (blue) into the page and negative V (green) out of page. The contour interval is 3 cm/s. (Adapted from Ref. 2.)

Once the narrow, strongly cyclonic shear region emerges, the stage is set for the formation of the cyclonic eddy and spiral. Figure 6 shows the model sea surface at day 2.54. For better viewing, the cyclonic shear region has been shifted to the center of the plot. The velocity vector plots show that the center of the enhanced cyclonic shear zone rapidly develops a bulge in which a closed cyclonic circulation forms and evolves into a nearly circular eddy. This development can be explained in terms of the wellknown shear flow instability process, in which concentrated shear induces its own across-stream circulation. Shown below each velocity vector plot is the simulated "surfactant" tracer field evolved from an initially uniform distribution. The bright bands or lines are high surfactant concentrations produced by the surface flow convergence occurred during the inertial instability. These plots show how the central bright "slick" line is eventually wound up by the vortical motion into a cyclonic spiral. These simulated patterns of slicks are thus similar to those in Fig. 4. The formation of a spiral from inertial instability is reproducible by using initial velocity distributions that differ from the case illustrated here, and the process is presently being quantified.

FIGURE 6
Plan view of the model sea surface. The longest velocity vector is 19.6 cm/s. The relative concentration of "surfactant" tracer is shown, with the upper 10% in white and lower 2% in blue.

Summary: Space-borne remote sensing is relied upon today by the Navy as well as the civilian community for gathering up-to-date information about the ocean environment. To be able to extract useful information from remote sensing requires proper interpretation of what has been observed. The intriguing spiral feature discovered through remote sensing has been shown by our modeling study to likely be a product of near-surface current inertial instability. NRL is planning a series of field experiments to measure the spiral and associated slick lines so that a full understanding of this feature can be achieved.

[Sponsored by ONR]

References
¹ W. Munk, L. Armi, K. Fischer, and F. Zachariasen, "Spirals on the Sea," Proc. Roy. Soc. Lond. A 456, 1217-1280 (2000).
² C.Y. Shen and T.E. Evans, "Inertial Instability of Large Rossby Number Horizontal Shear Flows in a Thin Homogeneous Layer," Dyn. Atmos. Oceans 26, 185-208 (1998).