Dynamic Ocean Fronts

A.L. Cooper, R.P. Mied, G.J. Lindemann, and M.A. Sletten
Remote Sensing Division

Introduction: Density fronts are ubiquitous in remote ocean imagery. They are driven by buoyancy effects associated with such phenomena as thermal plumes from power plant effluents, spreading oil and pollution slicks, and estuary and river discharges into a higher salinity environment. Understanding these features is important in enhancing the Navy's ability to interpret remotely sensed imagery for extracting useful environmental and tactical information.

Observations: Figure 3 is a radar image (9.375 GHz center frequency, horizontal polarization) of a front at the edge of the Chesapeake Bay tidal out-flow plume. It displays distortions commonly observed in the frontal outcrop line. Waves, sharp corners, bulges, and other small-scale structure on scales of hundreds of meters to a few kilometers can be present. The bulges are oriented toward the heavier fluid, and the sharp corners are directed toward the lighter fluid. Fronts appear as regions of large radar cross section, which is generally attributed to an enhanced gravity-capillary wave spectrum and attendant wave breaking caused by surface convergence across the front.¹

Figure 4 shows the complete 4-hour frontal evolution sequence.² Each segment indicates the position and shape of the front as determined by a particular radar image in the sequence. Early in the sequence, a single bump can be observed in the front near (36° 57' N, 75° 57' W), and this structure is emphasized by delineating it with a thicker line than the one used to represent the remainder of the front. The bump appears to originate over a region with steep bottom topography. Over the next 4 hours, its amplitude and width grow substantially as the bulge translates to the southeast.²

Evolution Model: To understand the evolution of fronts such as those in Figs. 3 and 4, we have developed a new two-dimensional buoyant plume model based on gas dynamic shock-tube theory,³ but germane to the unique flows in gravity current fronts.⁴ In the model, we assume

• Geometric optics (the ray assumption), which presumes that each element of the front propagates along a ray that is locally normal to the front.
• One-dimensional nonlinear fluid motion, which treats the frontal propagation as the collective motion of a bundle of gently bending ray tubes in which the dynamics in each one is governed locally by the one-dimensional equations of fluid mechanics.
• Reduced-gravity physics, which allows us to view the buoyant fluid as floating on top of a lower water layer of effectively infinite depth. This assumption is approximately satisfied in coastal waters, rendering the details of the underlying bathymetry unimportant.
• Frontal jump conditions, which constrain the velocity and layer thickness at the plume nose.

The resulting model is hyperbolic, and, therefore, the frontal evolution is an intial value problem with the self-generated subsequent behavior completely defined once initial conditions are prescribed.

Model Results: The length scales of frontal perturbations can be as large as a few tens of meters to several kilometers. In Fig. 5, we assume an initial periodic perturbation

X0 = a cos (δy),

(1)

where a = 0.04 km, δ = 10.5 km^-1 (600-m wavelength), and a uniform initial local front-normal propagation speed of 0.18 m/s. Natural fluctuations with this magnitude might be induced by a number of me-chanisms, such as an instability of an along-front current or a spatially varying wind stress.

Substantial frontal changes occur while the front oscillates. That is, a trough in the initial configuration evolves into a crest (and vice versa) in an astonishingly short time (≈ 0.75 h). This oscillatory process is explained by the nonlinear focusing of the front by its own curvature.^4,5 By the end of the simulation (1.5 h), the front consists only of a series of crests joined at sharp angular junctions called "breaking frontal waves," which point toward the lighter fluid as seen in the observations.

Along-front wavelengths vary temporally. At t ≈ 1 h for instance, corrugations with wavelengths of ~0.4 and ~0.2 km are visible. This is similar to the observations in Fig. 4 and may suggest that these mixed-wavelength shapes are simply products of natural frontal evolution.

Conclusions: Under the idealized conditions assumed, the frontal evolution is a self-generated initial value problem. Clearly, the actual frontal conditions and evolution displayed in Figs. 3 and 4 are significantly more complicated than may be captured in the simulations. Nevertheless, a number of inferences have been drawn from the simulations shown, and much of the modeled behavior mimics the observations.

[Sponsored by ONR]

References

¹ R.W. Jansen, C.Y. Shen, S.R. Chubb, A.L. Cooper, and T.E. Evans, "Subsurface, Surface, and Radar Modeling of a Gulf Stream Current Convergence," J. Geophys. Res. 103, 18,723-18,743 (1998).
² M.A. Sletten, G.O. Marmorino, T.F. Donato, D.J. McLaughlin, and E. Twarog, "An Airborne, Real Aperture Study of the Chesapeake Bay Outflow Plume," J. Geophys. Res. 104, 1211-1222 (1999).
³ G.B. Whitham, Linear and Nonlinear Waves (John Wiley and Sons, Somerset, NJ, 1974).
⁴ A.L. Cooper, R.P. Mied, and G.J. Lindemann, "Evolution of Freely Propagating, Two-dimensional Surface Gravity Current Fronts," J. Geophys. Res. 106, 16,887-16,901 (2001).
⁵ R.P. Mied, A.L. Cooper, G.J. Lindemann, and M.A. Sletten, "Wave Propagation Along Freely Propagating Gravity Current Fronts," Dyn. Atmos. Oceans 36, 59-81 (2002).