**5. Numerical Modeling**

The ADvanced CIRCulation (ADCIRC) code was used for the numerical modeling in this study. The model is depth-integrated, and it is assumed that the simulated two-dimensional hydrodynamics are a major contributor to the transport of suspended materials, including oil tar balls contained within the water column. The model does not account for resuspension of settled materials or for the chemical evolution of oil tar balls. A previously developed model for the South Atlantic Bight [13], including Florida's First Coast and the St. Johns River, was utilized. Boundary conditions included tides on the open-ocean boundary located in the deep ocean along the 60°W meridian. In this implementation of the model, only tides and tidal circulation were considered as the hydrodynamic driving force. In future implementations, the model will be additionally forced with winds, which are important to circulation, transport and waves whereby the wave-driven hydrodynamics will be fed back into the circulation and transport. The purpose of excluding winds in the current model implementation was to be able to obtain a picture of the tidally driven transport, before we explore the transport driven by tides plus winds and waves.

Tidally driven transport is closely related to the velocity residuals at tidal and subtidal frequencies; *i.e.*, tidally time-averaged velocities [14,15]. Tidal currents are the dominant driver of seawater movement in coastal seas; however, to study tidally driven transport, it becomes necessary to extract the velocity residuals from the oscillating tidal currents. Eulerian velocity residuals are the rectification of transiently oscillating tidal velocities at a fixed position using a time-averaging scheme [16]. Calculation of the Eulerian velocity residuals in this work is performed using the concept of the tidal cycle mean operator [17].

Figure 4 shows vectors of velocity residuals, and the associated contours of magnitudes, computed from a harmonic analysis of 45 days of simulated (fully dynamic) tidal currents. The velocity residuals shown correspond to the STEADY constituent (frequency of zero/period of infinity) vector in the harmonically analyzed velocity (fort.54) file of ADCIRC [18]. The velocity residuals exhibit an ebb pattern through the inlet, with counter-rotating eddies spinning off the inlet. The ebb tidal velocities through the throat of the inlet reach as high as 15 cm/s in magnitude. The north eddy is approximately 3 km in diameter and produces velocity residuals of 0.5–2.5 cm/s. The north eddy directs velocity residuals toward Little Talbot Island (the north site). The south eddy is approximately 6 km in diameter and produces velocity residuals of 0.5–2.5 cm/s. The south eddy directs velocity residuals toward Atlantic Beach to Mayport (the south site).

There were 14 oil tar balls found on the north site and there was 1 oil tar ball found on the south site (Figure 3b). The north and south sites are located in the face of the shoreward components of the counter-rotating eddies of tidally driven velocity residuals ebbing from the inlet (Mayport) of the St. Johns River (Figure 4a). It is interesting that only 1 oil tar ball was found on the south site, compared to 14 oil tar balls that were found on the north site, which cannot be explained by the numerical modeling as implemented in this study. Future work will impose wind forcing on the model as well as can explore the wave climate and resulting field of wave radiation stresses that could drive oil tar ball transport toward the shore. Local sources of oil (likely relic oil from historical bilge dumping that would take place offshore before ships would port into Jacksonville)

could also be more prevalent north of the inlet and sparser south of the inlet. In this implementation of the model, it can only be concluded that there is a tendency in the tidal circulation for transport to be directed onto the north and south sites via tidally driven eddies.

**Figure 4.** Tidally driven velocity residuals: (**a**) vectors and (**b**) the associated contours of magnitudes for the offshore waters of Florida's First Coast.

#### **6. Conclusions**

This study was spawned as a pilot project to define a methodology for establishing baseline conditions of beached oil tar balls along Florida's First Coast. As a result of the pilot project, a research team (local to Jacksonville) of mappers, modelers and field experts has been formed. In addition, the pilot project has established fieldwork protocols for collecting oil tar balls on Florida's First Coast beaches, modeling methods for simulating hydrodynamics in the St. Johns River and offshore waters and laboratory tests for confirming or negating collected samples as being oil tar balls.

The methodology presented in this paper for defining baseline conditions of beached oil tar balls along Florida's First Coast was designed with up-scaling in mind. The project could be scaled spatially by including a longer stretch of beach. In temporal scope, the project could involve more frequent site visits or the collection period could be extended. In the laboratory, there could be more extensive testing with the goal of more conclusively identifying oil tar balls.

The study concludes that a limited amount of oil tar balls wash up during normal conditions, suggesting that the port activity in the St. Johns River is not a major contributor of oil tar ball washup on Florida's First Coast beaches. Future work will be to conduct a temporal analysis of the data to discover any trends or causative factors (e.g., storms) to oil tar ball wash-up. Finally, the numerical modeling will be extended to incorporate transport into the hydrodynamic simulation as well as to explore the effect of waves and wave-induced current as transport mechanisms.
