1. Analytical Benthic Flux Model Forced by Surface-Gravity Waves Application to the South Atlantic Bight j.n. king U.S. Geological Survey Florida Integrated Science Center Fort Lauderdale, FL, USA Definition ◊ Model ◊ SAB ◊ Conclusions

2. Benthic flux is the rate of flow of some quantity across the bed of a water body, per unit area of bed. Benthic flux is a vector quantity, where the vector is oriented normal to the bed. Benthic flux units are a function of the quantity under consideration: volume quantity: L 3 T -1 L -2 (=LT -1 )volume quantity: L 3 T -1 L -2 (=LT -1 ) mass quantity: M T -1 L -2mass quantity: M T -1 L -2 Benthic flux is a transient process. Definition :: Benthic Flux Definition ◊ Model ◊ SAB ◊ Conclusions

3. Definition :: Benthic Flux Benthic flux is the rate of flow of some quantity across the bed of a water body, per unit area of bed. Benthic flux is a vector quantity, where the vector is oriented normal to the bed. Benthic flux units are a function of the quantity under consideration: volume quantity: L 3 T -1 L -2 (=LT -1 )volume quantity: L 3 T -1 L -2 (=LT -1 ) mass quantity: M T -1 L -2mass quantity: M T -1 L -2 Benthic flux is a transient process. Definition ◊ Model ◊ SAB ◊ Conclusions

4. Burnett et. al. (2003) Also known as: Seepage Irrigation Flushing Ventilation Percolation Sub-tidal pump Submarine ground water discharge (SGD) Submarine ground water recharge (SGR) Submarine pore water exchange (SPE) Related processes: Deposition & Resuspension Bio-turbation Bio-irrigation Salt fingering Fluidization of sediment in the surf zone newer … older Benthic flux is independent of direction: benthic discharge (flux): gw => swbenthic discharge (flux): gw => sw benthic recharge (flux): sw => gwbenthic recharge (flux): sw => gw Benthic flux is independent of water body: wetland, river, lake, estuary, lagoon, ocean Benthic flux is independent of location in the water body: surf zone, shelf, deep ocean Definition ◊ Model ◊ SAB ◊ Conclusions

5. Processes that Drive Benthic Flux Definition ◊ Model ◊ SAB ◊ Conclusions

6. Surface-Gravity Wave over Rigid, Porous Media Assume (DBBC) (KBBC) (DFSBC) (Bernoulli) (velocity potential) (Darcy) Reid & Kajiura (1957) +x +z z=-h 4Unknowns – 4Equations z=0 (KFSBC) Definition ◊ Model ◊ SAB ◊ Conclusions

8. King, Mehta & Dean (2008?) Generalized Analytical Model for Benthic Water Flux Definition ◊ Model ◊ SAB ◊ Conclusions

9. Moore (1996) Moore (1999) Definition ◊ Model ◊ SAB ◊ Conclusions

10. Moore (1996) A 226Ra = 0.19 dpm/L 0.01 dpm/L 0.08 dpm/L Estuaries Ocean SAB A 226Ra.Excess = 0.19-0.01-0.08 = 0.10 dpm/L V SAB.InS = 20km × 320km × 10m = 6.4×10 13 L T residence.226Ra = 30d Å 226Ra.Excess = 0.10×(6.4×10 13 )÷30 =2.1×10 11 dpm/d Moore (1999) Definition ◊ Model ◊ SAB ◊ Conclusions

11. Moore (1996) A 226Ra = 0.19 dpm/L 0.01 dpm/L 0.08 dpm/L Å 226Ra.Excess =2.1×10 11 dpm/d Estuaries Ocean 7 dpm/L Pore Water SAB Q Moore =2.1×10 11 ÷7 =3×10 10 L/d =350m 3 /s q Moore =0.5cm/d Definition ◊ Model ◊ SAB ◊ Conclusions

12. Li and others (1999) Three (nearshore) processes: – Tidal pumping on sloped beach 130m 3 /s or 37%Q Moore – Wave set up 190m 3 /s or 54%Q Moore – Terrestrial hydraulic gradient (from Younger,1996) 14m 3 /s or 4%Q Moore Linear sum = 14+130+190 = 334m 3 /s or 95%Q Moore Definition ◊ Model ◊ SAB ◊ Conclusions

13. Application of Case I to SAB shoaled and damped Definition ◊ Model ◊ SAB ◊ Conclusions Riedl et al. (1972) canonical Riedl et al. (1972) bathymetry from Riedl et al. (1972)

14. Moore & Wilson (2005) 0.2dpm/L 1.3dpm/L Moore & Wilson (2005) Martin et. al. (2006) Wave mixed zone 7dpm/L? Definition ◊ Model ◊ SAB ◊ Conclusions

15. Updated Moore (1996) A 226Ra = 0.19 dpm/L 0.01 dpm/L 0.08 dpm/L Estuaries Ocean Pore Water SAB Q Moore = 2.1×10 11 ÷0.3 = 7×10 11 L/d = 8100m 3 /s q Moore = 11cm/d 0.5 dpm/L 0.19dpm/L Definition ◊ Model ◊ SAB ◊ Conclusions 7 dpm/L Pore Water

16. Conclusions Waves matter! Waves matter! Surface gravity waves advect pore water constituents into surface waters. Shelf-wide processes are probably larger contributors than near-shore processes. = 8,100m 3 /s too large? What about bedform effects? Definition ◊ Model ◊ SAB ◊ Conclusions

17. Future Work (?) Wave mixed-zone Wave mixed-zone: other forcing mechanisms transport pore water constituents onto the wave-mixed zone – Density gradients – Pressure gradients – Concentration gradients – Episodic gradients Numerical model! Definition ◊ Model ◊ SAB ◊ Conclusions

18. Questions?