Water Bodies Subjected to Waves

Transcription

1 The Transport of Oil in Water Bodies Subjected to Waves Jim Weaver, PhD National Exposure Research Lab, Athens GA Michel C. Boufadel, PhD, PE Temple University, Philadelphia Pennsylvania

2 PROBLEM STATEMENT - Traditional oil spill models focus on large-scale transport -The physics of waves and their effects on oil droplets are not directly addressed d The situation where dispersal of oil has just occurred: How are droplets transported in non-breaking waves?

3 Oil Droplet Transport NUMERICAL Concept MODEL Wave Theory: water velocity Buoyancy and Dispersion Movement of Oil Droplets Boufadel, Bechtel, and Weaver, Marine Pollution Bulletin, 2006 Boufadel, fdldu, Kaku, Kk and dweaver, Environmental tlmdli Modeling & Software, 2006

4 Convection-Diffusion Convection Diffusion Equation with Buoyancy z c w W y c V x c U t c B z c D z y c D y x c D x z y x t z y x z z y y x x Numerical solution suffers from numerical dispersion Numerical solution suffers from numerical dispersion Use Langrangian (particle tracking) approach Neglibible transverse velocity (v = 0)

5 Bouyant Velocity, w B w B, d, B 1 C d Δρ = density difference = ρ w ρ o d = particle diameter C d = drag coefficient w, d, B C d w, d, B o C d 0 w B 0.15 Smaller or more dense vs. Larger or less dense

6 Non-dimensional Particle Tracking x z n 1 xn u t R 2D t n w w t R D t 1 zn B 2 Updated particle positions due to Time (Δt) Velocity (u, w) Turbulent Diffusion ((2DΔt) 0.5 ) Randomness (R) Wave Steepness (ε) (in z) buoyancy (w B )

7 u w Velocities from Stokes Second Order Wave theory 2 Hk Hgk 3 kz H k 2kz e cos kx t e cos 2 kx t 2 Hgk 2 e kz sin u u ; w L T H = wave height L = wave length T = wave period σ = 2π/T H k 16 2kz kx t e sin 2 kx t w H T k 2 2 ; L T

8 Velocity distribution beneath a progressive wave

9 Oil Droplet Positions

10 Monte Carlo Simulation Wave steepness: BuoyancyVelocity: y y w B B w H T Dimensionless turbulent diffusion coefficient: H L 0.05 and 0.0 to D D H T particles and 500 simulations

11 Effect of buoyancy on the vertical location of the centroid, Zc for H/L==0.1. Depth unit is wavelength Lighter, larger droplets near surface Neutrally bouyant or smaller drop

12 Effect of buoyancy on the horizontal location of the centroid, Xc for H/L= = Stoke s drift velocity: 2 H C 4 z exp L 2 L Z = 0 at water surface Lighter, larger experience higher velocity

13 Effect of buoyancy on the dimensionless vertical variance, z2 for H/L= =0.1. Lighter, larger droplets remain in smaller zone with lower variance

14 Effect of buoyancy on the dimensionless horizontal variance, 2 x for =0.1. VarX Lighter, larger 5 wb= droplets spread wb=0.02 wb=0.05 wb=0.08 less less X 4 _ wb= wb=0.15 X variation in X 3 Stoke s velocity 2 1 X_ + X_ + X _ + X _ + 0 X_ X _ Time (Wave Periods) + X _ + X _ + _ +

15 Dimensionless spreading coefficients E x as function of time for H/L E 2 d dt 2 Horizontal spreading coefficients tend toward constant value: D + drift

16 For the same size distribution, light oils moves faster but spread less than heavy oils. In fairly CONCLUSIONS general conditions, the oil droplets become well mixed in the top 5 meters of the water column within 15 to 20 minutes. A novel dimensionless formulation to generalize the results to any oil was introduced.

17 ACKNOWLEDGEMENTS Although this work was reviewed by EPA and approved dfor presentation, ti it may not necessarily reflect official Agency policy. Mention of trade names or commercial products does not constitute endorsement or recommendation for use.

18

19