LE Windage Math Christopher H. Barker, January 10, 2001 Background For many years at HAZMAT, we have described the movement of oil by wind in terms of factors like: “1% to 4% of the wind speed.” This is based on a combination of an analytically derived factor of 3% of wind speed, and the empirical observation that oil tends to spread out in the direction of the wind. After a lot of experimentation and observation, using 1%-4% with OSSM seemed to work pretty well, and could be adjusted when overflights indicated that the oil was spreading in the direction of the wind either more or less that the model runs predicted. As a way of explaining the physics of this phenomenon, we can say that a given oil droplet is, in fact, being pushed up and down from the actual surface of the water by wave action, etc., so it will move faster and slower depending on how close the surface it is at any given moment. Computation In order to compute the windage, both the On-Scene Spill Model (OSSM) and General NOAA Operational Modeling Environment (GNOME) pick a random number between the range of windage values for each Lagrangian element (LE), and move it according to that number at each time-step. The result is that the LEs spread out in the direction of the wind. This method is very similar to the method used to compute diffusion, except that the spreading happens only in the direction of the wind. The amount of spreading is given by Equation 1, Equation 1. Amount of spreading from windage. where is the variance of the LEs locations, and S(t) is a spreading parameter that is a function of time, because the wind velocity is a function of time. For a constant wind, S would be constant and Equation 2 would follow: Equation 2. Variance of LEs from windage over time. that is, the variance of the particles grows linearly in time, the same as diffusion with a constant diffusion coefficient. The Problem With the algorithm used by OSSM and GNOME, at any given time-step you have Equation 3: Equation 3. LE spreading by wind resulting from the OSSM and GNOME methods.
LE Windage Math Christopher H. Barker, January 10, 2001 Background For many years at HAZMAT, we have described the movement of oil by wind in terms of factors like: “1% to 4% of the wind speed.” This is based on a combination of an analytically derived factor of 3% of wind speed, and the empirical observation that oil tends to spread out in the direction of the wind. After a lot of experimentation and observation, using 1%-4% with OSSM seemed to work pretty well, and could be adjusted when overflights indicated that the oil was spreading in the direction of the wind either more or less that the model runs predicted. As a way of explaining the physics of this phenomenon, we can say that a given oil droplet is, in fact, being pushed up and down from the actual surface of the water by wave action, etc., so it will move faster and slower depending on how close the surface it is at any given moment. Computation In order to compute the windage, both the On-Scene Spill Model (OSSM) and General NOAA Operational Modeling Environment (GNOME) pick a random number between the range of windage values for each Lagrangian element (LE), and move it according to that number at each time-step. The result is that the LEs spread out in the direction of the wind. This method is very similar to the method used to compute diffusion, except that the spreading happens only in the direction of the wind. The amount of spreading is given by Equation 1, Equation 1. Amount of spreading from windage. where is the variance of the LEs locations, and S(t) is a spreading parameter that is a function of time, because the wind velocity is a function of time. For a constant wind, S would be constant and Equation 2 would follow: Equation 2. Variance of LEs from windage over time. that is, the variance of the particles grows linearly in time, the same as diffusion with a constant diffusion coefficient. The Problem With the algorithm used by OSSM and GNOME, at any given time-step you have Equation 3: Equation 3. LE spreading by wind resulting from the OSSM and GNOME methods.