VELOCITY DISTRIBUTIONS

The Gulf Stream Current Has Excellent Velocity Distribution

To fully appreciate the generating power that is contained in the Gulf Stream off South Florida, not only do we need to know about the range of the current’s velocities, but also about how those velocities are distributed. The designers of wind turbines must know the probabilities of various wind speeds to optimize their designs to minimize the generating costs.  They use the Weibull system to measure those probabilities for the potential sites.  When we apply that system to the Gulf Stream, we get an interesting result.  The winds are erratic because they are driven by the imbalances of air pressures caused by changing air densities produced by the uneven heating of the atmosphere – whereas, the Gulf Stream is driven by those steady forces produced by the Earth’s eastward rotation.   

In the examples of the Weibull plottings that follow, the vertical scales represent the percentages of time that the Gulf Stream (red) and Florida’s wind (blue) would be flowing at those speeds on the horizontal scale, stated in both meters per second and in miles per hour. Half the time the velocities will be above the median (the vertical line) and half the time they will be below it.  Since the probability that the wind will be blowing at some wind speed, including zero, must be 100 percent, the areas under the curves will always equal 1.  The Weibull plottings show estimated velocities in the Gulf Stream’s central axis, at a typical wind site in Florida, and at a good wind site (from the Danish Wind Industry Association’s website at www.windpower.org).  The kinetic energy is proportional to the densities, multiplied by the cubes of the velocities.  Because the water’s density is 854 times greater than an equal volume of air, its kinetic energy is 854 times greater at the same velocities. 


A better understanding of the Gulf’s Stream’s generating potential can be gained by spreading the current’s velocities out over more intervals.  Because we want to maintain a relationship to wind power for comparison, we will convert the estimated speeds of the heavier water into the speed equivalents of the air by using this equation:


The next graph adjusts the distribution of the water velocities to the equivalents of the wind.  It does not reflect the differences in power caused by the cubing of the velocities.  Because the stronger currents produce most of the power, much more power can be produced because of the distribution of the velocities than would be produced if the current always flowed at its average speed.


The velocities on the surface can be affected by strong winds.  The velocities at the turbines’ operating depths would be less affected by the winds and more by the Coriolis force from the Earth’s eastward rotation.  For this reason the velocity distribution at the turbine’s operating depths should have a smaller spread between the highest and lowest speeds.  The following graph on the left shows a Weibull Distribution analysis of the possible water velocities at the water’s surface and the Gulf Stream Turbines’ operating depths.



The above graph that is on the right shows the estimated distribution of the power near the surface of the Gulf Stream’s central axis.  This is the Wiebull distribution percentages, multiplied by both the density and the velocities cubed.  Because the kinetic energy increases with the cube of the velocities, the power curve shifts to the right of the Wiebull plot of the velocity distribution shown in the both the upper graph and by the blue line in the graph to the left.

 

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