A calculation procedure is described to represent the displacement of a surface oil spill under the action of time-varying surface wind stress components; predictions using this technique are carried out for the 1970 Arrow spill in Chedabucto Bay, Nova Scotia.
The procedure presented is based on a convolution integral of the x- and y- components of a time-varying wind stress and is approximated in summation form for computer application. For an impulsive wind stress, it is demonstrated that the summation form is in agreement with an analytical solution by Fredholm.
The Arrow oil spill occurred on 4 February, 1970 and during the first week of March, oil was observed on the beaches of Sable Island some 120 miles Southeast of the spill location. Meteorological data in the form of reduced geostrophic winds have been published by Neu. These winds were utilized to predict the oil spill trajectory based on:
a surface velocity equal to 3% of the wind speed and aligned with the wind direction, and
a surface velocity determined from the convolution procedure presented in this paper.
The ability to predict the displacement of an oil slick is essential to proper planning of petroleum terminal facilities and allocation of clean-up resources in the event of an oil spill. The primary factors governing the displacement of an oil slick are the prevailing water currents which may be seasonal in nature and the winds which can be highly variable.
Most of the previous efforts (1),(2) to calculate the displacement of oil slicks have considered the slick velocity to be aligned with the wind velocity with a magnitude of a few percent of that of the wind. It is well-known, however that the earth's rotation causes a surface velocity which, in the northern hemisphere, is directed to the right of the wind vector. Also, the underlying layers of water cause a "memory" effect, Le. if the wind stress vanishes, the water currents exhibit a damped "rotary" motion feature as friction causes the current magnitude to approach zero. The effect of the earth's rotation can be quite significant in predicting the displacement of an oil slick.
The surface velocity (magnitude and orientation) resulting from a given applied wind stress depends on the turbulence structure distribution throughout the depth. The turbulence level is represented (rather artificially) via a linearized vertical eddy viscosity.
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For the general case in which s varies with depth, it is not possible to obtain an analytical solution for the surface velocity due to an applied wind stress. For an s value which is uniform over depth, the solutions for either a steady state wind or an impulsively applied wind stress are presented by V. W. Ekman (3).