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Deutsche Hydrografische Zeitschrift

, Volume 39, Issue 3, pp 113–137 | Cite as

Shear diffusion and the spread of oil in the surface layers of the North Sea

  • Alan J. Elliott
Article

Summary

Controlled releases of oil and dye have been made in the southern North Sea, and the slicks observed during the six hours following release compared with the results of a numerical model. The model included the vertical and lateral shears associated with the tidal streams, the vertical shears due to Stokes drift and a logarithmic wind-driven velocity profile. A patch of oil was modelled as a distribution of droplets whose individual buoyancies depended on droplet size, and the turbulence in the water column was represented by a three-dimensional random walk process. The elongation and orientation of the predicted slicks were in good agreement with observations, suggesting that near-surface vertical shears are dominant in determining the spreading rate of a slick soon after release. The buoyancy of the droplets effectively limits the depth through which the oil can mix, consequently the oil spreads in a manner that represents a combination of first and second stage shear diffusion processes. Numerical results showed that the major axis of a slick should elongate linearly with time, while the width of a slick will grow ast0.5. The model correctly predicted the occurrence of thicker oil towards the leading edge of a slick, and the alignment of slicks in the direction of the wind.

Keywords

Droplet Size Spreading Rate Vertical Shear Lateral Shear Random Walk Process 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

List of symbols

CD

surface drag coefficient

Δx, Δz

horizontal and vertical step sizes during the random walk

Δt

time interval in the random walk

d

diameter of an oil droplet

dc

critical diameter for rise velocity

H

water depth

Hs

significant wave height

k

2π/L, circular wave number

Kh

horizontal diffusivity

Kv

vertical diffusivity

L

wavelength of the surface waves

S

velocity shear

T

tidal period, wave period

U*

surface friction velocity

UB

vertical rise velocity

Us

wind-driven surface velocity

W10

wind speed

z

depth beneath the surface

z0

thickness of the uniform velocity wind-driven surface layer

|

analogous to a roughness length

Zc

depth to which wind effects penetrate

α

wind penetration factor,zcL

η

Von Karman's constant

ϱo

oil density

ϱw

water density

σx, σy

standard deviations of concentration along and across a patch

ω

2π/T, circular frequency

ν

viscosity

Scherungsdispersion und die Ausbreitung von Öl in der Oberflächenschicht der Nordsee

Zusammenfassung

Öl und Farbe wurden in der südlichen Nordsee kontrolliert eingebracht und über sechs Stunden verfolgt. Die beobachteten Flecken werden mit den Ergebnissen eines numerischen Modells verglichen. Das Modell beinhaltet vertikale und laterale Scherung des Gezeitenstroms und vertikale Scherung durch Stokes Drift und ein logarithmisches Windprofil. Der Ölfleck wird modelliert als Verteilung von Tröpfchen, deren individueller Auftrieb vom Durchmesser der Tröpfchen abhängt. Die Turbulenz in der Wassersäule wird mit dreidimensionalem “Random Walk” simuliert. Die Ausdehnung und Richtung der vorhergesagten Flecken sind in guter Übereinstimmung mit den Messungen. Die Ergebnisse deuten darauf hin, daß die vertikale Scherung an der Meeresoberfläche der entscheidende Faktor für die Ausbreitungsrate der Flecken kurz nach der Einbringung ist. Der Auftrieb der Tröpfchen limitiert die Mischungstiefe von Öl, d. h. die Ausbreitung des Öls kann verstanden werden als Kombination von Scherungsdispersion erster und zweiter Ordnung. Die Ergebnisse des numerischen Modells zeigen, daß die Hauptachse des Flecks linear mit der Zeit wächst, während die Breite des Flecks mitt0,5 zunimmt. Das Modell liefert eine größere Schichtdicke von Öl am äußersten Rand des Flecks und eine Ausrichtung der Flecken in Windrichtung.

Diffusion du cisaillement et dispersion des hydrocarbures dans les couches superficielles de la Mer du Nord

Résumé

Des émissions contrôlées d'hydrocarbures et de matières colorantes ont été effectuées en Mer du Nord méridionale; les nappes ont été observées durant les 6 heures suivant l'émission et comparées aux résultats d'un modèle numérique. Ce modèle incluait les cisaillements horizontaux et verticaux associés aux courants de marée, les cisaillements dus à la dérive de Stokes et un profil de vitesse logarithmique induite par le vent. Une tache d'hydrocarbure était modélisée comme une répartition de gouttelettes dont la flottabilité individuelle dépendait de leur dimension; la turbulence dans la colonne d'eau était représentée par un processus de déplacement tridimensionnel aléatoire. Les prédictions concernant l'allongement et l'orientation des nappes étaient en bon accord avec les observations, et laissent supposer que les cisaillements verticaux près de la surface déterminent principalement le taux de dispersion d'une nappe peu après son émission. En réalité, la flottabilité des gouttelettes limite la profondeur à laquelle les hydrocarbures peuvent se mélanger, en conséquence ces derniers se dispersent d'une manière qui représente une combinaison de processus de diffusion du cisaillement de premier et deuxième ordre. Les résultats numériques ont montré que l'axe principal de la nappe devait croitre linéairement avec le temps; tandis que la largeur de la nappe augmenterait comme une fonction det0,5. Le modèle a prédit correctement l'apparition d'une couche plus épaisse près de la bordure extérieure de la nappe, et l'alignement des nappes dans la direction du vent.

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Copyright information

© Deutsches Hydrographisches Institut 1986

Authors and Affiliations

  • Alan J. Elliott
    • 1
  1. 1.Unit for Coastal and Estuarine StudiesMarine Science LaboratoriesMenai BridgeGroßbritannien

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