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Dispersion of matter at sea under homogeneous conditions

Dispersion von Stoffen im Meer unter homogenen Bedingungen

Dispersion de substances en mer dans des conditions homogènes

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Summary

In this paper the dispersion of a solute at sea is examined by means of a horizontal 2-D approach. The velocity field is horizontally homogeneous and is characterized by a velocity ellipse with axes of arbitrary magnitude. Stratification is absent. Because of the tidal motion the dispersion tensor is time dependent. In the case of instantaneous release of a solute an analytical solution for its spreading is derived. It is particularly shown that the initial behaviour of the concentration is very variable and depends on the moment of release and on the dispersion transverse to the mean velocity. The “Breeveertien” experiment (North Sea) is analyzed in terms of the theory presented. In an appendix estimates for dispersion coefficients under homogeneous conditions are derived.

Zusammenfassung

In dieser Arbeit wird die Dispersion eines gelösten Stoffes im Meer mit Hilfe eines horizontalen, 2dimensionalen Modells untersucht. Das Geschwindigkeitsfeld ist horizontal homogen und charakterisiert durch eine Geschwindigkeitsellipse mit Achsen von beliebiger Größe. Schichtung ist nicht vorhanden. Infolge der Gezeitenbewegung ist der Dispersionstensor zeitabhängig. Für den Fall einer Momentanquelle wird eine analytische Lösung der Ausbreitung hergeleitet. Insbesondere wird gezeigt, daß das Anfangsverhalten der Konzentrationsverteilung sehr variabel ist und von dem Zeitpunkt der Freigabe und der Dispersion senkrecht zur mittleren Geschwindigkeit abhängt. Das „Breeveertien-Experiment” (Nordsee) wird auf Grundlage der vorgelegten Theorie ausgewertet. In einem Anhang werden Abschätzungen für Dispersionskoeffizienten unter homogenen Bedingungen hergeleitet.

Résumé

On examine dans cet article, la dispersion d'un corps dissous en mer au moyen d'un modèle horizontal à deux dimensions. Le champ de vitesse est horizontalement homogène et il est caractérisé par une ellipse de vitesse aux axes de grandeur arbitraire. Il n'y a pas de stratification. Par suite du mouvement des marées le tenseur de dispersion est une fonction du temps. Dans le cas d'une décharge instantannée d'un corps dissous, une solution analytique de sa dispersion est dérivée. Il est montré en particulier que le comportement initial de la concentration est très variable et dépend du moment de la décharge, et de la dispersion perpendiculairement à la vitesse moyenne. L'expérience de „Breeveertien” (Mer du Nord) est analysée dans les conditions de la théorie présentée. Dans un appendice des estimations des coefficients de dispersion dans des conditions homogènes sont fournies.

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Abbreviations

c :

concentration

e‥:

dispersion coefficient

e o :

dispersion coefficient

f‥:

time integral ofe‥

f :

Coriolis parameter

f c :

shape function ofz and α

g :

acceleration due to gravity

h :

depth

m c :

m 1(1/2-α)

m 1 :

numerical constant (=3)

n :

horizontal coordinate

s :

horizontal coordinte

u. :

velocity component

x :

horizontal coordinate

y :

horizontal coordinate

z :

vertical coordinate

C :

2-D transform ofc Chézy friction coefficient

M :

total amount of dye

α:

friction coefficient

β:

coefficient

δ:

coefficient for turbulent transverse dispersion

ε:

ratio of the long and short axes of an ellipse

θ:

exponent

ϰ:

von Karman's constant (≈0.4)

v t :

turbulence viscosity

Φ:

phase angle

ψ:

ωt+Φ

ω:

angular speed

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Author notes

  1. Jan P. Th. Kalkwijk

    Present address: Department of Civil Engineering, Laboratory of Fluid Mechanics, Technische Hogeschool Delft, Delft University of Technology, P. O. Box 5048, NL-2600 GA, Delf, Niederlande

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    1. Jan P. Th. Kalkwijk
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    Kalkwijk, J.P.T. Dispersion of matter at sea under homogeneous conditions. Deutsche Hydrographische Zeitschrift 38, 245–260 (1985). https://doi.org/10.1007/BF02226313

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    • DOI: https://doi.org/10.1007/BF02226313

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