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Numerical simulation of tides in the World Ocean: 2. Experiments of the sensitivity of the solution to choice of the shelf effect parameterization and to variations in shelf parameters

Numerisches Modell der Gezeiten im Weltozean: 2. Versuche über das Lösungsverhalten bei der Wahl der Methode der Parametrisierung der Schelfeffekte und bei Veränderung ihrer Parameter

Simulation numérique de marées dans l'océan mondial: 2. Essais sur la sensibilité de la solution au choix de méthode de paramétrisation des effets du plateau et aux variations des paramètres du plateau

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Summary

A numerical solution to the problem of tides in the World Ocean taking into account the shelf effects is described. Results of the numerical experiments show that the spatial structure and energetics of global semi-diurnal tides are quite sensitive to the choice of the shelf effect parameterization and to the variations in shelf parameters. This fact can be regarded as indirect evidence of the resonant nature of semi-diurnal tides in the World Ocean.

Zusammenfassung

Numerische Lösungen für ein Gezeitenmodell des Weltozeans unter Berücksichtigung von Schelfeffekten werden beschrieben. Die Ergebnisse der numerischen Experimente zeigen, daß die räumliche Struktur und die Energetik der globalen halbtägigen Gezeiten höchst empfindlich auf die Wahl der Parametrisierungsmethode der Schelfeffekte und auf deren Parameter reagieren. Dieser Umstand kann als indirekte Bestätigung des Resonanzcharakters der halbtägigen Gezeiten im Weltozean dienen.

Résumé

On décrit une solution numérique au problème de la marée dans l'Océan Mondial en tenant compte des effets du plateau. Les résultats des essais numériques montrent que la structure spatiale et le bilan d'énergie de la marée semi-diurne globale sont très sensibles au choix de méthode de paramétrisation des effets du plateau et aux variations des paramètres du plateau. Ce fait peut être considéré comme une preuve indirecte de la résonance de la marée semi-diurne dans l'Océan Mondial.

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Abbreviations

a :

Earth's radius

a 0 :

oscillator parameter

b :

real parameter occurring in boundary condition (A5) in GK 1

b 0 :

oscillator parameter

C :

constant defined by initial conditions

c :

real parameter occurring in boundary condition (A5) in GK 1

E :

finite-difference analog of net energy

F :

(F λ,F ϕ, 0) vector of frictional forces

f :

Coriolis parameter

g :

gravity acceleration

H :

ocean depth

h :

index showing application to grid function space

h 0 :

depth of net absorption of tidal energy in Jeffreys' condition

j, k :

coordinates of lattice grids

L :

length of side of spherical rectangle adjacent to boundary of lattice region

l :

index showing application of functions to boundary grids of lattice region

m :

index showing application to averaged functions

n :

integer

p :

function connected toq-relationship (10)

q :

normal component of total transport in boundary grids of lattice region

r :

coefficient of bottom friction

r 0 :

oscillator parameter

S :

area of spherical rectangle adjacent to boundary of lattice region

s :

index showing application to eigenoscillations

T :

vector of tide-generating forces as expressed allowing for static effect of Earth tides

t :

time

u, v :

components of vertical-mean velocity of tidal current

w :

vector with componentsu, v, ζ

x, y :

arbitrary vectors

α, β:

parameters dependent on σ and σs

γL :

Love's reduction factor

ζ:

deviation of free surface of ocean from its undisturbed position

ζ:

height of static tide in ocean

σ:

frequency of forced (tidal) oscillations

σs :

frequency of free oscillations

λ:

longitude counted east of Greenwich meridian

Φ:

time-dependent function

ϕ:

latitude

ψ:

eigenvector of operator ℒh

ℒ:

Laplace's tidal operator

ℒh :

finite-difference analog of operator ℒ

*:

symbol denoting complex conjugation

References

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Author notes

  1. Vadim Yu. Gotlib &  Boris A. Kagan

    Present address: Leningrad Branch, P. P. Shirshov Institute of Oceanology, Academy of Sciences USSR, 30, Pervaya Liniya, 199053, Leningrad, USSR

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    1. Vadim Yu. Gotlib
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    2. Boris A. Kagan
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    Gotlib, V.Y., Kagan, B.A. Numerical simulation of tides in the World Ocean: 2. Experiments of the sensitivity of the solution to choice of the shelf effect parameterization and to variations in shelf parameters. Deutsche Hydrographische Zeitschrift 35, 1–14 (1982). https://doi.org/10.1007/BF02226635

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    • DOI: https://doi.org/10.1007/BF02226635

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