Skip to main content Accessibility help
×
Home

Comparison of Three Contemporary Flow Laws in a Three-Dimensional, Time-Dependent Glacier Model

  • L. A. Rasmussen (a1) and W. J. Campbell (a1)

Abstract

A numerical model for three-dimensional, time-dependent glacier flow (Campbell and Rasmussen, 1970) treated the ice as a Newtonian viscous fluid and related its dynamics to two large-scale bulk parameters: the viscosity v determining the ice-to-ice friction, and a basal friction parameter A determining the ice-to-rock friction. The equations were solved using the relatively simple flow law of Bodvarsson (1955) in which the basal shear stress is proportional to volume transport. Recent research suggests that a more realistic basal flow law is one in which the basal shear stress to some lower power (1–3) is either proportional to the vertically averaged velocity (Glen, 1958; Nye, 1960, 1963[a], [b], [c], 1965[a], [b], [c]) or to the ratio of the vertically averaged velocity to glacier thickness (Budd and Jenssen, in press).

In the present study a generalized flow law incorporating all of the above bulk basal flow laws is applied to the Campbell–Rasmussen momentum equation to form a generalized two-dimensional transport equation, which, when combined with the continuity equation, yields a numerically tractable set of equations for three-dimensional, time-dependent glacier flow. Solutions of the model are shown for steady-state flow and surge advance and recovery for a typical valley glacier bed for powers 1, 2, and 3 for each of the basal flow laws for a steady-state climate input and a given ice-to-ice viscosity parameter.

Un modèle numérique à trois dimensions pour un écoulement de glacier fonction du temps (Campbell et Rasmussen, 1970) traitait la glace comme un fluide visqueux Newtonien et rapportait sa dynamique à deux paramètres d’ensemble à grande échelle: la viscosité v représentant le frottement glace–glace et un paramètre de frottement basal A représentant le frottement glace–rocher. On résolvait les équations en utilisant la loi d’écoulement relativement simple de Bodvarsson (1955) dans laquelle l’effort de cisaillement basal est proportional au volume transporté. Des recherches récentes suggèrent qu’une loi d’écoulement basal plus réaliste serait celle selon laquelle l’effort de cisaillement à la base à une puissance inférieure (1–3) est proportionnelle soit à la vitesse moyenne le long d’une verticale (Glen, 1958; Nye, 1960, 1963[a], [b], [c], 1965[a], [b], [c]) soit au rapport entre la vitesse moyenne le long d’une verticalle à l’épaisseur du glacier (Budd et Jenssen, sous presse).

Dans la présente étude, une loi d’écoulement générale englobant toutes les lois d’écoulement d’ensemble ci-dessus est appliquée à l’équation des moments de Campbell–Rasmussen pour former une équation générale du transport à deux dimensions qui, combinée avec l’équation de continuité fournit un système d’équation traitable numériquement pour l’écoulement tridimensionnel du glacier en fonction du temps. On montre les solutions de ce modèle pour un écoulement permanent et pour un épisode d’avance et de retrait après une crue dans une vallée glaciaire typique avec des puissances de 1, 2 et 3 pour chacune des lois d’écoulement à la base sous un climat constant et une valeur donnée du paramètre viscosité glace–glace.

Zusammenfassung

Ein numerisches Modell für dreidimensionales, zeitabhängiges Gletscherfliessen (Campbell und Rasmussen, 1970) behandelte das Eis als eine Newton’sehe viskose Flüssigkeit und beschrieb seine Bewegung mit Hilfe zweier makroskopischer Massenparameter: der Viskosität v, welche die Eis-zu-Eis-Reibung bestimmt, und einem Grundreibungsparameter A, der die Eis-zu-Fels-Reibung bestimmt. Die Gleichungen wurden mit dem relativ einfachen Fliessgesetz von Bodvarsson (1955) gelöst, in dem die Scherspannung am Untergrund proportional zum Massentransport ist. Neuere Untersuchungen deuten daraufhin, dass in einem realistischeren Gesetz für das Fliessen am Untergrund eine gewisse niedrige Potenz (1–3) der Scherspannung proportional entweder zur vertikalen Durchschnittsgoschwindigkcit (Glen, 1958; Nye, 1960, 1963[a], [b], [c], 1965[a], [b], [c]) oder zum Verhältnis von vertikaler Durchschnittsgeschwindigkeit und Gletscherdicke (Budd und Jenssen, im Druck) angenommen werden sollte.

In der vorliegenden Untersuchung wird ein allgemeines Fliessgesetz, das alle oben genannten Fliessgesetze für Massen am Untergrund einschliesst, auf die Campbell–Rasmussen’sche Momentengleichung angewandt; daraus ergibt sich eine allgemeine zweidimensionale Transportgleichung, die in Verbindung mit der Kontinuitäisgleichung ein numerisch lösbares Gleichungssystem für ein dreidimensionales zeitabhängiges Gletscherfliessen liefert, Lösungen des Modells werden für stationäres Fliessen sowie für einen ausbruchartigen Vorstoss und dessen Regeneration in einem typischen Talgletscherbett mit den Potenzen 1, 2 und 3 in jedem der drei Fliessgesetze unter der Annahme stationärer Klimaverhältnisse und mit einem gegebenen Eis-zu-Eis-Viskositätsparameter aufgezeigt.

  • View HTML
    • Send article to Kindle

      To send this article to your Kindle, first ensure no-reply@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about sending to your Kindle. Find out more about sending to your Kindle.

      Note you can select to send to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be sent to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

      Find out more about the Kindle Personal Document Service.

      Comparison of Three Contemporary Flow Laws in a Three-Dimensional, Time-Dependent Glacier Model
      Available formats
      ×

      Send article to Dropbox

      To send this article to your Dropbox account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Dropbox.

      Comparison of Three Contemporary Flow Laws in a Three-Dimensional, Time-Dependent Glacier Model
      Available formats
      ×

      Send article to Google Drive

      To send this article to your Google Drive account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Google Drive.

      Comparison of Three Contemporary Flow Laws in a Three-Dimensional, Time-Dependent Glacier Model
      Available formats
      ×

Copyright

References

Hide All
Bodvarsson, G. 1955. On the flow of ice-sheets and glaciers. Jökull, Ár 5, p. 18.
Budd, W. F. 1969. The dynamics of ice masses, ANARE Scientific Reports. Ser. A(IV). Glaciology. Publication No. 108.
Budd, W. F., and Jenssen, D. In press. Numerical modelling of glacier systems.
Campbell, W. J., and Rasmussen, L. A. 1969. Three-dimensional surges and recoveries in a numerical glacier model. Canadian Journal of Earth Sciences, Vol. 6, No. 4, Pt. 2, p. 97986.
Campbell, W. J., and Rasmussen, L. A. 1970. A heuristic numerical model for three-dimensional time-dependent glacier flow. [Union Géodésique et Géophysique Internationale. Association Internationale d’Hydrologie Scientifique.] [International Council of Scientific Unions. Scientific Committee on Antarctic Research. International Association of Scientific Hydrology. Commission of Snow and Ice.] International Symposium on Antarctic Glaciological Exploration (ISAGE) Hanover, New Hampshire, U.S.A., 3–7 September 1968, p. 17790.
Colbeck, S. C. Unpublished. The flow law for temperate glacier ice. [Ph.D. thesis. University of Washington Seattle, Washington, 1970.]
Glen, J. W. 1955. The creep of polycrystalline ice. Proceedings of the Royal Society, Ser. A, Vol. 228, No 1175, p. 51938.
Glen, J. W. 1958. The flow law of ice: a discussion of the assumptions made in glacier theory, their experimental foundations and consequences. Union Géodésique et Géophysique Internationale. Association Internationale d’Hydrologie Scientifique. Symposium de Chamonix, 16–24 sept. 1958, p. 17183.
Lliboutry, L. A. 1968. Théorie complète du glissement des glaciers, compte tenu du fluage transitoire. Union de Gédésie et Géophysique Internationale. Association Internationale d’Hydrologie Scientifique. Assemblée générale de Berne, 25 sept.–7 oct. 1967. [Commission de Neiges et Glaces.] Rapports et discussions, p. 3348.
Lliboutry, L. A. 1970. Current trends in glaciology. Earth Science Reviews, Vol. 6, No. 3, p. 14167.
Nye, J. F. 1960. The response of glaciers and ice-sheets to seasonal and climatic changes. Proceedings of the Royal Society, Ser. A, Vol. 256, No. 1287, p, 55984.
Nye, J. F. 1963[a]. On the theory of the advance and retreat of glaciers. Geophysical Journal of the Royal Astronomical Society, Vol. 7, No. 4, p. 43156.
Nye, J. F. 1963[b]. The response of a glacier to changes in the rate of nourishment and wastage. Proceedings of the Royal Society, Ser. A, Vol. 275, No. 1360, p. 87112.
Nye, J. F. 1963[c]. Theory of glacier variations. (In Kingery, W. D., ed. Ice and snow; properties, processes, and applications: proceedings of a conference held at the Massachusetts Institute of Technology, February 12–16, 1962. Cambridge, Mass., M.I.T. Press, p. 15161.)
Nye, J. F. 1965[a]. The flow of a glacier in a channel of rectangular, elliptic or parabolic cross-section. Journal of Glaciology, Vol. 5, No. 41, p. 66190.
Nye, J. F. 1965[b]. The frequency response of glaciers. Journal of Glaciology, Vol. 5, No. 41, p. 56787.
Nye, J. F. 1965[c]. A numerical method of inferring the budget history of a glacier from its advance and retreat. Journal of Glaciology, Vol. 5, No. 41, p. 589607.
Raymond, C. F. 1971 [a]. Determination of the three-dimensional velocity field in a glacier. Journal of Glaciology, Vol. 10, No. 58, p. 3953.
Raymond, C. F. 1971 [b]. Flow in a transverse section of Athabasca Glacier, Alberta, Canada. Journal of Glaciology, Vol. 10, No. 58, p. 5584.
Weertman, J. 1957. On the sliding of glaciers. Journal of Glaciology, Vol. 3, No. 21, p. 3338.
Weertman, J. 1964. The theory of glacier sliding. Journal of Glaciology, Vol. 5, No. 39, p. 287303.
Weertman, J. 1969. Water lubrication mechanisms of glacier surges. Canadian Journal of Earth Sciences, Vol. 6, No. 4, Pt. 2, p. 92942.

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed