The thickening of ice covers has traditionally been calculated using a method in which the thickness is assumed proportional to the square root of the accumulated freezing degree days. Particularly for newly formed thin ice this method overpredicts the ice thickness. Consideration of the thermal resistance between the top of the ice and the atmosphere results in a method which predicts linear growth with time for thin ice and transitions to the t½ growth at large thicknesses. The method proposed here is not new but seems to be rarely used even though it requires selection of only one coefficient. Data from several sources including initial river ice growth, sea ice growth, and sludge freezing are used to validate the method and bracket the coefficient.
The deterioration of floating ice covers is analyzed to determine under what conditions the ice cover loses strength due to internal melting. The analysis considers the interaction between sensible heat transfer and long wave radiation loss at the surface, the surface albedo, the short wave radiation penetration and absorption and the unsteady heat conduction within the ice. The thermal analysis then leads to a determination of the porosity of the ice that allows strength analysis to be made using beam-type analyses. The results provide criteria to determine when and how rapidly the ice cover loses strength and under what conditions it will regain the original strength associated with an ice cover of full integrity.
ABSTRACT. The conditions under which a fl oating fragm ent of ice is either entrained under the upstrea m edge of a d own -stream ice cover or accumul a ted up-stream a re exa mined by mea ns of dimensiona l a na lysis and a simplified an a lysis of the mo ments acting on a n idealized ice fragm ent. The significant pa rameter descriptive of the critical conditio ns is found to be a Froude number based on block thickness. The influence of the ratio of thickness to flow depth is shown to be due to the effect of th e block constricting the flow cross-section, thus amplifying the velocity in accord a nce with simple continuity. Under-turning insta bility occurs a t a lower c ritical velocity th a n required for vertical submergence. Compa riso n of experimental data with the theoretical r esults show good agreement a nd de monstrates the vital dependence on fragm ent thickn ess as well as providing a criterion readil y a pplica bl e to special flow conditions wh ere a Froude number based on flow d epth is illogi cal. RESUME. l'epaisseur a la profondeur d e l'ecou lement es t due a l'effe t du bloc resserra nt la sec tion tra nsversale de l'ecoul ement e t a mplifia nt done la vitesse du coura nt en vertu d es simples lois d e la continuite. L 'insta bilite a u re tournement se produit pour une vitesse critique infe rieure a cell e necessaire pour la submersion verticale.La compara ison d es d onnees experimentales avec les resulta ts th eoriques fa it a ppa raitre un e bonn e concordance, montre le role essentiel j oue pa r l'epaisseur du fragment e t procure un critere facil ement applicabl e a d es conditions speciales d 'ecoul ement lorsqu' un no mbre de Froude base sur la profondeur de l'ecou lem ent est illogique. ZUSAMMENFASSUNG . Froude-Kriterium f ur die Stabilitiit van E isblocken. Die Bedingungen, unter denen ein Stuck Treibeis entwed er unter den R a nd einer stromabwarts gelegenen Eisdecke gedruckt wird od er sich stromaufwarts anlagert, werde n mit Hilfe einer Dimensionsa na lyse und einer vereinfacht"n Analyse d er a n einem idealisierten Eisstuck angreifend en M omente untersucht. Als wesentlicher Para meter zur D a rstellung der kritischen Bedingungen erweist sich eine a us der Bl ockdicke hergel eitete Froude-Zahl. D er Einfluss d es V erhaltnisses zwischen Di cke und Gerinn etiefe beruht a uf d er T a tsache d ass der Block den Querschnitt des Gerinnes verringert, wodurch gemass einfacher Kontinuita t die G eschwindigkeit stromaufwa rts erhoht wird. Insta bilita t, die zum Abkippen fuhrt, tritt bei einer geringeren Geschwindigkeit ein als bei der fur vertika les Unterta uchen beno tigten. Vergleiche zwischen Versuchsdaten und theoretischen Ergebnissen zeigen gute Ubereinstimmung und beweisen die wesentliche Abha ngigkeit von d er Sch ollendicke. Ausserdem liefern sie ein Kriterium , d as ohn e weiteres a uf spezielle Fliessbedingungen a ngewandt werde n kann, wenn ein e am der Gerinnetiefe abgel eitete Froude-Za hl unlogisch wa re. INTROD UCTIONThe prediction of the velocity at which a floating fr...
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