Ripples on Underside of River Ice Covers

by George D. Ashton, Hydrol.; U.S. Army Cold Regions Res. and Engr. Lab., Hanover, NH,
John F. Kennedy, Dir.; Inst. of Hydr. Res., Univ. of Iowa, Iowa City, IA,

Serial Information: Journal of the Hydraulics Division, 1972, Vol. 98, Issue 9, Pg. 1603-1624

Document Type: Journal Paper


A mathematical model is developed to predict the occurrence and describe the properties and behavior of ice ripples that form on the underside of river ice-covers. The local rate of freezing or melting at the ice-flow interface is related to the difference between the local heat transfer rates by conduction through the ice and by turbulent transfer from the flow to the ice. The local heat flux to the interface from the flow is expressed as a small perturbation expansion in terms of the steepness of the monochromatic interfacial wave, and is assumed to be shifted relative to the interface wave. The analysis yields a stability criterion and expressions for the amplification rate and celerity of the ripples. Laboratory data are used to obtain values for the constants introduced into the theory and to corroborate the analytical results. Field data are examined in the light of the laboratory results.

Subject Headings: Rivers and streams | Ice | Heat flow | Mathematics | Mathematical models | Hydrologic models | Freezing | Snowmelt

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