The vertical concentration distribution of frazil-ice crystals in a stream during the formation and gro~lth of frazil ice was discussed in a preliminary way by Gosink and Osterkal!1p (1981). This paper extends and completes the analysis of buoyant rise velocities of frazil-ice crystals and applies the results to an interpretation of measured velocity profiles in rivers during frazil-ice events. Additional experimental data are also presented. Two tillle scales are defined: the buoyant time scale TB, whi ch represents the time requi red for a frazil crystal to rise, huoyantly, from the river DOttOI!1 to the water surface, and the diffusive time scale TO, which represents the time required for a frazil crystal to be transported by turbulence through the de[lth. It is shown that the ratio of the time scales TB/To defines the nature of the layering processes; in particular, if TB/To<1, then buoyant forces ~ill lift a frazil crystal faster than turbulent diffusion can redistribute it and the f10\'/ will be layered. Conversely, if TB/TO>1, turbulent mixing will proceed faster than buoyant 1 ifti ng and the fl ow ~Ii 11 be well-mixed. This ratio, for frazil particles of di arneter 2 i"l1I11 or more, corresponds to rul e-of-thumb velocity criteria developed in Non'lay and Canada to di sti ngui sh 1 ayered frazi l-i ce/l'later fl O~I froi"1 wellmixed flow.The development of this theory depends in large part upon the deterr.lination of TB, which depends upon the rise velocity of frazil-ice crystals. A force ba 1 ance ,node 1 was developed for the ri se velocity of a frazil crystal. Field observations during frazilice formation in Goldstream Creek and in the Chatanika River north of Fairbanks are reported, including a series of measure~ents of the rise velocities of frazi1-ice crystals. Typical particle size of frazi1 ice was about 2 n~ with a rise velocity of about 10.0 mm S-I. The agreement of measured rise velocities with the theoretical model is good considering uncertainties in the drag coefficient and in the deterlllination of frazil crystal sizes under field conditiolls.Velocity profiles in the Chatanika River and in Soldstream Creek during frazil formation suggest that the time-scale ratio may serve as a transition criteri 011 betv/ee'l 1 ayered frazil-i ce/water flow and \~ell IIlixed flow. This ratio was calculated with the rise velocity of frazil-ice crystals arbitrarily chosen to be 0.01 m s-l. I >.JTRODUCTI ONObservations of ice formation in northern rivers during the freeze-up period show that three ice-flo\~ regimes are common: sheet ice, floating frazil ice and a well-mixed flow (frazil-ice crystals and water). In the last case, if the velocity of the river is sufficiently high, open water conditions may persist throughout the winter.Designers of hydraulic structures such as canals, water transportation facilities, hydroelectric power structures, water-intake structures, etc., may require inforMation on which flow regime to expect under a given set of flow conditions and on the transition from an ic...

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Solutions to the Stefan problem for the motion of the base of ice‐bearing permafrost in response to changes in paleoclimate were obtained using perturbation, finite difference, and finite element methods. Paleotemperature models were used to investigate the thickness response, to compare solution methods, to determine the current state of the permafrost, and to determine constraints on the models. The perturbation and finite difference methods used the approximation of linear temperature profiles, while the finite element method did not. There was a transient thickness response of about 41 kyr, implying that paleotemperature records of greater length are needed for models and that the permafrost loses its “memory” of past conditions for much longer times. Faster thawing rates, slower freezing rates, and greater variations in thickness were found for the perturbation and finite difference solutions compared to the finite element solution. These results appear to be caused by the simplifying assumptions in the former solutions. A lag (about 20 kyr) exists between changes in surface temperature and thickness response, and a small thermal offset is apparent in the finite element solution. Small asymmetries exist in the freezing and thawing rates and the thickness response. Paleotemperature models based on ice cores predict current permafrost thicknesses that are too large. Models with the long‐term mean surface temperature of permafrost within a few degrees of the current value of −11°C and with the last glacial period temperatures no more than 6°–8°C lower are compatible with current Prudhoe Bay conditions. These include models developed for East Siberia, from isotopic profiles in deep‐sea sediments, and for Barrow, Alaska, modified for Prudhoe Bay. These models predict that the permafrost thickness at Prudhoe Bay varied by about ±10% or less (±60 m) over the last glacial cycle. Freezing and thawing rates were less than 6 mm yr−1. At present this permafrost should be near its long‐term equilibrium thickness and thawing at <1 mm yr−1.

The Colorado School of Mines (CSM) curriculum was recently modified by replacing laboratory courses in electrical circuits, fluid mechanics and stress analysis with a sequence of Multidisciplinary Engineering Laboratory courses (MEL I, II, and III). The MEL sequence prepares students for their professional careers by integrating discipline‐specific components into systems and building subject‐matter depth through a vertical sequence. The experiments move beyond basic theory verification by requiring students to practice higher level thinking. In addition, the systems experiments encourage students to reorganize knowledge and discover the connections among concepts in several courses. The MEL sequence helps students understand relationships among science, engineering science, and engineering design. The MEL experiments develop life‐long learning skills by encouraging higher levels of thinking on the Perry scale and requiring students to use a variety of Kolb's learning styles. This paper describes the educational objectives and experiments for the MEL I course. The paper gives assessment results for MEL I and compares it with traditional laboratories.

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