Session B.pdf - Clarkson University

- maximum length of an ice field is known;
- time (date) of a beginning of formation of a jam and its destruction are known;
- on a considered site of the river a jam only one, but can form in different places of
a site;
- the total discharge of water and ice on the source boundaries of settlement area
are known.
With allowance for of listed above assumptions the one-dimensional mathematical
model both program of account of formation and development of jams in region of city
Lensk was developed. On this site 6 constants of places of jams are known (fig. 1).
Because of digital model of a relief and with the help of especially of developed
program for a site 95 cross sections of a channel and valley of the river were
constructed. The cross sections are located on a distance about 1.5 Km from each other,
with a pitch 25 m between verticals (on some cross sections the number of verticals
reached 400).
Cross sections have formed the basis for construction of a one-dimensional
mathematical model of current, which has allowed to expect passing high waters on a
considered site, including formation of ice jams. The model is based on a numerical
solution of the one-dimensional equations of the Saint-Venant on algorithm [1, 13] and
is supplemented by an elementary model of increase of length of a jam depending on
concentration of ice, approaching to a jam, and flow rate at a leading edge of a jam.
Basic data for a model are:
- hydrograph in a first cross section, as which was accepted of the hydrograph of a
post Krestovsky, with allowance for of lag channel, equal to 12 hours;
- hydrograph of the river Nuy (was set to constants: Q = 100 m 3 /s);
- factor of concentration of ice in a first cross section (was accepted in a range
0,5 − 0,7);
- place of formation of a jam (one from four specific, since of an island
Batamaisky);
- factors of a roughness (on Manning) the channels (n = 0,023) and flood plane of
the river (n = 0,05) in a stream without ice (were determined by calibration of a
model under the fact sheet);
- additional factor of a roughness of a jam (ice surface), which was determined on
full-scale dates for winter conditions with allowance for adjustments on an
increased roughness of ice in a jam (was accepted equal n = 0,03);
- maximum length of a jam (was accepted under the fact sheet or more);
- time of a beginning of formation and the destructions of a jam were accepted on
actual approximate dates.
On the last boundary of a stream it was put the «not reflecting» boundary condition
appropriate to relation between of discharges and levels accordance the equation of
Shezy for known of slope of a water surface (was accepted I = 0,0001).
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