Golovin et al.: Frazil Ice FOl7lUltion during the Spring Flood
133
still be able to estimate the probability of supercooling in the river-sea water contact zone.
The dynamic aspect of frazil ice formation
Studies of double-diffusion frazil ice formation under laboratory conditions have shown that if
the external turbulent effect in both layers of a two-layer system is absent, and the heat and salt
exchange through the density interface between fresh and saline water is at the molecular level,
then the value of supercooling is not large and the density interface is "diffused" by molecular
diffusion (Krylov and Zatsepin, 1992; Martin and Kauffman, 1974; McClimans et a!., 1978;
Stigebrandt, 1981). Here less than several millimeters of frazil ice can form in a day. This
important result is in good agreement with frazil ice growth observed in a summer lead filled
with melt freshwater (Golovin et aI., 1996). Obviously, such small ice formation rates cannot
produce meter-layers of frazil ice observed near Arctic river mouths and in the coastal regions
of Antarctica (Bulatov, 1963; Kozlovsky, 1971; Cherepanov and Kozlovsky, 1972).
Laboratory experiments showed (Krylov and Zatsepin, 1992) that under artificially created
turbulence of a two-layer system and the increased heat-salt exchange through the pycnocline,
the rate of frazil ice formation strongly increases. This was confirmed by later laboratory
experiments (Voropayev et aI., 1995). Turbulence in the layers and turbulent entrainment in the
contact zone between freshened and saline waters provide for intense frazil ice formation, with
ice crystals subsequently surfacing and sticking together (Krylov and Zatsepin, 1992,
Voropayev et aI., 1995).
Both-scale studies and laboratory experiments show that supercooling and frazil ice occur in a
comparatively thin contact zone at the upper boundary of the pycnocline (Golovin et aI., 1996,
Krylov and Zatsepin, 1992, Voropayev et aI., 1995). Hence, for investigating the rate of frazil
ice formation depending on the level of the heat-mass exchange, the parameters and structure of
turbulence near the density interface should be known.
In some laboratory experiments turbulence was generated by velocity shear (Turner, 1973;
Kantha and Phillips, 1977; Kato and Phillips, 1969; Kan and Tamai, 1994). Such experiments
were carried out in circulate flumes. Shear flow was either generated by a rotating plastic screen
(Turner, 1973) or by belts installed (Kan and Tamai, 1994) on the bottom and surface of on of
the flume straight parts. Roughness elements were attached on the belts. In other laboratory
experiments turbulence was generated by oscillating grids (Turner, 1973; Krylov and Zatsepin,
1992; Voropayev et aI., 1995). The grids attached to a single rod were mechanically activated.
Turbulence induced by these means is called "grid" turbulence. Its structure near pycnocline
differs from that of the turbulence generated by velocity shear (the latter predominates in natural
environments). Hence, as noted by Turner (1973), this makes comparison of the results of
these experiments difficult. However, since "grid" turbulence is more easily parametrizated,
this way of turbulence generation is more frequently used in laboratory experiments studying
the processes of properties transmission through pycnocline.
Studies of the rate of frazil ice formation (Krylov and Zatsepin, 1992; Voropayev et aI.,
1995) were performed by means of "grid" turbulence. In these experiments, parameterization of
the non-dimensional entrainment velocity Ve/V. through the pycnocline at turbulent mixing
between the layers and interpretation of the results, including the rate of frazil ice formation,
were performed by means of the local Richardson number Ri. = g·(ilp/p)· LlV.2. The local
Richardson number is an analogue of the global number, but the external scale of mean
horizontal velocity V is replaced by the root-mean-square velocity of turbulent variations V.
near the density interface. Also, the thickness of the mixed layer Z is substituted to the integral
scale of turbulence L. The latter characterizes the mean scale of the most energy-carrying eddies
near the density interface which then penetrate the pycnocline and participate in turbulent
entrainment (Prandtl, 1949; Turner, 1973; Shlikhting, 1974).
133
still be able to estimate the probability of supercooling in the river-sea water contact zone.
The dynamic aspect of frazil ice formation
Studies of double-diffusion frazil ice formation under laboratory conditions have shown that if
the external turbulent effect in both layers of a two-layer system is absent, and the heat and salt
exchange through the density interface between fresh and saline water is at the molecular level,
then the value of supercooling is not large and the density interface is "diffused" by molecular
diffusion (Krylov and Zatsepin, 1992; Martin and Kauffman, 1974; McClimans et a!., 1978;
Stigebrandt, 1981). Here less than several millimeters of frazil ice can form in a day. This
important result is in good agreement with frazil ice growth observed in a summer lead filled
with melt freshwater (Golovin et aI., 1996). Obviously, such small ice formation rates cannot
produce meter-layers of frazil ice observed near Arctic river mouths and in the coastal regions
of Antarctica (Bulatov, 1963; Kozlovsky, 1971; Cherepanov and Kozlovsky, 1972).
Laboratory experiments showed (Krylov and Zatsepin, 1992) that under artificially created
turbulence of a two-layer system and the increased heat-salt exchange through the pycnocline,
the rate of frazil ice formation strongly increases. This was confirmed by later laboratory
experiments (Voropayev et aI., 1995). Turbulence in the layers and turbulent entrainment in the
contact zone between freshened and saline waters provide for intense frazil ice formation, with
ice crystals subsequently surfacing and sticking together (Krylov and Zatsepin, 1992,
Voropayev et aI., 1995).
Both-scale studies and laboratory experiments show that supercooling and frazil ice occur in a
comparatively thin contact zone at the upper boundary of the pycnocline (Golovin et aI., 1996,
Krylov and Zatsepin, 1992, Voropayev et aI., 1995). Hence, for investigating the rate of frazil
ice formation depending on the level of the heat-mass exchange, the parameters and structure of
turbulence near the density interface should be known.
In some laboratory experiments turbulence was generated by velocity shear (Turner, 1973;
Kantha and Phillips, 1977; Kato and Phillips, 1969; Kan and Tamai, 1994). Such experiments
were carried out in circulate flumes. Shear flow was either generated by a rotating plastic screen
(Turner, 1973) or by belts installed (Kan and Tamai, 1994) on the bottom and surface of on of
the flume straight parts. Roughness elements were attached on the belts. In other laboratory
experiments turbulence was generated by oscillating grids (Turner, 1973; Krylov and Zatsepin,
1992; Voropayev et aI., 1995). The grids attached to a single rod were mechanically activated.
Turbulence induced by these means is called "grid" turbulence. Its structure near pycnocline
differs from that of the turbulence generated by velocity shear (the latter predominates in natural
environments). Hence, as noted by Turner (1973), this makes comparison of the results of
these experiments difficult. However, since "grid" turbulence is more easily parametrizated,
this way of turbulence generation is more frequently used in laboratory experiments studying
the processes of properties transmission through pycnocline.
Studies of the rate of frazil ice formation (Krylov and Zatsepin, 1992; Voropayev et aI.,
1995) were performed by means of "grid" turbulence. In these experiments, parameterization of
the non-dimensional entrainment velocity Ve/V. through the pycnocline at turbulent mixing
between the layers and interpretation of the results, including the rate of frazil ice formation,
were performed by means of the local Richardson number Ri. = g·(ilp/p)· LlV.2. The local
Richardson number is an analogue of the global number, but the external scale of mean
horizontal velocity V is replaced by the root-mean-square velocity of turbulent variations V.
near the density interface. Also, the thickness of the mixed layer Z is substituted to the integral
scale of turbulence L. The latter characterizes the mean scale of the most energy-carrying eddies
near the density interface which then penetrate the pycnocline and participate in turbulent
entrainment (Prandtl, 1949; Turner, 1973; Shlikhting, 1974).