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A Model for Entrainment of Sediment Into Sea Ice by Aggregation Between Frazil-Ice Crystals and Sediment Grains

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A Model for Entrainment of Sediment Into Sea Ice by Aggregation Between Frazil-Ice Crystals and Sediment Grains Journal of Glaciology, Vo l. 48, No.160, 2002 A model for entrainment of sediment into sea ice by aggregation between frazil-ice crystals and sediment grains Lars Henrik SMEDSRUD Geophysical Institute, University of Bergen, Allegaten 70,N-5007 Bergen, Norway E-mail:[email protected] ABSTRACT. Avertical numerical model has been developed that simulates tank experi- ments of sediment entrainment into sea ice. Physical processes considered were:turbulent vertical diffusion of heat, salt, sediment, frazil ice and their aggregates; differential growth of frazil-ice crystals; secondary nucleation of crystals; and aggregation between sediment and ice. The model approximated the real size distribution of frazil ice and sediment using five classes of each. Frazil crystals (25 mm to 1.5 cm) were modelled as discs with a constant 1 thickness of 30 their diameter. Each class had a constant rise velocity based on the density of ice and drag forces. Sediment grains (1^600 mm) were modelled as constant density spheres, with corresponding sinking velocities. The vertical diffusion was set constant for experi- ments based on calculated turbulent rms velocities and dissipation rates from current data. The balance between the rise/sinking velocities and the constant vertical diffusion is an im- portant feature of the model. The efficiency of the modeled entrainment process was esti- mated through , an aggregation factor. Values for are in the range h0.0003, 0.1i,but average values are often close to 0.01. Entrainment increases with increasing sediment con- centration and turbulence of the water, and heat flux to the air. 1. INTRODUCTION some experiments were completed in a larger tank at a scale more likely to represent natural conditions in time and Sediment-laden sea ice was observed during the first journey space (Smedsrud,1998, 2001; Haas and others,1999). across the Arctic Ocean (Nansen,1906), and later expeditions >Different approaches have been applied to model the have confirmed that such ice can be found in all parts of the entrainment numerically. Two different vertical models ocean (Barnes and others, 1982; Nu« rnberg and others, 1994; have been developed, both showing the temporal nature of Meese and others, 1997). Sediment in sea ice is often patchy the process (Eidsvik, 1998; Sherwood, 2000).The efficiency in nature; concentrations are usually in the range 5^500 of the aggregation was estimated using a simple box model mg L^1 and vary both horizontally and vertically at the cm based on classic aggregation theory, and the first set of scale. The entrainment processes appear to be governed by laboratory experiments (Smedsrud,1998). Frazil-ice growth episodic events (Eicken and others, 2000). and concentration in these models follow the simplifications Frazil-ice crystals are thin dendritic crystals that form in in Omstedt (1985). turbulent supercooled water (Martin, 1981). Granular ice is In this paper the model of Sherwood (2000) is developed congealed frazil ice, and sea ice with incorporated sediment further by including several important new processes.These is often granular ice. Such sediment-laden ice is assumed to be include a size distribution for frazil ice and sediment, differ- a result of sediment entrainment during formation of frazil ential growth of crystals, and secondary nucleation. Aggre- ice in open water, described as suspension freezing (Reimnitz gation between frazil ice and sediment is modelled using and others, 1992).When frazil ice stays in suspension due to different size classes. Results from Smedsrud (2001) are used turbulent diffusion it may ``scavenge'' suspended sediment to tune the model parameters, and a size-dependent aggre- (Osterkamp and Gosink, 1984), i.e. collide and aggregate, gation factor is calculated. Finally, the model sensitivity to and bring the sediment along to form the sediment-laden its key parameters is tested, and predictions are made for granular ice at the surface. If frazil-ice particles collide and different basic forcings to the model. aggregate with coarse objects at the bottom, or a lot of sedi- ment in suspension, the frazil ice will sink and form anchor 2. MODEL DEVELOPMENT ice. Such anchor ice may rise with its aggregated sediment, or become buoyant enough to bring coarse material to the sur- The frazil and sediment model (Frasemo) represents time- face, if the ice grows in volume. dependent vertical profiles of vertical mixing, temperature, Experiments conducted in small tanks with a short salinity and concentrations of sediment and ice. The model duration have shown high levels of entrainment for pro- was developed by Sherwood (2000) and mainly used to calcu- cesses that can be termed ``suspension freezing'' (Kempema late co-concentrations of sediment and ice for a given site in and others,1993; Reimnitz and others,1993; Ackermann and the Kara Sea, Russia, as a result of surface wind forcing and others,1994).The experiments had high levels of turbulence low air temperatures. and heat fluxes, but these were not quantified. Recently, The model is here set to represent the 1m deep tank in 51 Journal of Glaciology experiments A^D, described in Smedsrud (2001). Hereafter of, say, 18 mg L^1 contains an unknown size distribution. these experiments are referred to just by their letters (see The distribution is a balance between the upward diffusion table 1 in Smedsrud (2001) for a summary of experimental and the sinking velocities of the variously sized grains. To parameters). No attempt is made to model the horizontal solve this, a volume concentration, comparable to the total flow, and the aim is to model the vertical diffusion and con- added mass of sediment, is used for the initialization, with centrations satisfactorily. the observed size distribution. The model is then run for 2.1. Diffusion and turbulence 1hour with diffusion, but no cooling, to allow the largest grains to sink, and avoid any aggregation with frazil ice The vertical diffusion has implications for the vertical gra- before the steady-state balance is reached for the sediments. dients of heat, salinity, sediment and ice. Equations for the It is then controlled so that the total Cs matches the total approximate conservation of these are: measured mass concentration. ^8 ^1 @T @ @T Avery light snowfall is specified (1.0610 ms 0.9 mm w K w G CsÀ1 1 @t @z @z T per 24 hours)to simulate the ``snow'' falling from the ceiling. This snow was observed to consist of crystals 42^3 mm in @S @ @S w K w G (psu sÀ1 2 diameter, so it is specified as equally distributed over the @t @z @z S three largest size classes. The initial concentration of ice @C j @ @C j @C j s K s À w s 1sÀ1 3 crystals is zero for all classes, and increases after the first @t @z @z s @z hour when the ``snow''starts falling. @C k @ @C k @C k Air^sea heat flux is calculated by the model at the upper i K i À w i G k 1sÀ1: @t @z @z i @z I boundary, using standard bulk sensible-heat-flux param- 4 eterizations (Gill,1982). Because the circulating water spent 65% of the time under the insulating ice cover, the calcu- Here T is the water temperature, S is the salinity, C is the ^3 w w s lated heat-flux coefficient cH 2.73610 (Smedsrud, 2001) total volume concentration of sediments, Ci is the total is reduced to the standard ``open-sea''value of c 1.1610 ^3 volume concentration of ice, and K is the vertical eddy dif- H (Simonsen and Haugan, 1996). This value is kept constant, fusivity. G is the source of heat from the freezing crystals, T and the observed air temperatures of the tank, from the cor- G is the source of salt, and G is the source of frazil ice. w is S I i responding experiments A^D, are used during each run. the rise velocity of the crystals, and w is the sinking velocity s Numerical solutions are obtained using finite differences of the grains. A constant uniform vertical eddy viscosity, K, is set through the depth. K was estimated forA^D using the on a staggered vertical grid with constant spacing of 5 cm mean rms fluctuation velocity, q, and the turbulent rate of and a time-step of 1s. Apart from the specified flux of heat dissipation, ,asstatedinSmedsrud(2001). and snow at the surface, insulating boundaries are used for the other parameters at the top, and for all parameters at Equation (1) assumes that sediment Cs is at the same temperature as the local water, while the frazil ice Ci is the bottom. assumed to be at the freezing point. C j in Equation (3) s 2.3. Sediment consists of (j 5) size classes (Table 1), where the grain dia- meter (2rs) and the sinking velocity ws j) are given. Ci k For the sediment in suspension, a balance is reached in Equation (4) consists of (k 5) size classes, where a diam- between the upward diffusion and the downward advection eter di k and a rise velocity wi k are required (Table 2). of sediment grains, depending on their size and correspond- The vertical diffusion of T , S , C and C is modelled w w i s ing sinking velocity. with a fully implicit diffusion scheme (Patankar,1980).The The size classes used in the model are shown inTable 1. routine is run separately for the different size classes of sedi- All sizes are given as a grain diameter. These five classes ment and ice, as well as for T and S . w w approximate the real size distribution in A^C as shown in 2.2.
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