Journal of Glaciology, Vo l. 48, No.160, 2002

A model for entrainment of sediment into by aggregation between frazil-ice 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 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 Downloaded from https://www.cambridge.org/core. 30 Sep 2021 at 08:34:37, subject to the Cambridge Core terms of use. 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 ˆ 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 ˆ 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 ˆ 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 ˆ 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 ˆ 2.73610 (Smedsrud, 2001) total volume concentration of sediments, Ci is the total is reduced to the standard ``open-sea''value of c ˆ 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 ˆ 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 ˆ5) 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. Model initialization and forcing Smedsrud (2001, fig. 9).The sediment used in D consisted of clay and silts only, with a median diameter of 2.5 mm. The Each model run is started with both the measured Tw (close initial sediment volume was in this case set to 50% of Cs(1) to the freezing point) and the measured Sw, vertically and 50% of Cs(2).The sinking velocities are calculated from homogeneous. the Stokes settling velocities (Neilsen, 1992), using Tw ˆ The initial concentration of Cs is not straightforward, because the measured mass concentration at 0.5 m depth Table 2. Frazil-ice size classes, Ci k†, and calculated rise velocities based on equations (1^3) in Gosink and Osterkamp Table 1. Sediment size classes and sinking velocities (1 9 8 3)

Class Range Median size Sinking Class Range Median size Rise velocity Equiv. radius (2 rs) velocity (ws) (di k†) (wi k†) (rie k†) mm mmmms^1 mm s^1 mm

Clay (j ˆ1) 0.3^2 1.15 ^0.0005 Small (k ˆ1) 0 ^ 50 mm25mm0.0054.6 Fine and medium silt (j ˆ 2) 2^20 11.0 ^0.05 Fine (k ˆ 2) 50^500 mm250mm 0.054 46.0 Coarse silt (j ˆ 3) 20^63 41.5 ^0.76 Medium (k ˆ 3) 0.5^5.0 mm 2.5 mm 6.3 460.5 Fine sand (j ˆ4) 63^250 156.5 ^10.74 Coarse (k ˆ4) 5.0^10.0 mm 7.5 mm 21.2 1381.5 Medium and coarse sand (j ˆ 5) 250100 625 ^171.9 Large (k ˆ 5) 1^2 cm 1.5 cm 38.8 2763.0

52 Downloaded from https://www.cambridge.org/core. 30 Sep 2021 at 08:34:37, subject to the Cambridge Core terms of use. Smedsrud:Entrainment ofsediment into sea ice

^2.0³C, Sw ˆ 35 psu (practical salinity units) and a sedi- the residual between fresh and salt water, ment density of 2650 kg m^3. because Carstens (1966) reports only ``a few thousand'' after Assumptions about the form of the grains are necessary the first few minutes, while A^D show ``a couple of hundred'' for modelling the aggregation, but are not needed to model during 24 hours. sediment concentrations other than in these calculations. The salt-water experiment of Tsang and Hanley (1985) The ``sphere assumption'' is applied for the grain form, may be compared to A^D, but there seeding took place at although many different shapes can be found.The sediment different levels of supercooling. The residual supercooling is assumed to be non-cohesive.That is, it does not form sedi- was not mentioned explicitly, but the reported salinity ment^sediment aggregates. (Sw ˆ 29^30 psu) and residual Tw gives a residual super- cooling of 0.08^0.2³C after the first frazil formation took 2.4. Frazil ice place. The longest experiment lasted about 15min, and had a residual supercooling of 0.141³C (Sw ˆ 30 psu), compar- Frazil ice is the key factor in the entrainment process. It is able with A^D. Omstedt (1985) examined these experiments also a very dynamic and complex feature to model. The and found that the data could be represented using Nu ˆ volume concentration of the frazil ice increases steadily over 1 4.0, di ˆ1mm and ti ˆ 10 di. time due to the heat flux, but also the size distribution The models mentioned here describe the situation from a changes as time passes.The frazil-ice size range in the model state of supercooling, through a seeding process, until ``equi- is similar to the range in other numerical studies and experi- librium'' is reached.While the seeding gives an accurate start- ments (Gosink and Osterkamp, 1983; Hammar and Shen, ing point for the ice-growth process in the calculation, it does 1995; Svensson and Omstedt,1998).The frazil-ice size distri- not represent most natural conditions where some snow will bution is based on video images from D, and the constructed fall into the water before, as well as when, the water reaches size groups are shown inTable 2. its freezing point. Here an attempt is made to model the situ- The rise velocities are calculated using a constant ation from a start with a few crystals at the surface, through a thickness of 1 d as suggested by measurements (Gosink and 30 i maximum supercooling, and for a long period of time during Osterkamp,1983). A steady-state situation is reached in 0.3 s the subsequent ``equilibrium''as well. or shorter for the given size classes, so the rise velocities are The crystal is assumed only to grow at the edges, so the treated as constants in the main model. The calculated rise 1 active freezing area is di k†ti k† in Equation (5). ti ˆ 30 di, velocities are given in Table 2. For the ``Small'' crystal class and the heat flux from a crystal is therefore independent of the given value is obtained by linear interpolation between the thickness. The total heating of the surrounding water zero and the ``Fine''class. from the growth of each crystal class in Equation (1) can As Frasemouses wi and K to calculate vertical gradients then be calculated as of Ci with Equation (4), no assumption needs to be made about the crystal form. However, when collision between 4 w GT k†ˆ qi k†Ci k† crystals, and aggregation between frazil-ice and sediment di k† i grains, are modelled, the crystals are assumed to be spheres. 1 6† Á  CsÀ1†: When this is done, an equivalent radius rie is used, instead of Pkˆ5 wCpw 1 À kˆ1 Ci k† the given di. rie is calculated so that a disc of diameter di and thickness ti has the same volume as the sphere of radius rie. Here w is the density of water, i is the density of ice, Cpw ˆ Values for rie are also given inTable 2. ^1 ^1 Pkˆ5 3989 J kg ³C , the heat capacity of water, and kˆ1 Ci is the total ice concentration in the gridpoint. The total heat- 2.4.1. Differential growth P ing in a gridpoint in Equation (1)is then G ˆ kˆ5 G k†. The heat flux from the ice crystal of class (k)tothesur- T i T This heat flux results directly in freezing calculated with rounding water is described by T À T N K T À T † 8 q k†ˆN K f w d k†t k† W† : 5† ÁC k†ˆ u w f w C k† : 7† i u w 1 i i i  L i 2 d k† i w di k† 2 i ÁCi k† is calculated for each size class (k ˆ 1, 4), and Here Nu is a Nusselt number describing the ratio between the actual(turbulent) heat flux and the heat conduction. represents the growth of a number of ice crystals. Notice that the ``Large''crystals (k ˆ 5) are not permitted to grow, Nu may vary with the flow conditions, and has earlier been set on the order of 1 (Svensson and Omstedt,1994),or higher because they have already reached their maximum size. Because of the constant mean diameter in the size classes when Nu is set dependent on the turbulent dissipation rate () and the Kolmogorov length scale () (Hammar and (di k†) this growth has to be transformed to a certain Shen, 1995). The thermal conductivity of sea water is set to volume (or, alternatively, number) of crystals being trans- K =0.564Wm^1 ³C^1 (Caldwell,1974). ferred to the next size class (Hammar and Shen,1995): w  Equation (5) is comparable with Equation (3) in Svensson ÁC k À 1† ÁC k† G k†ˆ i À i v k† : 8† and Omstedt (1994), transferred from number of crystals per I Áv k À 1† Áv k† i volume of water to volume of crystals per volume of water. i i 1 The radius (2 di) is chosen as the characteristic length scale Here vi k† is the volume of the ice crystals in that specific following Hammar and Shen (1995). class, and Ávi k†ˆvi k ‡ 1†Àvi k†.With this formulation, The models of Svensson and Omstedt (1994) and Hammar the``Large''class increases in volume because of growth in the and Shen (1995) were validated by fresh-water laboratory ``Coarse''class, while the ``Small''crystals (k ˆ1) a lway s h ave experiments like that of Carstens (1966). Svensson and Omstedt a pure loss to the ``Fine''class due to the growth. Total growth Pkˆ5 (1994) also used direct observations of particle size and total of frazil ice is then GI ˆ i GI k†,and the growth results number of crystals. It seems that there must be a difference in in a salt flux calculated as GS ˆ SwGI in Equation (2). 53 Downloaded from https://www.cambridge.org/core. 30 Sep 2021 at 08:34:37, subject to the Cambridge Core terms of use. Journal of Glaciology

2.4.2. Secondary nucleation Here, frazil ice has the radius rie and sediment rs, and their Secondary nucleation is the term used for production of new number concentrations are ni and ns, respectively. small crystals by removal of nuclei from the surface of par- is a diffusive coefficient, dependent on the flow. For ent crystals. The main processes thought to occur are colli- conditions where there is no velocity, is the Brownian sion between crystals and a resulting small piece of ice motion (molecular diffusion). For turbulent conditions, (collision breeding), and detachment of surface irregular- and if the colliding particles are smaller than about 10 ities by fluid shear (Daly,1984).The simplified approach of (Shamlou,1993), Svensson and Omstedt (1994) is followed here. A crystal in  1=21=2 1  2 relative movement to the fluid will sweep a volume ÁVi r†ˆ r : 13† during a time interval Át: 15  2  ˆ 3=†1=4  350 mm, using the turbulent dissipation ÁVi ˆ UrrieÁt; 9† rate  from A^C, and a constant kinematic viscosity  ˆ where r 1.8610 ^6, and only the largest crystals approach 10.In  2 2 Equation (13), r is the size of the eddies. Ur ˆ 2rie k†† ‡ wi k† ; 10† 15 By setting the size of the eddies, r,equalto rie ‡ rs†,the incorporating both the rise velocity and the turbulence ``particle diameter'', an expression for the aggregation frequency, can be obtained. The increase in number of new intensity. rie, the equivalent radius, has to be used here, because the crystal can twist and turn in all directions, and aggregates nx can then be expressed as: no way has been found of modelling a disc in a turbulent 3 dnx rie ‡ rs† flow.The increase in volume for the ``Small'' size class from ˆ n n : 14† dt t i s collision between all the different size classes is then calcu- T lated as: Here tT isTaylor's time-scale, representing turbulent strength, t ˆ 15 =†1=2 (Tennekes and Lumley, 1994). The aggrega- X5 U k† T ÁC k ˆ 1†ˆ n r ‰r k ˆ 1†Š3C k†Át: 11† tion factor, , describes the statistical chance of aggregation i i r k† ie i kˆ1 ie between the frazil and the sediment, and incorporates a col- liding efficiency.This colliding efficiency describes the statis- ni is the average number of all the different ice crystals in the tical chance of a collision between the two, and is assumed to grid volume. ÁCi(k ˆ 1) in Equation (11) is always positive, and there is a corresponding loss of (exactly the same) be constant since collisions involve soft and non-uniform volume for the other classes for each part of the summation aggregates. Only a fraction of the collisions will lead to an aggregate, and values for are expected to be less than unity, in Equation (11). ni is a calibration constant, and a maximum value has been set for each model run, limiting the secondary with zero as the lower boundary.The aggregation factor is nucleation process. Values found are generally much lower similar, but not identical, to the collection efficiency E than the value of 4.0610 6 given in Svensson and Omstedt (Osterkamp and Gosink, 1984), and also associated with the ``frazil stickiness''discussed by Kempema and others (1993). (1994), and a further discussion of ni is given in section 4.2. The theoretical framework has been tested on mono-sized polystyrene and spherical latex particles, and fits well to 2.5. Aggregation experimental data (Higashitani and others, 1983; Gierczycki and Shamlou, 1996). It is expected that every substance has its All substances suspended in water have the potential to collide own aggregation factor (and also colliding efficiency), and and aggregate with others. Suspended frazil ice tends to form should therefore be looked upon more as an empirical constant. flocs (crystal aggregates) in fresh-water experiments, but this Here two different types of aggregates are classified, was not reported in Hanley and Tsang (1984) or A^D. Frazil with their own size distribution. Ice that has one or more will also collide and aggregate with sediment to some extent, sediment grains aggregated to the crystal will be termed and this occurred during experiments A^D. hybrid ice Cis k†. Cis has the same sizes as Ci k†. Likewise, The term aggregation is preferred as the general mechan- all the sediment that has aggregated to ice will be termed ism, instead of the terms coagulation or flocculation, which hybrid sediment Csi j†, with the same size as Cs j†. should refer to the process that makes two substances aggre- It is now assumed that the basic collision Equation (12) gate (Shamlou,1993). Coagulation is the preferred term when describes the situation even if some of the particles are not two substances are not in physical contact but separated by a floating alone. The sediment is assumed non-cohesive, and thin liquid film, kept together by London^Van der Waals frazil flocs are not very abundant. forces. Flocculation is when there is physical contact between Looking at the loss of sediment in the ``clay''class (j ˆ1), the two particles:ice-crystal to ice-crystal aggregation is Equation (14) becomes; thought to be primarily of this kind. Aggregation here also includes what has been termed ÁC j ˆ 1† X5 3 j† ‰r j ˆ 1†‡r k†Š3 s ˆÀ s ie ``scavenging''of sediment by frazil ice in suspension, or ``fil- 3 Át 4tT ‰rie k†Š 15† tration'' of sediment in the surface slush (Osterkamp and kˆ1 Gosink,1984), as well as ``mechanical trapping'', or whatever Á Cs j ˆ 1†‰Ci k†‡Cis k†Š : process makes the sediment and frazil stick together when This is identical to equation (3) in Smedsrud (1998), adding they collide. the five size classes. The transfer to volumes is achieved by The basic relationship for the number of collisions per multiplying with the volume of the respective (spherical) unit time, J , between frazil ice and sediment is given by 3 is particles, 4/3rs. When a clay grain collides with one of the Smoluchowski (1917): ice crystals, or one of the hybrid ice crystals that has already

Jis / rie ‡ rs†nins : 12† aggregated to a sediment grain, aggregation may occur.The sediment volume then has a statistical chance, , of being 54 Downloaded from https://www.cambridge.org/core. 30 Sep 2021 at 08:34:37, subject to the Cambridge Core terms of use. Smedsrud:Entrainment ofsediment into sea ice

transferred to Csi. The loss and gain are exactly the same volume, so ÁCsi j ˆ 1†ˆÀÁCs j ˆ 1†. Hereafter IRS refers to measurements of ice-rafted sediment, i.e. sediment that remained on drained frazil crystals or was sampled within solid ice in A^D, while Csi refers to model results. In the same way, the equation for loss in an ice class (e.g. k ˆ 5), becomes: ÁC k ˆ 5† ÁC k ˆ 5† i ˆÀ is Át Át X5 3 j† ‰r k ˆ 5†‡r j†Š3 ˆÀ ie s 4t 3 jˆ1 T rs j†

Á Ci k ˆ 5†‰Cs j†‡Csi j†Š 16†

which describes exactly the same processes. Cis and Csi are always increasing in volume. There are no such terms as Cis‰Cs ‡ CsiŠ as one might expect, because even if a hybrid ice crystal aggregates with Fig. 1. Modelled vertical volume concentration of sediment, a sediment grain, the volume concentration of C does not is C , as cooling starts in experiment B. increase. The ice crystal is already ``tagged''as hybrid. Like- s wise, a hybrid sediment already on an ice crystal does not pieces of material. Anchor ice may grow due to adherence change its type if it aggregates with yet another ice crystal, of additional crystals, or from to the super- i.e. there are no terms like Csi‰Ci ‡ CisŠ either. cooled water (Martin, 1981). This may happen with the The aggregation factor is now the only parameter not hybrid ice and sediment that has sunk in the model as well, measured in A^D, and the model is used to estimate it. From and this ice/sediment may rise again if enough frazil aggre- the box-model approach in Smedsrud (1998)  0.025, but gates or grows so that the hybrid ice volume increases signif- it might vary between the different size classes. icantly. From Equation (17) the theoretical maximum The results from the box model (Smedsrud, 1998, fig. 2) concentration of IRS in neutrally buoyant surface slush ^1 showed that Equations (15) and (16) give rise to exponential- using w is found to be 159 g L . This is much higher than like solutions of the increasing Csi. This is caused by the IRS observations from A^D, or from the field, which are product of the different volume concentrations in Equations usually 51gL^1 (Nu« rnberg and others,1994). (15) and (16). This fits qualitatively with the IRS data pre- sented in Smedsrud (2001). 3. MODEL TUNING Cis and Csi are modelled separately by their volumes, but in reality they have formed several combinations of hybrid The first hour of each run has no snow and no cooling (T ˆ particles, with an unknown combination of the10 size classes. a ^2.0³C), so the sediment is allowed to reach a steady-state These hybrids will now have a different rise or sinking vertical concentration.Then snow is added at the given rate velocity, depending on how much of each type is in a specific for 1hour, equally distributed over the three largest crystal gridpoint. The average density of the hybrid particles at any sizes. After 2 hours the air temperature is decreased linearly level is calculated using: over 1hour to the observed mean of the given experiment P5 P5 kˆ1 Cis k†i ‡ jˆ1 Csi j†s (Ta ˆh^10.43, ^17.17i³C). h ˆ P P : 17† 5 C k†‡ 5 C j† kˆ1 is jˆ1 si 3.1. Initial sediment concentrations ^3 Here i ˆ 920 kg m , the density of pure ice, and s ˆ ^3 The steady concentration of sediment in the model is a 2650 kg m , the density of the sediment. h is used to calcu- late the rise or sinking velocity by linear interpolation. For balance between the vertical diffusion K and the sinking velocities w . The size distribution is based on observations the hybrid ice Cis, s  À  and does not change between experiments A^C, but the w k†ˆw k† w h ;<  mass of added sediment is changed in the model to match is i  À  h w w i 18† the measured initial concentration. Hereafter the term sus-  k†À ˆ w h w ;>  ; pended particulate matter (SPM) is used when referring to s  À  h w s w measurements, and Cs when referring to model results. As B will be used to calculate aggregation factors in section 4, the and for the hybrid sediment Csi,  À  initial Cs of that experiment is discussed here as well. w k†ˆw k† h w ;>  C is fairly homogeneous in the upper 0.5 m, and the value si s  À  h w s s w 19† at 0.5 m matches the observed SPM of 18 mg L^1 in the begin- w À h ˆ wi ;h < w : ning of B (Fig.1). As the total volume of sediment in the tank w À i remains constant, the steady-state situation will remain until ^3 w ˆ 1025 kg m is the time-averaged water density over the aggregation starts to be effective, and a significant volume the length of the experiment. This makes the range of wis of Cs is transferred to the hybrid class Csi. This decreases the and wsi equal to the range of wi and ws. The hybrid aggre- sinking velocity, and depending on the volume of the hybrid gates will tend to sink if the volume of Csi in a gridpoint is ice Cis, some sediment will be diffused upwards by the turbu- larger than 6% of Cis. Then anchor ice will be produced, lence from the situation shown in Figure 1. The added SPM i.e. frazil ice kept close to the bottom by sediment or larger corresponds to a homogeneous vertical concentration of 55 Downloaded from https://www.cambridge.org/core. 30 Sep 2021 at 08:34:37, subject to the Cambridge Core terms of use. Journal of Glaciology

Fig. 2. Temperature Tw (solid line),salinity Sw (dot-dashed line) and the corresponding freezing point Tf (dashed line) at 0.5 m depth as calculated by the model for experiment D. Fig. 3. Modelled vertical profile of frazil ice in suspension, The measured Tw (jagged line) is also plotted for comparison. Ci, 5 hours into experiment D. 40 mg L^1, or a total dry weight of 5.16kg. The total added 3.3. Frazil-ice volumes mass of sediment was 7.8 kg, including about 35% water. The SPM used in D consisted of Cs(1) and Cs(2) only. Volumes of frazil ice in suspension were measured during all Due to their small ws and the stronger vertical diffusion, experiments A^D, but most measurements were taken ^1 initial Cs was homogeneous with depth, at 12.0 mg L , during C and D, so they will be used here. Hereafter the equally divided between the two classes. term Ci is used for modelled values of frazil ice, and ``frazil ice'' is used for measured values. Ci at different depths is dependent on two parameters, the rise velocity, w k†, and 3.2. Supercooling i the (constant) vertical turbulent diffusion, K. wi k† depends on size as well as thickness, and a mean 1 Experiment D is used to tune Frasemo to the observed super- crystal-thickness to -diameter ratio of ti ˆ 30 di given by cooling and frazil size distribution. The supercooling drives Gosink and Osterkamp (1983) is used. In A^D the thickness the formation of frazil ice as described by Equation (5), and was not measured directly, only qualitatively estimated as thereby also influences the frazil size distribution. Experi- ti < 1mm, for the crystals with di  20 mm. Values for K ments A^C have salinity and temperature records, and are are estimated using the rms fluctuation velocity q, and the used as a control of the modelled supercooling. The given turbulent dissipation rate  (equation (5) in Smedsrud, equations and forcing leave two parameters to tune, the 2001). In C K ˆ 5.9610 ^3, using the mean q ˆ 10.3 cm s^1, ^4 Nusselt number Nu in Equation (5), and the ni in Equation (11). and  ˆ 3.7610 . ^3 ^1 The choice of Nu has minimal impact on the total Ci,and In D K ˆ111.4 610 , using the mean q ˆ 6.8 cm s , and ^6 the measured supercooling becomes insignificant at 24 hours  ˆ 3.7610 . The vertical profiles of Ci k† in D show that ^1 (0.002³C). Observations show that Tw is  0.02 below Tf 2^5 the two smallest classes have concentrations of 51mgL hours into experiments, and that Tw increases to  0.01below (Fig.3). Ci(3) and Ci(4) are close to vertically homogeneous, Tf after 6^20 hours. This is achieved using Nu 1. and the major part of the volume is found as Ci(5).The total This is somewhat surprising since it indicates that the calculated volume is close to the measured range of frazil ice turbulence does not increase the crystal growth, and it is 3.0^4.3 g L^1between 0.1and1m depth during D (Smedsrud, close to a situation with conduction only. A constant Nusselt 1998, fig. 1). At 6 hours Ci has a surface concentration of number implies that the crystals are large in comparison to 5gL^1,decreasing to 3.7g L^1 at 1.0 m depth. the turbulent dissipation length scale. This is discussed In C, more of Ci is close to the surface due to the lower ^1 further in section 4. Avalue of Nu ˆ 1.5 provides results that vertical diffusion. Surface concentrations reach 23 g L in fit A^D quite well. 10hours, and 58 g L^1 in 20 hours. Frazil-ice measurements ^1 Figure 2 shows the time evolution of Tw and Sw, and the indicate a linear increase at 0.5 m depth to around 1g L at corresponding freezing point Tf (same data as shown in fig- 10hours. This is also calculated by the model. Frazil-ice ure 1 of Smedsrud, 1998). The modelled salinity differs values from 0.25 and 0.75 m depth are also close to 1g L^1, ^1 50.05 psu from the observations (not shown here), which but Ci has a larger gradient, giving values from 0.7g L at ^1 makes Tf differ 50.003³C.The calculated Tw follows obser- 0.75 m to 7 g L at 0.25 m. vations to within 0.01³C as seen in Figure 2.The decrease of Tw to a minimum temperature, and then a return to an 3.4. Frazil-ice size ``equilibrium'' temperature slightly less than Tf is a well- documented feature and is found in all frazil-ice experi- The relative concentrations of frazil ice in the surface were ments (Carstens,1966; Daly,1984). counted from video images filmed during D. Countings For the 24 hour experiments A^C, model results are resulted in a close to constant distribution in time, where qualitatively the same. Supercooling of about 0.02^0.04³C 60% of the ice belonged to the Large class, 37% to the persists for up to 10hours, and then slowly decreases to Coarse class and 3% to the Medium class.Volumes of the 50.01³C at 24 hours. two smallest classes are insignificant, both in the model and 56 Downloaded from https://www.cambridge.org/core. 30 Sep 2021 at 08:34:37, subject to the Cambridge Core terms of use. Smedsrud:Entrainment ofsediment into sea ice

in the observations. This is consistent with the thermo- dynamic stability of frazil crystals, whereby the crystals have a maximum diameter given by their thickness ti,the level of supercooling and a number concentration (Forest, 1986). For a supercooling of 0.005³C and a number concen- tration of 107m3, the maximum diameter of 2 cm corres- ponds to a thickness of 47 mm. This process limits the growth of frazil-ice crystals over long time-scales. At 1.25 hours into D, frazil-ice sizes were 52.3% for the Large class (k ˆ 5),43.5% for the Coarse class (k ˆ 4), and 4.1% for the Medium class (k ˆ3).With time, the volume of the Large class increased most efficiently, and at 6 hours the relative concentration was 63.7%. The size distribution predicted by the model generally differs 55% from the observations. Towards the end of the experiment the model predicts too high an increase for Ci(5), and corresponding lower values for Ci(4) and Ci(3). The relative concentration of C (5) at 5 hours at the surface i Fig. 4.Vertical profiles of sediment aggregated to frazil ice at in Figure 3 is 69.4%. ForA^C, C (5) dominates, with 85% i 23 hours in experiment B. of the volume at the surface, while Ci(4) holds about 14% of the volume. Less than 1% is left for Ci(3), and again the two duced, up to the level where all SPM has transferred to IRS. smallest sizes are insignificant. The estimated values are (1, 2, 3, 4) ˆ (0.2, 5.0, 0.85, 16.5)610 ^3. (5) is set to zero to reproduce the observations 3.5. Size-dependent aggregation of no grains larger than 150 mmintheIRS. Values for j† are found within a fairly compact range. Observations of IRS show high variation, and the focus here It is therefore tempting to include a constant case. An of ^1 is therefore to model the average values of the aggregation 0.01 gives a surface Csi of 103 mg L and the same vertical process; the variation and sensitivity will be discussed in the gradients as in Figure 4. However, the Csi size distribution next section. Samples of SPM and IRS were taken in all shows a significant trend towards smaller grains, and the experiments A^D, but the size distribution of the IRS was values for the surface are Csi(1,2,3,4,5)ˆ (2.5, 17.1, 35.7, only measured in B. B is therefore used to calculate the 43.4, 1.3)%. Notice that only 1.3% of Cs(5) ends up as IRS, size-dependent aggregation factors, and A, C and D are despite the large size of these coarse and medium sand used to discuss the model sensitivity. grains. This indicates that collisions between Cs(5) and ice The increased chance of collision between larger parti- occur quite rarely. This must be due to the low value of cles is accounted for by the different radii in Equation (15). Cs(5) close to the surface (Fig. 1) where Ci has the largest This means that the chance of aggregation for each sedi- volume, as well as the small Ci volumes close to the bottom ment size class reflected by is dependent on more than of the tank where Cs(5) has high concentrations. Vertical size, for instance shape of the grains. distribution of modelled Ci in B and C is very similar, so sur- Because of the large variations of the IRS concentrations, face Ci are roughly 10 times higher than bottom values. For j† is adjusted to give the average IRS of 100mg L^1 with the three smallest sediment classes, almost nothing remains the measured relative concentrations. Some of the measured as Cs(1^3) in the constant case, and they are mostly trans- IRS concentrations are 4100 mg L ^1. These are probably ferred to hybrid sediments. local maxima from the horizontal variations. The measured SPM of 7.6 mg L^1 at the end of B provides a control for the mass of sediment entrained into the surface slush and ``lost'' 4. MODEL SENSITIVITY from the water. No grains larger than 150 mm were found in the IRS, so Much of the forcing and initialization in the model is robust and based on measurements where the physical process is Csi(5) ˆ 0. The four remaining Csi size classes show similar vertical gradients (Fig.4).This is because they are aggregated well understood, and the variations are known to be within a given range (T ;S ;T ;q and C ). Other settings (; K to ice and have a hybrid rise/sinking velocity wsi depending w w a s ^1 and C ) are partly based on measurements, where values are on Cis and Csi.InA^DCis was usually 1^100g L ,much i ^1 within the observed range, or measurements were qualitative higher than Csi, in the range 1^100mg L . This results in h close to the ice density, calculated by Equation (17), and cor- only, or showed high variations. A few settings (Nu; ni and ) are tuned constants, values chosen to make the model predic- responding rise velocities calculated by Equation (19). wsi in B is13.0 mm s^1at the surface, and decreases to 6.3 mm s^1at the tions comparable to observations. The sensitivity to the less bottom after 23 hours. robust parameters is discussed in this section. The relative concentrations of the different grain-sizes at the surface are close to the observed values.The major mass is 4.1. Turbulence Csi(4) (66.8%). There is 17.5% of Csi(3), and 18.3% of Csi(2) and only 0.4% of Csi(1). The differences between the calcu- The vertical turbulent diffusion, K, controls the vertical gra- lated size distribution and the measured size distribution of dients of Cs andCi as described by Equations (3) and (4). If K the surface IRS (Smedsrud, 2001, fig.17), are 51mgL^1. is very low, sediments are found close to the bottom, ice stays As j† is treated as an empirical constant in Equation at the surface, and no aggregation can occur.Turbulence also (15), any concentration of the different classes can be repro- affects the collision frequency, through tT in Equation (15), 57 Downloaded from https://www.cambridge.org/core. 30 Sep 2021 at 08:34:37, subject to the Cambridge Core terms of use. Journal of Glaciology

and the secondary nucleation of frazil crystals through Ur in erly, in situ size distribution over time would be appropriate, Equation (10). and this has not been accomplished to date. K is estimated with a common parameterization assuming Increasing Nu in Equation (5) to 3.0 reduces Tw to a homogeneous vertical density (Mellor and Yamada, 1982), ^2.005³C in Figure 2. Further increase of Nu to 6.0 reduces using q and  (Smedsrud, 2001). Measurements of q are robust, Tw to ^1.995³C. Neither size distribution nor vertical gradi- but the 95% confidence level of the  estimate covers an order ents are altered significantly by the change in Nu. Setting of magnitude (Smedsrud, 2001).The overall range of K calcu- Nu ˆ 1.0, the lower limit, reduces Tw to ^2.04³C, a super- lated from the current data of A^D was h1.7, 111.4 i610 ^3.There cooling of 0.02³C too much. is spatial and time variation of the turbulent parameters in the The value of ni in Equation (11) represents the average tank. For instance, the increasing ice concentration at the sur- value for the number of crystals in a gridpoint. Number con- ^1 face affects the flow, through both wave dampening by the centrations of crystals are quite high, with Ci(5) ˆ 10gL , ^1 6 ^3 slush, and increase in viscosity. ni  123.000 L ,or123.0610 m . The process of secondary A density interface also develops at the lower side of the nucleation is not well understood, and many of the new crys- slush, while the bed load of sediment has a minor effect on the tals that are created by collisions between the larger ones (with density. The assumption of a homogeneous water column, highest size, inertia and rise velocities) might be smaller than and thereby the constant K with depth also, is supported by the critical size at the present level of supercooling (Daly,1994). the fact that it is possible to reproduce measurements. These new, very small crystals will then dissolve, and not start Ci shown in Figure 3 is not very sensitive to K. Increasing to grow. The ones that are larger than the critical radius will K by 100% to 222.8610 ^3 decreases the vertical gradient, start to grow.As the level of supercooling decreases, the critical and Ci becomes almost vertically homogeneous. Decreasing radius increases, and thus there is less chance of producing new K to 55.7610 ^3 increases the gradient, and now a surface nuclei that are large enough. This limits the process, at the ^1 ^1 concentration of 4.3 g L is reached in 5 hours with 2.5 g L same time as ni increases, and provides a physical explanation at the bottom. of why an upper limit on ni is necessary. The maximum value of ni that gave satisfactory results was 1.06103 m^3. No significant changes appear with a 10- 4.2. Frazil ice fold decrease or increase of this value. Setting ni ˆ 1.0610 6, of the same order as proposed by Svensson and The volume and size of the snow are qualitative obser- Omstedt (1994), leads to quite a large difference. The mini- vations, and have to be considered. Completely removing mum Tw reaches only ^2.0³C, and returns to Tf before the snow causes the supercooling to reach 0.45³C in 6 hours, 2 hours is past, and follows Tf closely.The size distribution and still no frazil ice is produced. Reducing the snow from changes significantly, comparable to including small ice ^1 0.9to0.09mmd , produces a maximum supercooling of particles in the snow, with 45% in Ci(3) and Ci(4). 0.12³C, much higher than observations. A ten-fold increase The surface frazil size distribution is based on counting of the snow to 9 mm d^1 makes the maximum supercooling the individual frazil crystals on a monitor during D, and is 0.01³C, which is less than observed. This volume of snow qualitatively observed in the other experiments. While the starts to be significant compared to Ci; in 6 hours the snow range is robust, the individual concentrations in the size reaches 11.5 g L^1 if it is distributed over the upper 0.2 m. groups must be considered as estimates, but when both the If the size of the snow is changed to include the smallest size distribution and the Tw development are altered, this ice classes, then the supercooling is absent at 0.5 m, and only indicates consistency in the measurements, and demands a a very small supercooling is present in the upper 0.2 m. The tight forcing of the model. Ci size distribution is altered quite drastically to 45% of Calculation of wi is done using one set of experiments Ci(2) and Ci(3), and vertical concentrations become homo- (Gosink and Osterkamp, 1983). Alternative equations exist, geneous due to the small rise velocity of these ice classes. which generally give higher rise velocities. The velocity range The model sensitivity to volume and size of snow thus 0.01^80 mm s^1 is suggested by Daly (1984) for the size range 1 seems to be quite large. The measured time development of given in Table 2. By setting ti ˆ 10 di, the thickest crystals in Tw could not be reproduced using small sizes of snow, even the range of Gosink and Osterkamp (1983), wi(5) ˆ 73.9 ^1 when tuning the two other frazil coefficients Nu and ni.The mm s , close to the suggested value from Daly (1984). This ^1 ^1 volume of Ci does not change significantly with the vari- gives3.2gL of frazil at the bottom, 4.0 g L at 0.5 m depth, ations of snow, except for the added volumes themselves. and 5.3 g L^1 at the surface, again compared to Figure 3. The delicate balance between the snow size and the super- cooling indicates the tuning of the other two parameters con- 4.3. Aggregation trolling the ice growth, Nu and ni. Nu controls the heat conduction from each crystal, and ni the production of small crystals, which grow faster than the larger ones. As for the Vo lu m e s a n d s i z e o f Cs are considered robust, which pro- snow, Nu and ni does not alter the volume of Ci significantly, vides a control for the value of K, because the total Cs at a only the size distribution and the supercooling. given depth is known, and the model also ``predicts'' this Size- and turbulence-dependent Nu's are not included in volume concentration. The size distribution of Csi can only the model, but may be calculated using equations in Hammar be considered an estimate, but the range is robust. and Shen (1995). For  ˆ 3.7610 ^6 from D, the Kolmogorov The calculation of is one of the main results in this length scale becomes  ˆ 1120 mm. This results in Nu (1, 2, 3, work. Smedsrud (1998) showed to be most sensitive to the 4, 5) ˆ (239.7, 24.5, 4.1, 2.0, 1.3). These Nu would further dissipation rate, , and less sensitive to particle sizes. As a increase the more efficient growth of the smaller ice crystals spectrum of sizes is now used, and the ranges are considered and make it more difficult to reproduce the measured devel- robust, sensitivity studies of size are not needed.The sensitiv- opment of Tw. Tovalidate the theoretical values of Nu prop- ity of the constant is discussed, as a size-dependent can 58 Downloaded from https://www.cambridge.org/core. 30 Sep 2021 at 08:34:37, subject to the Cambridge Core terms of use. Smedsrud:Entrainment ofsediment into sea ice

way as B. The same parameters are used, except the meas- ured initial (homogeneous) values of Tw and Sw, the meas- ured average Ta, the measured average q, and the measured initial SPM (Cs). A g ive s a n XE of 3.35 after 23 hours using ˆ 0.01, and is also plotted in Figure 5. This is equal to an IRS concentration of 42 mg L^1, and the measured range ^1 was13^44mg L . In experiment C an XE of 2.8 is predicted (43 mg L ^1), higher than the observed range of 6^33 mg L^1. Experiment D is different because of the high K,the smaller size of the sediment, and the short duration of 6 hours. At the end of the experiment the impellers were switched off, and all frazil crystals in suspension rose to the surface with their aggregated sediment. The IRS sampling was done after this. At 6 hours the total calculated Cis over the 1m depth is added and divided over the two upper grid- ^1 points. Using ˆ 0.06, a surface Csi of 12.6 mg L is reached, the average of the five measurements. This is con- sistent with Figure 5, indicating that X  1 after 6 hours. Fig. 5. Normalized concentrations of sediment with time from E While the model cannot reproduce the exact concentration experiment A^D (XE ˆ IRS/SPM).The different XE's from the model are shown as (dashed line),and frazil, slush of IRS in each experiment, it does reproduce the main features, and granular IRS refers to whether the IRS was sampled in such as the highest IRS levels in B, and lower levels in A and C. The higher IRS values in B are a product of the high initial frazil ice, surface slush or surface granular ice. SPM and the high heat flux creating more frazil ice. always be calculated, and the calculated Csi did not deviate Why then does C have lower surface IRS than Awhenboth too much from the measured IRS values using a constant . the initial SPM and the heat flux are larger? The explanation As the aggregation factor is empirical, the sensitivity of is that there is more Csi in C, but less at the surface due to the should be tested against the other parameters of the larger K. model. The difference in IRS concentrations between A^D Waves are incorporated into the model in the way that the should also be discussed in this context. To do this, the en- measured higher turbulent rms velocities increase K.Inthis trainment factor, XE ˆ IRS/SPM, is utilized, as discussed way waves can increase turbulent diffusion of frazil ice down- in Smedsrud (2001). wards, and sediment upwards. But there is no mechanism Measured IRS, or calculated Csi, is compared with the that increases aggregation or entrainment by waves. initial SPM, or Cs, in each experiment. In this way the dif- Aggregation seems to occur mainly in the upper half of ferent experiments, A^D, can be easily compared. XE has the 1m deep water column in A^C due to the relatively high values of 51 when the surface Csi is smaller than the initial frazil concentrations there. Towards the bottom, less frazil ice Cs at 0.5 m. With time the IRS concentration increased in is found, as well as the larger sediment grains. Even with a the tank experiments (Fig. 5).The calculated surface Csi in constant for all classes of Cs j† almost no Csi(5) was created. ^1 B at 23 hours,100 mg L , results in XE ˆ 5.6. With the larger K and smaller sediment in D, the aggre- For a given time evolution with associated concentra- gation process takes place efficiently at all depths. Under tions and size of Ci and Cs,the relationship =tT from Equa- such conditions the ``box-model approach'' (Smedsrud, tion (15) has to be constant to give a certain volume of Csi in 1998) seems appropriate. the surface.This indicates the connection between and the strength of the turbulence. For experiment B, =tT ˆ 0.037. Increasing and decreasing  by one order of magnitude 5. MODEL PREDICTIONS results in ˆh0.003, 0.032i, which corresponds approxi- mately to the observed range of  in A^C (Smedsrud, 2001, To further increase the understanding of the aggregation fig. 2). Setting ˆ 0.03 gives XE ˆ 9.1, and setting ˆ process, the model predictions are tested against three of 0.002 gives XE ˆ 3.9, both after 23 hours. As seen in Figure the central and robust parameters. These are the constant 5, both these values are within the measured variation. air temperature, Ta, driving the formation of frazil ice, the ^1 The maximum IRS concentration (200 mg L in B, XE initial sediment concentration Cs(1,2,3,4,5)andtheturbu- = 11.1) indicates an empirical maximum for the aggregation lent rms velocity, q. B is used to test these predictions, and process in the tank experiments. Using ˆ 0.1 gives Csi ˆ the corresponding size-dependent 's. ^1 202 mg L , and the time evolution of XE is the upper curve The mean Ta during B was ^17.17³C. Using a Ta of ^25.0³C ^2 ^2 in Figure 5. Now all the sediment in classes Cs(1, 2, 3) i s increases the total heat flux from 90 W m to 136 W m .The found only as Csi, and the bed load of the two remaining maximum supercooling reaches 0.07³C instead of 0.05³C.The classes has only 20 mg L^1. The size distribution improves surface slush increases from 207 g L^1 at the surface at 23 ^1 ^1 ^1 from the other constant runs, but only 0.5 mg L of Cs is hours to 298 g L . The surface Csi increases from 100 mg L ^1 ^1 left at 0.5 m, much lower than the observed 7.7mg L . The to 118 mg L . The size distribution of the Csi does not change abrupt change in XE at 4 hours occurs because there is no qualitatively. 2 more Cs in the near-surface layer; it has already trans- With a Ta of ^10.0³C, a mean heat flux of 46 W m leads to ^1 formed to Csi. The empirical minimum value of is found a supercooling of 0.03³C, and 112g L of ice in the surface. ^1 to be 0.0003 (Fig. 5), so the overall range is ˆh0.0003, 0.1i The Csi in the surface decreases to 68 mg L at 23 hours. based on A^D. Doubling the initial Cs gives an initial concentration of 40 ^1 Experiments A and C have been modelled in the same mg L at 0.5 m. The response in Csi is almost linear, giving 59 Downloaded from https://www.cambridge.org/core. 30 Sep 2021 at 08:34:37, subject to the Cambridge Core terms of use. Journal of Glaciology

204 mg L^1 at 23 hours at the surface. This is also true for level between laboratory experiments. Entrainment increases ^1 lowering the initial Cs to 9 mg L (half the initial volume), with increasing turbulence and waves, and increases close to ^1 which gives a Csi of 52 mg L at 23 hours at the surface. The linearly with sediment concentration of the water. Lower air size distribution of Csi does not change significantly. temperatures lead to larger heat fluxes from the water to the Changing the rms fluctuation velocity q changes only the air, and corresponding higher concentrations of frazil ice, value of K. It does not alter the efficiency of the aggregation which also increases entrainment. process, only the vertical distributions. Increasing q from The model sensitivity to the different parameters is 7.4 cm s ^1 to 14cm s^1 leads to a 10 times increase in K to tested, and the average values from experiments A^D should ^3 ^1 21.2 610 . The initial Cs becomes 38 mg L . The increased provide a basis for using the developed model in natural ^1 vertical diffusion reduces the surface Ci to 40 g L at 23 case-studies. hours, but as the volume does not change, more Ci is in sus- pension. The surface Csi decreases too, reaching only 43 mg ^1 ACKNOWLEDGEMENTS L , but the total sum of Csi increases. If all Csi rose to the surface, it would now be 32.2 g mÀ2,compared to 18.4 g mÀ2 The cooperation of C. Sherwood, who developed the basic in the normal case. Using q ˆ 5.0 cm s^1 (K ˆ 0.34610 ^3) model, is gratefully acknowledged. He also organised a ^2 makes the vertical sum of Csi 3.7 g m . research period at the Commonwealth Scientific and Indus- The surface size distribution of Csi changes significantly trial Research Organisation where we had many clarifying with q. The high q makes Csi consist of larger grains, while discussions.Thanks to A. Omstedt and A. Foldvik, as well as the low q leads to smaller grains in the Csi. This is because E. Kempema for many helpful suggestions as a reviewer, high vertical diffusion tends to distribute larger grains more and the scientific editor M. Lange.This work was supported uniformly through the water column. by the Norwegian Research Council, under contract No. The model predictions of Csi are close to linear for 71928/410. increased heat fluxes (or Ta with constant wind), and initial concentrations of C . The turbulence in the model depends s REFERENCES on both q and , and the associated balance between K and the rise/sinking velocities is quite delicate. Ackermann, N. L., H.T. Shen and B. Sanders.1994. Experimental studies of The effect of changing Ta, Cs and q shows that the aggre- sediment enrichment of Arctic ice covers due to wave action and frazil gation process is strongly dependent upon these parameters. entrainment. J. Geophys. Res., 99(C4),7761^7770. They are all needed to estimate the IRS content of newly Barnes, P. W.,E. Reimnitz and D. Fox.1982. 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MS received 3 April 2001and accepted in revised form 8 January 2002

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