ICES mar. Sei. Symp., 192: 33-38. 1991

Factors affecting the vertical distribution of eggs

Svein Sundby

Sundby, S. 1991. Factors affecting the vertical distribution of eggs. - ICES mar. Sei. Symp., 192: 33-38.

The spatial distribution of eggs and larvae is a function of the properties of the ambient water (the density, current, and turbulent diffusion) and of the physical properties of the eggs (the buoyancy and dimension). Study of the vertical distribution is the first step towards understanding the horizontal transport of eggs and larvae. Two models are applied to demonstrate how the physical and biological conditions influence the vertical distribution of the three main categories of eggs, here defined as pelagic, bathypelagic, and bottom eggs. In particular, the physical conditions affecting the distribution of bathypelagic eggs are studied. Wind-induced turbulence, the most important ambient factor for the vertical distribution of pelagic eggs and larvae, contributes to mixing the buoyant eggs and larvae throughout the wind-mixed layer. The vertical spreading of bathypelagic eggs depends mainly on the buoyancy distribution of the eggs. The model demonstrates that non-adhesive demersal eggs will be partly mixed into the water column, this mechanism contributing to the horizontal transport of demersal eggs.

Svein Sundby: Institute of Marine Research, Department of Marine Environment, P. O. Box 1870 Nordnes, N-5024 Bergen, Norway.

Introduction and understanding the vertical distribution of eggs and larvae. This paper demonstrates how the physical The spatial distribution of eggs and larvae is influenced properties of eggs and the ambient physical forces influ­ by a set of biological and physical processes which ence vertical distribution. Two models for the vertical together contribute to determine the fate of the year distribution of eggs (Sundby, 1983; Westgård, 1989) are class. The importance of the distribution and transport applied to demonstrate the three main types of vertical of the early stages for the recruitment of stocks has distribution: pelagic, bathypelagic, and bottom dis­ been pointed out by many authors: it has been suggested tributions. The physical conditions for each type of that unfavourable drift of eggs and larvae beyond the distribution are analysed. appropriate distributional area will cause permanent loss from the population (Hjort, 1914). On the other hand it has been shown that anomalous transport from Results and discussion one region to the other may transfer recruits from one Basic equation stock to another. This has been described by Hansen and Buch (1986), who found that export of cod larvae The vertical processes which influence the distribution from the Iceland to the Greenland area increased the of eggs are studied and it is assumed that all horizontal stock. The importance of larval retention gradients are zero. The basic equation is then reduced within specific geographical regions during critical to the vertical component of the diffusion equation: periods has been outlined by lies and Sinclair (1982). Considering the large vertical variations of the hori­ zontal flow field, it is evident that the vertical dis­ 8C(z, t) 3[w(z, t)C(z, t)] d rir, dC(z, t)‘ ------= — K(z, t) ------tribution of eggs and larvae is important for their at dz dz L dz . horizontal transport and spreading and their survival. + S(z, t) + M(z, t) (1) Cushing (1982) gave an example of how the vertical distribution itself directly influenced recruitment: the rising halocline in the Baltic caused cod eggs and larvae where C(z, t) is the concentration of eggs in numbers to rise closer to the productive layers where their food per unit volume; w(z, t) is the vertical velocity of the is produced. Consequently, an important step towards eggs; K(z, t) is the vertical eddy diffusivity coefficient; understanding the recruitment processes is describing S(z, t) is the spawning production of eggs; M(z, t) is the

33 egg mortality; z is the vertical component, positive Egg buoyancy towards increasing depth; t is time. To solve the equation, the vertical velocity of the General knowledge concerning the buoyancy of fish eggs, w(z, t), and the vertical eddy diffusivity coef­ eggs has increased substantially during recent years, ficient, K(z, t), must be known. The vertical velocity is in particular since the density gradient column was expressed as w = f(d, Ap, v), where d is the diameter introduced by Coombs (1981). This instrument enables of the egg, Ap is the difference in density (buoyancy) us to measure the specific gravity of individual eggs with between the egg, pe, and the ambient water, pw, and v high accuracy and resolution. The physiological causes is the molecular viscosity of the water. Hence, the two of buoyancy in marine fish eggs have been studied by physical properties of the eggs, the buoyancy and the Craik and Harvey (1987). diameter, are key variables for modelling the vertical Since pelagic eggs have a specific density which is distribution. lower than that of the upper mixed layer of the sea, In the following sections it will be shown that changes they tend to rise towards the surface. Only a small in the buoyancy, Ap = pw - pe, result in the most pro­ fraction of such eggs, however, are found at the very nounced changes to the solutions of the basic equation surface, because the turbulent forces of the mixed layer (1). For this reason it is useful to classify eggs into three counteract the buoyant forces of the eggs. The eggs will main groups (see Fig. 1): A. Ap > 0, B. Ap = 0, C. concentrate to varying degrees towards the surface, Ap < 0. In this paper, group A will be defined as depending on the magnitude of the counteracting forces. “pelagic” eggs, group B as “bathypelagic”, and group Examples of eggs with such distributions are North Sea C as “bottom” eggs. Since there are few descriptions of plaice eggs (Pommeranz, 1973), North Sea mackerel the vertical distribution of eggs in relation to their eggs (Iversen, 1973; Coombs, 1981), and Northeast buoyancy, much of the literature is inconsistent in this Arctic cod eggs (Solemdal and Sundby, 1981). The question. It seems that eggs are often described as vertical distributions of these species have been mod­ “pelagic” if they are found in the water column and elled by Sundby (1983). “demersal” if they are found on the bottom. However, Bathypelagic eggs have a higher specific density than the solution to Equation (1) will show that all three the upper mixed layer of the sea, but lower than the groups defined above are found in the water column. density of the bottom layer. They are therefore dis­ Even demersal eggs, given they are non-adhesive, will tributed at mid-depths and quite frequently in the be mixed into the water column. In addition to the three pycnocline. Examples of species with this type of egg main types of eggs in Figure 1, there are also mixed distribution are Pacific halibut (Hippoglossus steno- types. Species with a buoyancy distribution between lepsis) (Thompson and van Cleve, 1936), the Baltic cod pelagic and bathypelagic have been reported by Coombs (Kändler, 1949), and the Atlantic halibut (Hippoglossus etal. (1985). hippoglossus L.) found in Norwegian fjords and coastal waters (Haug et al., 1984, 1986). Kendall and Kim (1989) have demonstrated how bathypelagic eggs of the

f walleye ( Theragra chalcogramma) substantially 0,5 changed their vertical distribution mainly due to changes in buoyancy during their development. 0.3 Bottom eggs have a specific density which is higher 0,1 than that of the bottom layer. In principle, demersal

30 31 32 33 36 37 38 3935 eggs are one kind of bottom eggs. However, it is essen­ I I i tial to distinguish between adhesive and non-adhesive eggs. With respect to the nature of the vertical forces acting on the eggs, there is no difference between non­ adhesive demersal eggs and pelagic eggs. Non-adhesive demersal eggs, unless buried in the seabed, will be mixed to varying degrees into the water column dep­ ending on the magnitude of the bottom turbulent mixing. One species with non-adhesive demersal eggs is the saffron cod (Eleginus gracilis) in the northeast Pacific Ocean (Dunn and Matarese, 1986). Even adhesive eggs may separate from each other and from 100 the seabed and be mixed into the bottom layers and transported away. This has been reported for Barents Figure 1. Buoyancy distribution of three categories of eggs Sea capelin eggs (Bakke and Bjørke, 1973). (upper part of the figure) in relation to the salinity profile (lower part of the figure). A: pelagic eggs, B: bathypelagic The density distribution of an egg population can eggs, C: bottom eggs. often be described by a Guassian distribution function.

34 Eggs from the Northeast Arctic cod are neutrally buoy­ distribution of air bubbles in the sea. Although their ant at an average salinity of 31.0 and standard deviation results differ to some extent, it may be concluded that of 0.55 (Solemdal and Sundby, 1981). Eggs from the the eddy diffusivity coefficient ranges from about Atlantic halibut are neutrally buoyant at an average 10 cm2 s“1 at wind speeds near zero to about 103 cm2 s-1 salinity of 34.2 with a standard deviation of 0.52 (Haug at wind speeds of approximately 20 ms-1. et al., 1986). The buoyancy of sprat eggs off the southern In the pycnocline the eddy diffusivity coefficient is coast of Great Britain ranged over about eight salinity inversely related to stratification and directly dependent units during the end of the egg stage (Coombs et al., on energy input. However, the functional relationship 1985). Consequently, it is assumed that there is a great to those parameters is still unknown. Several authors difference in the vertical distribution of the heaviest and have estimated the vertical eddy diffusivity in different lightest fractions of an egg population. In Figure 1 the fjords and coastal waters, e.g. Gade (1970) for Oslofjor- neutral buoyancy distributions of three different egg den, Kullenberg (1971) for shallow coastal waters, populations are drawn with a vertical salinity profile. Svensson (1980) for a Swedish fjord, and Buch (1982) Distribution A is consistent with pelagic eggs, e.g. the for two-layered Scandinavian fjords. Gargett (1984) eggs of Northeast arctic cod; distribution B is identical reviewed the literature on the vertical diffusivity coef­ with bathypelagic eggs such as the Atlantic halibut eggs, ficient in stratified systems. Depending on the degree and distribution C corresponds to bottom eggs. The of stratification, the eddy diffusivity coefficient ranges last-mentioned is a hypothetic distribution, since no from 0.5 x 10-2cm2s-1 to about l-4cm2s_1. reports of quantitative density measurements of non­ Bottom turbulence, which normally extends several adhesive bottom eggs are available. metres above the bottom, is mainly dependent on the There are, however, examples of species which are a boundary layer velocity and bottom roughness. Bowden mixture of the main types described above. Coombs (1962) reported values from several authors. In areas et al. (1985) investigated buoyancy and vertical dis­ of strong tidal mixing the eddy diffusivity coefficient tribution in eggs of sprat (Sprattus sprattus) and pilchard may exceed 100 cm2 s’ 1, although lcm 2s^' is more (Sardinapilchardus) off the south coast of Great Britain. common above the seabed in deep oceanic areas. These were a mixture of pelagic and bathypelagic eggs. In addition, specific gravity of the eggs changed through Vertical distribution of eggs development, and ambient salinity varied through spawning season. This will result in a variety of possible If the terms “spawning production”, S(z, t), and “mor­ vertical distributions with peak concentrations partly in tality”, M (z,t), are neglected in Equation (1) and the surface and partly in the pycnocline. stationary conditions are considered, the diffusion equation reduces to;

Vertical eddy diffusivity coefficient SC(z) -w(z) x C(Z) = K(z) (2) The other variable which influences the vertical dis­ tribution of eggs is the vertical eddy diffusivity coef­ ficient. Depending on depth, wind velocity, strati­ Equation (2) applies to the fraction of eggs which fication, tidal energy, and bottom stress it varies have reached the steady state distribution after being over approximately five orders of magnitude. It is largest spawned at some depth. We assume the buoyancy dis­ in the mixed layer and decreases to a minimum in the tributions shown in Figure 1 and a variation of the eddy pycnocline due to the stratification which reduces the diffusivity coefficient as shown in Figure 2 and apply vertical transport of turbulent energy. A slight increase the models for the vertical distribution (Sundby, 1983; occurs below the pycnocline due to the weaker strati­ Westgård, 1989). The three categories of eggs - pelagic fication followed by a pronounced increase in the bot­ (A), bathypelagic (B), and bottom eggs (C)-will appear tom layer due to bottom friction. The characteristics as shown in Figures 3a and 3b. are illustrated by the hatched area in Figure 2. It shows The distribution for low eddy diffusivity coefficients qualitatively how the vertical eddy diffusivity coefficient in the water column is shown in Figure 3a, cor­ may vary through a water column. responding to the lower range of eddy diffusivity profile Estimating the mixed layer eddy viscosity coefficient (Fig. 2). The value of the mixed layer is 75cm2s_1, is difficult, partly due to the great problems in separating corresponding to wind speeds of 0m s_1 (according to wave motion from turbulence. Sverdrup et al. (1942) Sundby, 1983). In the pycnocline the minimum eddy derived estimates of the eddy viscosity coefficient from diffusivity coefficient is 0.01 cm2s_1, and the value of the Ekman theory. Sundby (1983) estimated overall the bottom layer 6cm 2s_1. eddy diffusivity coefficients for the mixed layer from a The distribution for high eddy diffusivity coefficients model based on the vertical distribution of pelagic eggs. is shown in Figure 3b, corresponding to the higher range Thorpe (1984) estimated the eddy diffusivity coefficient of eddy diffusivity profile in Figure 2. The mixed layer in the surface layers based on a model of the vertical eddy diffusivity coefficient is 585 cm2 s_1 corresponding

35 S % o log K substantially. Consequently, the vertical spreading in 35 the pycnocline depends mainly on the density dis­ tribution of the eggs and the density profile, and not so much on the level of turbulence. To show this we solve the diffusion equation for eggs of a given density in a linear pycnocline. The eddy diffusivity coefficient can then be considered as constant with respect to depth. In a linear pycnocline, p(z) = kz + b, the vertical velocity, w(z), varies linearly within the Stokes regime. The vertical velocity may therefore be written:

100 4- _L 100 w(z) = m(z — zA) (3)

Figure 2. Ranges of the vertical distribution of the eddy dif­ where m is a constant, and zA is the level where Ap(z) = fusivity coefficient, K, in cm2 s '1 (right part) for a hydrographic 0, i.e. the level of neutral buoyancy of the egg. Equation profile (left part) identical with the profile in Figure 1. (3) is inserted into Equation (2):

3C(z) to a wind speed of 15 ms-1 (according to Sundby, 1983). —m(z — zA) X C(z) = K -— (4) O Z The minimum value of the pycnocline is 0.5 cm2 s-1, while the value for the bottom layer coefficient is 90cm2s~1. The solution to Equation (4) is: The curves in Figure 3a and 3b show that the vertical distribution of pelagic eggs (A) is very sensitive to C(z) = C A exp - ^ (z - zA)2 (5) variations in the wind-reduced turbulence, as also demonstrated by Sundby (1983). The curves also show that varying bottom turbulence levels influence the ver­ where CA is the concentration of eggs at the depth of tical distribution of bottom eggs (C). However, the neutral buoyancy, zA. According to Equation (5) the vertical distribution of bathypelagic eggs (B) confined eggs are vertically distributed as a normal distribution, to the pycnocline is fairly insensitive to variations in the where the standard deviation: pycnocline turbulence. The pycnocline eddy diffusivity coefficient is increased by a factor of 50 from Figure 3a to Figure 3b, but the vertical spreading is not changed a = V(K/m) (6)

b CONCENTRATION (No/m3) CONCENTRATION (No/m3) 100 150 200 100 150 200

25

£ 50 x h— i— Q_ CL LU LU □ □

75 75 -

100 100

Figure 3a. Vertical distribution of pelagic (A), bathypelagic Figure 3b. Vertical distribution of pelagic (A), bathypelagic (B), and bottom eggs (C) during low turbulence (see numerical (B), and bottom eggs (C) during high turbulence (see numerical values in the text). The neutral buoyancy distributions, salinity values in the text). The neutral buoyancy distributions, salinity profile, and eddy diffusion profile as shown in Figures 1 and 2. profile, and eddy diffusion profile as shown in Figures 1 and 2.

36 When the velocity of the eggs is confined within the than the bottom water layer, here defined as bottom Stokes regime, the Stokes equation for the terminal eggs (distribution C in Figs. 3a, 3b), has the inverse velocity is valid and the expression for m becomes: distribution of that of pelagic eggs. Since the bottom turbulence is generally much lower than turbulence in m = 1/18 d2 v 1 pwN2 (7) the upper mixed layer, the bottom eggs will be more concentrated towards the boundary than the pelagic where d is the diameter of the egg and N is the Brunt- eggs. For low levels of bottom turbulence (Fig. 3a), less Väisälä frequency. The value of the molecular viscosity, than 3% of the eggs are mixed more than 3 m above v, has been tabulated by Riley and Skirrow (1975) the seabed. However, in shallow regions where the tidal (e.g. at 5°C and salinity 30 the molecular viscosity is induced bottom turbulence is high, and where the mixed 0.016 gcirT1 s’ 1). layer may even extend to the bottom, the bottom tur­ We take, as an example, the vertical distribution of bulence coefficient may exceed 100 cm2 s’ 1, and the Atlantic halibut in the pycnocline of fjords in northern eggs will be distributed as C in Figure 3b. In this example Norway described by Haug et al. (1986), where the 40% of the eggs are more than 3 m above the seabed. squared Brunt-Väisälä frequency, N2, ranged from 0.5 x 10’ 4to 2 .0 x 10’ 4 s’ 2. From the above-mentioned Development of steady state egg profiles literature on the influence of stratification on the tur­ bulence, the eddy diffusivity coefficients range from 0.1 In the previous section, distributions based on balance to 0.5 cm2 s’ 1. When these values are inserted into between the buoyancy force of the eggs and the vertical Equations 6 and 7, the standard deviation, a, of the turbulence forces were studied, i.e. when 3C/5t = 0 vertical spreading of one buoyancy group of halibut (steady state). The time it takes to reach steady state eggs will range from 0.4 to 1.6 m. According to Haug distribution depends on the spawning depth, the buoy­ etal. (1986), the older eggs (which definitely have come ancy, and the turbulence. The way in which the mixed to a steady state vertical distribution) extend over a 150— layer turbulence influences the time required to reach 250 m water column. Consequently, the large vertical the steady state profile for pelagic cod eggs spawned at spreading of halibut eggs in the water column is due to 120 m depth is illustrated in Figure 4. The buoyancy the neutral buoyancy distribution of the eggs alone and distribution of these eggs equals those of the cod eggs, not to the vertical turbulence. distribution A, in Figure 1. The figure shows the con­ The vertical distribution of eggs with a density higher centration profile for every 6th hour after spawning near

W - O m / s

30h 36h

500 1000 1500 2000 0 500 0 500 500 500 500 500 CONCENTRATION (No/mB)

W = 15 m Is

18h

7

100

0 500 0 500 0 500 0500 0 500 CONCENTRATION (N o /m 3 )

Figure 4. Development of the vertical profile of pelagic eggs (A) from an initial distribution, i.e. spawning near the bottom, to steady state for two events of mixed layer turbulence. Upper part: wind velocity, W = 0 ms Lower part: wind velocity, W = 15 ms^1.

37 the bottom. It takes 48 h to reach the steady state Gargett, A. E. 1984. Vertical eddy diffusivity in the ocean distribution during calm wind conditions, while it takes interior. J. Mar. Res., 42: 359-393. Hansen, H., and Buch, E. 1986. Prediction of year-class only 30 h to reach steady state at wind speed of 15 m/ strength of ( morhua) off West Greenland. s. It can also be shown that there are large variations NAFO Sei. Coun. Studies, 10: 7-11. in the time required to reach steady state for the heavy Haug, T., Kjørsvik, E., and Solemdal, S. 1984. Vertical dis­ fraction and the light fraction of the eggs. While the tribution of Atlantic halibut (Hippoglossus hippoglossus) eggs. Can. J. Fish, aquat. Sei., 41: 798-804. buoyancy of pelagic eggs is constant as they rise through Haug, T., Kjørsvik, E. and Solemdal, S. 1986. Influence of the mixed layer, the buoyancy of bathypelagic eggs some physical and biological factors on the density and decreases as they move toward the depth of equilibrium. vertical distribution of Atlantic halibut (Hippoglossus hip­ This implies that the vertical velocity also decreases, poglossus) eggs. Mar. Ecol. Prog. Ser., 33: 207-216. and it takes a relatively long time to reach steady state Hjort, J. 1914. Fluctuations in the great fisheries of northern Europe viewed in the light of biological research. Rapp. P.- for bathypelagic eggs. v. Réun. Cons. int. Expior. Mer, 20: 1-228. Iles, T. D., and Sinclair, M. M. 1982. Atlantic herring: Stock Conclusion discreteness and abundance. Science, 215: 627-633. Iversen, S. A. 1973. Utbredelse og mengde av makrellegg The vertical distribution of pelagic eggs is influenced (Scomber scombrus) og zooplankton i den nordlige delen av mainly by wind-induced mixing. Buoyancy distribution Nordsjøen i årene 1968-1972. (Distribution and abundance of mackerel eggs (Scomber scombrus) and zooplankton in determines the vertical distribution of bathypelagic the Skagerrak and northern parts of the North Sea during eggs, while vertical spreading in the pycnocline of these the years 1968-1972.) Cand. Real-thesis, University of eggs is essentially insensitive to vertical mixing. Model Bergen, 71 pp. (In Norwegian). results show that non-adhesive demersal eggs will be Kandier, R. 1949. Untersuchungen über den Ostseedorsch warend der Forschungsfahrten mit dem R.F.D. “Poseidon” found to some extent in the water column. This will in den Jahren 1925-1938. Berichte der Deutschen Wis­ contribute to advection of demersal eggs. The time it senschaftlichen Kommission für Meeresforschung, Neue takes to reach a steady state vertical egg distribution Folge, 11: 162-168. depends on spawning depth, buoyancy distribution of Kendall, A. W., Jr., and Kim, S. 1989. 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