Numerous conductivity-temperature-depth data obtained in the Arctic basins are analyzed to describe structural features of intrusive layering. Special attention is paid to large intrusions (vertical scale of 40–100 m) observed in upper, intermediate and deep layers (depth ranges of 150–200, 200–600 and 600–1000 m, respectively). The analysis of the intrusions is accompanied by descriptions of the frontal zones where the layering was observed. Based on observations detailed estimates of frontal zone parameters are presented. Vertical profiles of temperature and salinity are found to have a well-defined “sawtooth” or “cog” shape, displaying a sequence of relatively thick, weak gradient layers, where temperature and salinity are decreasing with depth, interleaved with relatively thin, high-gradient sublayers, where temperature and salinity are increasing with depth. Some hypotheses about causes responsible for cog structure existence are discussed. Intrusions with high-amplitude anomalies in the vertical profiles of temperature and salinity are shown to be present at baroclinic fronts. Based on models of interleaving and data analysis the apparent vertical and lateral diffusivity in the frontal zones of the upper and deep ocean layers are estimated, and the slope of unstable modes relative to the isopycnals is examined at the baroclinic front in the situation when both temperature and salinity are stably stratified.
 Striking features of the Arctic Ocean water column are the presence of step structures in temperature and salinity and the existence of inversions and thermohaline intrusions. Step structures were first observed from ice camps in the late 1960s in the deep thermocline above the temperature maximum in the Canada Basin [Neal et al., 1969] but are found in the thermocline over the entire Arctic Ocean. Inversions and intrusions were reported and discussed by Perkin and Lewis  from the Eurasian Basin northeast of Svalbard and the Yermak Plateau. Perkin and Lewis assumed that the intrusions were created by lateral mixing between Atlantic water entering the Arctic Ocean through Fram Strait and older Atlantic water cooled in the Arctic Ocean, the Arctic Atlantic Water (AAW).
 The continued studies of the water structure in the Arctic Ocean have shown that thermohaline intrusions are observed practically everywhere [Padman and Dillon, 1988; Quadfasel et al., 1993; Rudels et al., 1994; Anderson et al., 1994; Carmack et al., 1995; Schauer et al., 1997; Rudels et al., 1999]. A brief recent summary of double diffusive convection and of thermohaline intrusion in the Arctic Ocean is given by Rudels et al. . The intrusions may have different shapes and scales, but a common feature for almost all of them is high lateral coherence. For example, large intrusive about 150 m thick layers cover basin-wide areas of the Eurasian basin, identified by a similar shape in the vertical temperature and salinity profiles. Therefore, it cannot be excluded that intrusive layering contributes significantly to the lateral mixing in the central Arctic Ocean.
 Theoretical studies of Arctic intrusions are still not numerous. An analytical stability model for purely thermohaline Arctic frontal zones taking into account the fluxes through the diffusive interfaces and the temperature dependence of thermal expansion coefficient, α (i.e., the nonlinearity of the equation of state of seawater) was considered by Walsh and Carmack . Assuming that in some cases the combined effect of double diffusive convection and baroclinicity can be important for the development of the intrusive layers May and Kelley considered a two-dimensional stability model of a thermohaline and baroclinic front.
 However, interleaving structures in the Arctic Ocean are observed in all possible background stratifications, not just where the water column is diffusively unstable or salt finger unstable. This implies that other approaches than the linear stability analysis introduced by Stern must be invoked to explain the existence of intrusions also in the stable-stable stratification in the Arctic Ocean.
 Essentially two most likely approaches have been followed to explain the presence of intrusions where both components, temperature and salinity, are stably stratified.
 1. The intrusions are generated at frontal zones like the confluence area of the two Atlantic inflow branches north of the Kara Sea [Rudels et al., 1994]. This is similar to the configuration studied in the laboratory by Ruddick and Turner  and Holyer et al. . Here strong lateral motions, perhaps initially created by inertial waves or internal tides can induce the initial finite disturbances that lead to inversions, to double diffusive convection and to double diffusively driven intrusions.
 2. The second possibility is differential mixing. Hebert  and Merryfield  proposed that the fact that heat might diffuse faster than salt in weakly turbulent surroundings [see, e.g., Turner, 1973], could lead to the creation of large layer structures, if horizontal gradients of temperature and salinity are present. To model interleaving in the first case one has to apply the nonlinear approach, while in the second case the linear approach can be used.
 Here we shall model the interleaving structures observed in the Arctic Ocean in the interior of the basins away from the sharp frontal zones found at the continental slopes and at the boundaries between the basins, using the gradients of the mean and smoothed horizontal and vertical background property fields. The focus will be on evaluating effective lateral diffusion coefficients and comparing the estimates with results obtained by Walsh and Carmack [2002, 2003]. We shall also theoretically analyze the slopes of unstable modes due to combined effect of baroclinicity and differential mixing at fronts found in the stable-stable stratification. One motivation here is to examine, if baroclinicity can be an important factor in creating the interleaving structures found in the Arctic Ocean.
 However, before this is attempted a detailed and quantified description and classification of the different intrusive layer structures encountered in the Arctic Ocean will be given. The hydrographic section across the Eurasian Basin taken by R/V Polarstern in 1996 will be used as the principal example but also other observations will be invoked. This more descriptive part can be considered as an elaboration and quantification of the results obtained by Rudels et al. . However, the focus of our investigation is to study not only structures of interleaving but also structure of the fronts where the interleaving was observed. This was not done in the earlier work.
 The conductivity-temperature-depth (CTD) observations used were obtained in the Nansen, Amundsen and Makarov basins and over the Lomonosov Ridge from R/VPolarstern in 1996 (hereinafter PS96) and IB Oden in 1991 (hereinafter Oden91) (Figure 1). The instruments used were Neil Brown MarkIIIb CTDs and occasionally Sea-Bird SBE-11.Figure 1 gives positions of all CTD casts used in the analysis. The temperature and salinity profiles have been constructed from the processed 2 db average data (occasionally 1 db). Detailed descriptions of the data are given by Anderson et al. , Rudels et al.  and Schauer et al. .
3. Empirical Analysis of Structural Features of Intrusive Layers
Figure 2shows a sequence of salinity profiles from the main PS96 transect. Here six different types of intrusive layers can be distinguished, depending upon the length scales and the shapes of salinity and temperature profiles and the mean thermohaline stratification: (1) Inversions and intrusive layers in the upper part of the thermocline where the stratification is favorable for diffusive convection. (2) Large, extensive inversions and intrusive layers present between the temperature maximum and the salinity maximum but extending below the salinity maximum. (3) Deep intrusive layers existing in absolutely stable thermohaline stratification. (4) Intrusions present in narrow thermohaline/baroclinic front zones. (5) Weak intrusions present in the interior and at the boundary of thicker layers (intrusions). (6) Weak intrusions present in the layer favorable of salt finger convection below the large intrusions (type 2) but above the stable-stable stratification.
 Here we focus on the strong, distinct and coherent intrusions of types 1, 2 and 3, but the other types will be discussed briefly.
3.1. Upper Layer Intrusions (Type 1)
Figures 3a–3c displays a sequence of vertical profiles of density (Figure 3a), temperature (Figure 3b) and salinity (Figure 3c) from the upper part of the Atlantic Water layer (150–350 m) in the frontal zone between the Fram Strait and the Barents Sea inflow branches close to the Kara Sea continental slope (stations 36–41). Between 150 m and 270 m the temperature and the salinity increase with depth (stratification favorable to diffusive convection), but below the temperature maximum at 270 m the salinity increases and the temperature decreases with depth and the water column has an absolutely stable stratification.
 The most intensive intrusions are observed at stations 37–39 between 150 and 220 m. The vertical scale of the intrusions is approximately 30–40 m. At stations 35 and 36 the vertical scale of intrusions at similar depth is somewhat smaller (∼20 m), and at stations 40 and 41 intrusions are absent in this depth range. The vertical scales and amplitudes of the intrusions decrease with depth and at 250 m the thickness of the intrusions is reduced to 10–20 m.
 In the density field the intrusions between 150 and 270 m are seen as steps, i.e., a sequence of hydrostatically stable high- and low-gradient layers. The corresponding vertical profiles in temperature and salinity can in some cases be referred to as having a “sawtooth” or “cog” structure (stations 37–39), where relatively thin, strong gradient layers of the increasing temperature and salinity with depth are interleaved with thicker, weak gradient layers of temperature and salinity decreasing with depth.
 Since the prominence of the intrusions tends to obscure the background salinity and temperature stratifications, it is of interest to determine the characteristics of the mean thermohaline fields that is important for quantifying the effects of baroclinicity and thermoclinicity on interleaving. Figures 3d–3f shows the mean density (Figure 3d), temperature (Figure 3e) and salinity (Figure 3f) fields on the section drawn using data from stations 35–41. The thermohaline fields were constructed using mean vertical profiles (z), (z) and (z) obtained from the ‘instant’ vertical profiles T(z), S(z) and ρ(z) by applying a low-pass cosine filter with a smoothing parameter ofLm = 50 m. A comparison between Figures 3a–3c and 3d–3f shows that the most intensive intrusions in the depth range of 150 to 200 m are observed in a frontal zone (stations 37–39), while in the region of weak horizontal thermohaline gradients the intrusions are practically absent (stations 40–41).
 The mean horizontal thermohaline gradients x(z), x(z) and x(z) at a level z in the frontal zone were estimated by means of linear regression of values of (z), (z) and (z) from a given range of distances (for details of data processing see paper by Kuzmina et al. ). Table 1lists hydrological parameters such as the Brunt-Väisälä frequencyN, the density ratio RρS = βz/αz, where α is the coefficient of heat expansion and β is the coefficient of salt contraction and z(z) and z(z) are the mean vertical gradients of temperature and salinity (for convenience, we will in this paper use two definitions of density ratio, RρS = βz/αz for the diffusively unstable stratification and RρT = αz/βz for the salt finger unstable stratification). The parameter χδ = x/ρ0α(1 − γ) x, is a measure of relative importance of baroclinicity and thermoclinicity in double diffusive interleaving [see, e.g., Kuzmina and Zhurbas, 2000]. Here ρ0 is the reference density and γ = βFS/αFT, the ratio of the density normalized salt and heat fluxes through a diffusive interface (here we adopt the value γ = 0.15 suggested by Turner ). When χδ < 1 it implies that the interleaving is controlled by thermoclinicity, and when χδ > 1 it indicates interleaving controlled by baroclinicity [Kuzmina and Zhurbas, 2000]. All parameters were calculated for 40 m thick layers in the depth range of 110–310 m.
Table 1. Hydrological Parameters Evaluated From Set of Vertical Profiles of Stations 37–39 as Described in Section 3.1
x (×106 m−1)
x (×105 °C m–1)
 It is seen from Table 1 that the mean horizontal gradients of temperature in the frontal zone is less than 1°C/100 km. However, since χδ < 1 in the depth range 150–310 m, we can infer that the thermohaline factor dominates in the generation of intrusions. This agrees with the T, S and σθ,S diagrams in Figure 4, which show that warm and salty (cold and fresh) intrusions crossing the front become heavier (lighter) in accordance with a dominating buoyancy transport through the diffusive interfaces.
 It is worthwhile to stress some additional features in the T, S diagrams. The T, S curves in Figure 4 (left) do not display high coherence, however, Figures 4 (middle) and 4 (right) demonstrates that T, S characteristics of the salt finger stratification layers are grouped in well defined lines crossing the isopycnals.
3.2. Large-Scale Intrusive Layers in the Vicinity of the Salinity Maximum (Type 2)
 The large-scale intrusive layers observed in the depth range of 200–600 m are characterized by high coherence over distances of the same order as the Eurasian Basin (Figure 2).
Figure 5 presents vertical profiles of density (Figure 5, top), temperature (Figure 5, middle) and salinity (Figure 5, bottom) in a depth range of 200–600 m for stations 40, 41, 43, 45, 49, 52 and 56. In the density profiles the intrusive layers have also here a step-like structure, while in temperature and salinity they display a well-pronounced sawtooth or cog appearance. The thickness of the high-gradient layers is 20–30 m, while the low-gradient layers are much thicker (100 m and more). Three pronounced large-scale layers can be identified and within these layers and their boundaries there are weakly indicated intrusions with typical vertical length scale of 10 m. The latter can be classified as intrusions of type 5, which can be observed in stratifications favorable of both salt fingering and diffusive convection.
 The large-scale layers are present in the Nansen Basin and extend up to the center of the Amundsen Basin (up to station 57) (Figure 2). Closer to the Lomonosov Ridge and the Makarov Basin they are hardly identified and the anomalies in the vertical profiles are weakly pronounced and have a different structure. From station 63 to station 72 another system of intensive layers can be observed between 200 and 400 m, but here the vertical scale is somewhat smaller.
 The profiles on stations 42 and 54 (marked by gray color in Figure 2) are substantially different from those on the adjacent stations. This can be understood by examining salinity and temperature sections from stations 30 to 72 (Figure 6). Here stations 42 and 54 are identified by the presence of isolated boluses of saline and warmer water, which may be interpreted as mesoscale, anticyclonic eddies [Schauer et al., 2002]. This would then indicate that mesoscale eddies can move as isolated water bodies through the layer structures practically without losing their identity.
Figure 7 shows T, S curves from stations 40, 41, 43–52, 54, 55 and 56. T, S curve from station 54 (marked by gray color) demonstrates the thermohaline structure of mesoscale eddy. The T, S curves from stations 40, 41 and 43–46 intersect the isopycnals and indicate that warm and saline (cold and fresh) intrusions descend (rise) relative to the isopycnal surfaces. However, T, S curves at the stations 47–52, 55 and 56 show practically an alignment of the layers with the isopycnals.
 The results presented in Figures 6 and 7show that in the region filled with the large-scale intrusive layers one can distinguish three zones with different values of hydrological parameters. In zone 1 (stations 40, 41 and 43–46), there are comparatively large horizontal gradients of temperature and salinity and the slope of isopycnals to the horizontal,γρ, is larger than zero. In zones 2 (stations 47–51) and 3 (stations 51, 52, 55, 56), the horizontal gradients of temperature and salinity are weak and γρ > 0 in zone 2 while γρ < 0 in zone 3. Tables 2a–2c give values of the hydrological parameters for zone 1 (Table 2a), zone 2 (Table 2b) and zone 3 (Table 2c). The mean vertical profiles were in this case obtained by low-pass cosine filtering with the smoothing parameter ofLm = 200 m. Here the definition of density ratio in the form of RρT = αz/βz is used. Tables 2a–2c also give the values of slopes γρ, γS (slope of isohalines), γT (slope of isotherms).
Table 2a. Hydrological Parameters Evaluated From Set of Vertical Profiles of Stations 40, 41 and 43–46 as Described in Section 3.2
x (×106 m−1)
x (×105 °C m–1)
Table 2b. Hydrological Parameters Evaluated From Set of Vertical Profiles of Stations 47–51 as Described in Section 3.2
x (×106 m−1)
x (×105 °C m–1)
Table 2c. Hydrological Parameters Evaluated From Set of Vertical Profiles of Stations 51, 52, 55 and 56 as Described in Section 3.2
x(×105 °C m–1)
 As can be seen from Tables 2a–2c, the hydrological situations in zones 1, 2 and 3 are quite different. In zone 1 the horizontal gradients of temperature and salinity have the same signs and diminish the horizontal density gradient. By contrast, in zone 3 the horizontal gradients of temperature and salinity have the opposite sign, which results in a stronger horizontal density gradient. Also the structure of intrusive layers in zones 1 and 2 is not identical. In zone 1 the vertical changes in temperature and salinity in the layers are larger than that of zone 2.
 An important feature of the large-scale intrusive layers is their insensitivity to the mean thermohaline stratification. In the depth range of 230–290 m both the mean salinity and mean temperature increase with the depth (diffusively unstable stratification), in the depth between 310 m and 410 m the mean stratification is stable both in temperature and salinity and below 420 m both the mean salinity and mean temperature decrease with the depth (salt finger unstable stratification), while large-scale intrusive layers are observed in the entire depth range of 230–600 m.
3.3. Deep Intrusive Layers at Stable-Stable Thermohaline Stratification (Type 3)
Figures 8a–8c show vertical profiles of density (Figure 8a), temperature (Figure 8b) and salinity (Figure 8c) from stations 36 to 50 for the depth range of 600–1050 m. At stations 40–46 in the depth range of 600–750 m, where the thermohaline stratification is favorable for salt finger convection, intrusions are weakly pronounced and have small vertical scale, approximately 10–15 m. Deeper, between 800 and 1050 m, in the region of absolutely stable thermohaline stratification, intensive, coherent intrusive layers are observed having clearly expressed sawtooth shape in the salinity and temperature profiles. The thickness of high-gradient layers, where temperature and salinity increase with depth, is 10 m, while the low-gradient layers, with temperature and salinity decreasing with depth, are about three times as thick (30–40 m).
 Mean salinity, temperature and density contours versus distance and depth for stations 36–50 and the depth range of 600–1050 m are given in Figures 8d–8f. The mean vertical profiles are here obtained by low-pass cosine filtering with the smoothing parameter ofLm =100 m. The mean thermohaline fields are characterized by a strong variability. In particular, fronts are observed at the boundaries of low-salinity regions.
 A T, S diagram drawn for stations 36–50 and the depth range of 800–1050 m (Figure 9) reveals the presence of two water masses, one warm and saline, the other cold and fresh. Between the T, S curves of the “parent” water masses the T, S curves display high variability due to the presence of intrusive layers. The intrusive layers are coherent, and cross the isopycnals with warm and saline (cold and fresh) intrusions becoming more (less) dense. This fact, together with information about the slopes of isopycnal surfaces to the horizontal (Figure 8), shows that the intrusions slope strongly than the isopycnals. Thus, the slope of the intrusions lies outside the wedge of baroclinic instability [May and Kelley, 1997; Kuzmina and Zhurbas, 2000].
 To study coherence of the intrusive layers in more detail the T, S diagrams in the depth range of 600–1050 m were drawn separately for stations 40–43 (Figure 10a) and 40, 41, 44 and 45 (Figure 10b). It is easily seen that the coherence is missed for intrusions in the depth range 600–800 m where the thermohaline stratification is favorable for salt fingering. In the depth range 800–1050 m where the thermohaline stratification is absolutely stable the coherence of intrusive layers are high within groups of stations, e.g., 40–42, 44 and 45. This coherence is somewhat violated by station 43. Since station 43 is located in the center of the intrusive zone, it suggests that the intrusions are created around a mesoscale eddy of Barents Sea branch water being detached from the boundary current at the slope [see, e.g., Rudels, 2009].
Table 3 presents the mean hydrological parameters calculated for the highly coherent intrusive layers in the absolutely stable thermohaline stratification: stations 40–42. The values ρx/βSx and ∣ρx/αTx∣ are above one and consequently the baroclinicity of the front has to be taken into account. Thus, we can suggest that baroclinicity should influence interleaving despite of the fact that the slope of the intrusions lies outside the wedge of baroclinic instability.
Table 3. Hydrological Parameters Evaluated From Set of Vertical Profiles of Stations 40–42 as Described in Section 3.2
N (×102 s–1)
Sx (×107 m–1)
Tx (×106 °C m–1)
 One more example of baroclinic fronts and related intrusions with high-amplitude anomalies in the vertical profiles of temperature and salinity is given inFigure 11. In this figure data from the central Nansen Basin across the Amundsen Basin and the Lomonosov Ridge into the Makarov Basin, taken on the Oden91 expedition, are presented (stations 9–26; see Figure 1). The mean thermohaline fields (Figures 11d–11f) and successive CTD profiles (Figures 11a–11c) are shown together for comparison. Station numbers, as before, are given near the profiles (see upper part in the left side). The positions of the CTD stations are also shown in the mean density transect.
 It is clear that the intrusive layering is intermittent, i.e., fronts with intrusions alternate with the regions where intrusions are weak or absent (e.g., stations 21–24). Comparing the mean thermohaline fields with the features of the successive CTD profiles shows that intensive intrusive layering is observed at both pure thermohaline (stations 15–19) and at baroclinic (stations 10–14) fronts.
3.4. Characteristic Features of Intrusive Layering and Frontal Zones
 The features of the fronts and the related intrusive layers are summarized below:
 1. The frontal zones of the Eurasian Basin are characterized by large structural variety. There are purely thermohaline fronts (e.g., Table 1), hybrid cases, both thermohaline and baroclinic fronts (e.g., Table 2b, below 310 m) and essentially baroclinic fronts (e.g., Table 3). However, despite their structural differences, all types of frontal zones display intense intrusive layering.
 2. The mean lateral gradients of temperature and salinity in the frontal zones decrease with depth, sometimes the decrease is as large as an order of magnitude and even larger (cf. Tables 1 and 2b). Nevertheless, the intensity of intrusions decreases less drastically, in the deep layers it is typically about half of that in the upper layers, but sometimes it remains practically unchanged (cf. anomalies on vertical profiles presented in Figures 3 and 5).
 3. In all cases of observations except for the frontal zone 2 (Table 2b and section 3.2) where the intrusive layers are aligned to isopycnals, the warm and saline (cold and fresh) intrusions deepen (rise) relatively to the isopycnals. However, this does not always mean that the warm and saline (cold and fresh) intrusions also deepen (rise) relatively horizontals (see Figures 5 and 6).
 4. Vertical profiles of salinity and temperature as well as T-S curves of the observed intrusions have had a special shape we call sawtooth or cog like (see section 3.1 for details) in contrast to the step or staircase structure (see reviews on thermohaline staircases by Merryfield  and Kelley ).
 The cog-like structure is quite different from the step-like structure because the former has no quasi-uniform layers. It can be observed at different types of stratification, particularly at hydrostatically stable stratification in both temperature and salinity. A striking feature of the cog-like structures is that itsT, S diagram displays a clear resemblance to an idealized broken line consisting of segments of approximately constant density ratio within alternate layers of salt fingers and diffusive convection stratification.
 The amplitude of the temperature inversions in the cog-like structure, in accordance with our data, varies with the intensity of the thermohaline fronts. For example, the amplitude of temperature inversions was as high as ∼0.4°C in frontal zones with high lateral thermohaline gradients but ∼0.15°C in areas where the lateral gradients were weaker (seeTables 2a and 2b and Figure 7).
 5. In some cases above presented data have shown that being plotted on T, S plane (see, for example, Figure 7, T, S structures at stations 41 and 43–45 and Figure 4), the T, S indices of salt finger stratification layers are grouped along parallel lines crossing the isopycnals, so that for any layer is right the following: the T, S indices belonged the layer taken from different CTD casts lie on the segments of the same line and these segments are displaced relatively each other along this line. Mathematically it means that there is a constant ratio l ≈ z, between the mean vertical density ratio z across the layers and the mean lateral density ratio along the layers l. In case of ideal thermohaline staircase [Schmitt et al., 1987] when both temperature and salinity jumps vanish within layers, z becomes uncertain and the equality loses meaning.
 In the other cases (see, for example, Figure 10a, T, S structure at stations 40–42) the T, S curves in the layers dominated by salt finger stratification are parallel and following equality is true: l ≈ kz (k < 1).
 6. Features of the fronts in the upper and deep layers (Tables 1 and 3) along with disposition of intrusive layers relatively to horizontal suggest that intrusive layering results from instability of the fronts due to diffusive convection in the first case and differential mixing in the second case.
 The intermediate layer intrusions (section 3.2) can be called “strange interleaving” for following reasons. On the one hand, they are horizontally coherent throughout the Eurasian Basin and their T, S curves display nested structures (the last term was introduced by Walsh and Carmack ). On the other hand, frontal zones of the intermediate layer the intrusions run through have different hydrological parameters (see Table 2). Moreover, within each of the frontal zones there are strong vertical variations of the mean density ratio (either RρT or RρS) and isoline slopes of salinity and temperature.
4. Modeling and Evaluations of Vertical and Lateral Diffusivities
 Full description of interleaving includes both initial state models when perturbations have a sinusoidal shape and quasi-stationary state models when perturbation shape is far from sinusoidal. Here we will focus on an initial state model for intrusions of types 1 and 3 using common approach of double diffusive interleaving. The model results along with observational data will be applied to estimate apparent diffusivities caused by intrusive layering in the upper and deep Arctic layers, as well as to treat the effect of baroclinicity on interleaving at stable-stable thermohaline stratification.
 In accordance with our empirical considerations (see sections 3.1, 3.3 and 3.4) the upper layer front and the deep layer front have different structure. There are two basic parameters that make the two fronts so different: baroclinicity (which is almost absent in the upper layer front and essential in the deep layer front) and the mean thermohaline stratification (favorable for diffusive convection in the first case and stable-stable in the second case). For this reason we will use two different models of instability.
4.1. Upper Layer Intrusions (Type 1)
 To describe the generation of the intrusions in the upper part of the water column we use a 3-D model for instability at a thermohaline front with finite width driven by diffusive convection. This model is presented in detail in the paper byKuzmina et al. . Based on the observations the parameters required by the model such as the stability parameter εz = g(1 − γ)αz/N2 (where g is the gravity acceleration and N the buoyancy frequency) for layer between 150 and 230 m (where intrusions with vertical scale 30–40 m are observed) were taken at εz = −0.35 and N = 0.0045 s−1. For the Coriolis parameter f and for a typical horizontal scale of front d, we use f = 1.4 × 10−4 s−1 and d = 2 × 104 m.
 Since double diffusive interleaving acts to reduce the mean temperature gradients, it is plausible that observed mean gradients in regions of fully developed interleaving are smaller than the initial gradients relevant for a linear stability analysis. For this reason values of Tx from 1 × 10−5 °C m−1 (approximately equal to the observed value) to 2.5 × 10−5 °C m−1 (twice as large as the observed value) are used.
 With these input parameters, the values of vertical diffusivity and the Prandtl number were varied with the aim to obtain satisfactory agreement between the vertical scale calculated from the interleaving model and observed vertical scales of the intrusions. The magnitudes of the maximum growth rate λ*, wave number m* and vertical scale h* of the intrusions found for different values of coefficients of diffusivity and Prandtl number are presented at Table 4.
Table 4. Maximum Growth Rate λ*, Respective Wave Number m* and Vertical Scale h* of Unstable Modes Calculated at Different Values of the Mean Lateral Temperature Gradient Tx, Vertical Diffusivity KT and Prandtl Number Pra
3 × 10−5
5 × 10−5
7 × 10−5
2 × 10−4
All values are given in SI units system (International System of Units).
Tx = 10−5
Pr = 1
λ* = 2.5 × 10−7,m* = 0.2,h* ≈ 15
λ* = 2.25 × 10−7,m* = 0.12,h* ≈ 27
λ* = 2.25 × 10−7,m* = 0.09,h* ≈ 35
λ* = 2.25 × 10−7,m* = 0.08,h* ≈ 41
λ* = 2.25 × 10−7,m* = 0.06,h* ≈ 49
λ* = 2.2 × 10−7,m* = 0.05,h* ≈ 70
Pr = 2
λ* = 1.8 × 10−7,m* = 0.16,h* ≈ 20
λ* = 1.8 × 10−7,m* = 0.09,h* ≈ 33.6
λ* = 1.8 × 10−7,m* = 0.07,h* ≈ 43.4
λ* = 1.8 × 10−7,m* = 0.06,h* ≈ 52
λ* = 1.8 × 10−7,m* = 0.05,h* ≈ 62
λ* = 1.75 × 10−7,m* = 0.036,h* ≈ 87
Tx = 2.5 × 10−5
Pr = 1
λ* = 5.6 × 10−7,m* = 0.3,h* ≈ 10
λ* = 5.6 × 10−7,m* = 0.18,h* ≈ 17
λ* = 5.6 × 10−7,m* = 0.14,h* ≈ 23
λ* = 5.6 × 10−7,m* = 0.12,h* ≈ 26
λ* = 5.6 × 10−7,m* = 0.1,h* ≈ 31
λ* = 5.6 × 10−7,m* = 0.07,h* ≈ 43
Pr = 2
λ* = 4.4 × 10−7,m* = 0.26,h* ≈ 12.2
λ* = 4.4 × 10−7,m* = 0.15,h* ≈ 21.3
λ* = 4.4 × 10−7,m* = 0.11,h* ≈ 27.6
λ* = 4.4 × 10−7,m* = 0.095,h* ≈ 33
λ* = 4.4 × 10−7,m* = 0.08,h* ≈ 39.3
λ* = 4.4 × 10−7,m* = 0.06,h* ≈ 55
 As is seen from the table, the calculated values of wave number (and vertical scales of intrusions h* = π/m*) are very sensitive to the magnitudes of mean temperature gradients at the frontal zone Tx. However, if we take Tx = 1 × 10−5 − 2.5 × 10−5 °C m−1 (see above arguments), the satisfactory correspondence between observed and modeled vertical scales of intrusions is found when the value of vertical temperature diffusivity is in the range of KT = 3 × 10−5 − 2 × 10−4 m2s−1. We therefore consider KT ≈ 10−4 m2s−1 to be a rough estimate of the vertical diffusivity in the frontal zone during the formation of the intrusions.
 It is also of interest to evaluate an effective coefficient of lateral exchange in the frontal zone.
 The apparent lateral diffusivity caused by interleaving can be estimated as Kl = λ(d/2)2, where λ is the growth rate given by a linear instability theory [see, e.g., Richards and Edwards, 2003]. Taking * ≈ 3 × 10−7 s−1 (see Table 4) for λ in the above formula, we obtain Kl ≈ 1.2 × 102 m2 s−1. A second estimate of lateral diffusivity can be made by means of the Joyce  formula Kl = kz/ x2, where is the mean square amplitude of vertical gradient temperature fluctuations inherent to intrusive fine structure. Taking ≈ 1 × 10−4 °C2 m−2, kz ≈ 1 × 10−4m2 s−1, x ≈ 10−5 °C m–1, we arrive at Kl ≈ 100 m2 s−1, which is of the same order of magnitude.
4.2. Deep Layer Intrusions (Type 3)
 In section 3.3 it was shown that the intrusion slopes are larger than the isopycnal slopes for the deep layer baroclinic front (PS96 expedition). Thus, intrusions lie outside the wedge of baroclinic instability. However, in some cases this does not mean that baroclinicity cannot influence the growth rate and evolution of the initial disturbances. Indeed, in accordance with paper by McIntyre  at Pr < 1, where Pr is the Prandtl number, that is, the ratio of momentum to mass transfer coefficients, the intrusion slopes can be larger than the isopycnal slopes for the baroclinic front. But we do not see any reason to assume that Pr <1 in our case. Nevertheless, there may be other causes that result is such arrangement between intrusion and isopycnal slopes. To explore this possibility we will analyze the slopes of the unstable modes inherent to the differential mixing (DM) instability of baroclinic front at stable-stable stratification.
 In contrast to the model of pure thermohaline front instability presented by Merryfield , we consider the 2-D instability of an infinitely wide, baroclinic thermohaline front with constant background gradients of temperature ( x and z), salinity ( x and z) and density ( x = −αx + βx and z = −αz + βz) in the cross-front and vertical directions. Thez and y axes are directed upward and along front, respectively, and the initial stratification is taken to be stable in both temperature and salinity ( z < 0, βz < 0, −αz < 0). The basic state is the geostrophically balanced flow
where is the y component of background velocity and and are the undisturbed pressure and density. According to (1) and (2), the vertical shear, z, is related to horizontal density gradient by the thermal wind relationship .
 Using the hydrostatic approximation and neglecting the background horizontal shear, the linearized governing equations for two dimensional perturbations can be written in the form [Kuzmina and Zhurbas, 2000]
where u, v, w, p, T and ρ are perturbations of velocity components, pressure, temperature and density, k* is the apparent diffusivity for heat, salt and mass due to small-scale turbulence,η is the molecular viscosity, kT and kS are the molecular diffusivities for heat and salt. Equation (9) for density was obtained using the assumption that kS ≪ kT and kS ≪ k*. The combined effect of molecular transport and small-scale turbulence transport in the form of(3)–(9) is similar to parameterization of double diffusion and turbulence which has been studied in the framework of instability models by Kuzmina and Rodionov , Walsh and Ruddick , Kuzmina and Zhurbas  and Zhurbas and Oh .
 It is easy to see that our parameterization of DM is in accordance with the model by Merryfield . It is enough to introduce the notations KT = kT + k*, KS = ks + k* and A = η + Pr ⋅ k* = Pr(KT − kT) + η, which were used by Merryfield.
 Assuming that all coefficients in the system are constant, we seek solutions of (3)–(9) in the form
where φ denotes any of variables under consideration, φ* is the complex amplitude of φ, ω is the growth rate (real or complex) and l and mare the across-front and vertical wave number, respectively. Substituting(10) into (3)–(9) we obtain a quartic relationship in ω between the growth rate and wave numbers
where C0,C1,C2,C3 are expressions consisting of variables and parameters of the problem.
 If C0 < 0 we are assured of at least one real root exists for which ω is greater than zero [e.g., Stern, 1967]. In our case C0 is expressed as
where ζ = k*/kT, A = η + Pr k*. Taking into account that z < 0 and ∣α∣ < ∣ z∣, C0 can be less than zero if xl/m < 0 and/or xl/m < 0. In the case of ∣ x∣ ≪ ∣αx∣ the instability is determined by thermohaline factor, while in the case ∣ x∣ ≫ ∣αx∣ the baroclinicity is a main factor governing the generation of the interleaving. The last situation can be only realized at haline fronts.
 It is easy to show that in the case of strong baroclinic front (∣ x∣ ≫ ∣αx∣) at ζ = 0 the sufficient condition of instability reduces to
where εz* = is a nondimensional measure of the contribution of the mean temperature gradient to the vertical density gradient.
 At l/m > 0 and x < 0 we can rewrite (13) in the form
It is evident from (14) that the isopycnal slope can lie within the wedge of unstable modes. Also it can be shown that if εz* > 0.5 the most unstable mode slope can be larger than the isopycnal slope. If ζ ≪ 1, (14) becomes the following:
and the most unstable mode slope can be larger than the isopycnal slope under the assumptions of
 Thus, if the vertical density gradient is conditioned by the contribution of temperature and molecular diffusivity for temperature is larger than the turbulent diffusivity, the slope of the most unstable mode can be larger than the isopycnal slope.
 This result is new and not trivial. Such arrangement between the most unstable mode and isopycnals can be realized at prevailing contribution of temperature to stable-stable stratification only. This mode cannot be attributed to the baroclinic instability. Certainly, the difference of heat/salt diffusivities, baroclinicity and stable-stable stratification are responsible for its existence.
 In common case, when two factors, baroclinicity and thermoclinicity are important for the front destabilization, (15) can be rewritten in the form
 Let us now use our findings for interpretation of the arrangement between intrusion and isopycnal slopes described in the paragraph 3.3 (see Figures 8–10). Evaluating from Table 3 such parameters as εz* and χ′ = αx/ xthroughout a layer filled with intrusions at stable-stable stratification we obtain z* ≈ 5/6 and ′ ≈ −1/3. Therefore, the observed arrangement between intrusion and isopycnal slopes is really possible if ζ < 1/3. This inequality is useful to evaluate the upper limit for coefficient of turbulent mixing k* ≈ 0.45 × 10−7 m2 s−1 and vertical diffusivity of heat KT = kT + k* ≈ 1.85 × 10−7 m2 s−1. An estimate of lateral diffusivity can be done by means of the Joyce  formula Kl = kz/ x2. Taking = 2.5 × 10−5 °C2 m−2, kz = 1.85 × 10−7m2 s−1, x ≈ 5.3 × 10−7 °C m–1, we obtain Kl = 17 m2 s−1.
 To estimate the lateral heat diffusivity in regions of a pure thermohaline front we again use the expression Kl = λ(d/2)2 with the growth rate λ obtained by Merryfield . He analyzed the front between stations 16–18 and 30–32 from the Oden91 expedition. If the distance between stations 16 and 18 is taken as the width of the front, d, Figure 11 gives d ≈ 120 km. In accordance with Merryfield , the growth time of intrusions was estimated to 2 years. Substituting this value into the above expression for Kl we obtain Kl ≈ 57 m2 s−1.
 These two estimates obtained for baroclinic and thermohaline fronts by means of different methods show that even in the case of stable-stable stratification the lateral diffusivity caused by interleaving could be still high enough (cf. estimates ofsection 4.1).
5. Results and Discussion
 The thermohaline characteristics of fronts and intrusive layering observed in the Eurasian basin of the Arctic Ocean have been described in detail. The analysis has been based on CTD data obtained in PS96 and Oden91 expeditions and relevant hydrographic parameters have been evaluated at different frontal zones. New findings about structure of fronts and intrusions in the observing area were summarized in a view of short characteristics (see section 3.4). Special attention was paid to intensive intrusive layering observed in the thermocline in the upper part of the Atlantic water (intrusion type 1), in the core of the Atlantic layer between 300 and 600 m (intrusion type 2) and in the intermediate waters between 800 and 1100 m (intrusion type 3).
 All three types of intrusions have similar structural features: The shape of vertical profiles of temperature and salinity can be characterized as a sawtooth or cog structure where fairly thin, high-gradient layers with increasing temperature and salinity with depth are interleaved with relatively thick low-gradient layers of decreasing temperature and salinity with depth.
 Intrusions of type 1 had typical vertical scale of 30–40 m and were observed in the region, where the mean temperature and salinity increased with depth and the background stratification was unstable in the diffusive sense. A probable mechanism for generating these intrusions is therefore thermohaline instability at the front due to double diffusive convection through diffusive interfaces. To describe these intrusions we used an instability model presented in full in the paper by Kuzmina et al. . Using the observed hydrographic characteristics as input parameters of the model and varying diffusion coefficient of heat, KT and the Prandtl number, the modeled vertical scale of intrusions was made to fit the observations. Good correspondence between modeled and observed values of vertical scales of intrusions was found when the value of vertical temperature diffusivity was in the range of KT = 3 × 10−5 − 2 × 10−4 m2 s−1 (Table 4). We therefore adopted KT ≈ 10−4 m2 s−1 as a rough mean estimate of the vertical diffusivity in the frontal zone during the formation of the intrusions. Coefficient of lateral exchange was evaluated as Kl ≈ 1.2 × 102 m2 s−1 based on the formula Kl = λ(d/2)2, where λ is the mean growth rate calculated from our linear instability theory. A second estimate of lateral diffusivity was done by means of the Joyce  formula: Kl = 100 m2 s−1 (see section 4.1).
 The influence of baroclinicity at the front on interleaving due to differential mixing at stable-stable stratification was first considered. The slopes of unstable modes relative to the isopycnals were evaluated in the case where the mean horizontal density gradient was larger than the temperature gradient. Such situation can only be encountered at strong haline fronts. In the special case of no turbulence it was found that the slope of maximum unstable mode can exceed the isopycnal slope. This effect exists in the case of turbulence too, but only if the coefficient of turbulent diffusion is smaller than the molecular diffusion coefficient of heat. New theoretical findings were used to explain the arrangement between intrusion and isopycnal slopes at the baroclinic front at stable-stable stratification (seesections 3.3 and 4.2) and evaluate the vertical diffusivity: KT = 1.8 × 10−7 m2 s−1. An estimate of lateral diffusivity in this baroclinic front was done by means of the Joyce  formula: Kl = 17 m2 s−1. To estimate the lateral heat diffusivity in region of pure thermohaline front at stable-stable stratification we used the formulaKl = λ(d/2)2 and the growth rate λ obtained by Merryfield . Coefficient of lateral exchange due to interleaving was evaluated as Kl ≈ 57 m2 s−1. These two estimates obtained for baroclinic and thermohaline fronts in the deep layer show that even in the case of stable-stable stratification the lateral diffusivity caused by interleaving could still be high.
 As a matter of discussion, let us consider the following issues.
 The T-S indices in some intense cog structures evidence a relation l ≈ z (see point 5 of section 3.4). Such equality have been supposed to be formed due to oppositely directed along-layer motions within every large layer [Zhurbas et al., 1990; Walsh and Carmack, 2003]. In accordance with Walsh and Carmack such internal circulations can arise during a quasi-stationary state of double diffusive interleaving due to so-called slanted convection developed within layers of salt finger stratification. Using data of observations in C-SALT region and some model considerations,Zhurbas et al. showed that the intralayer circulations can be formed by pressure gradients arising due to slope of quasi-mixed layers relatively isopycnals. Intralayer circulations, regardless of their origin, can cause intensive cog-like shape of vertical profiles temperature and salinity.
 Since the above mentioned relation was observed in some cases only, it is natural to suggest that there are other mechanisms capable to form the cog structures. For example, in accordance to paper by Merryfield , being sinusoidal initially, the shape of disturbances in a nonlinear interleaving model can vary to acquire the cog-like appearance in the stationary state.
 One more cause for the appearance of the cog-like structures could be the different conditions at the diffusive and the salt finger interfaces. When interleaving structures are formed, there is no reason to assume that they are asymmetric and it is expected that warm and saline intrusions are as thick (or thin) as cold and fresh intrusions. The fact that the diffusive interfaces between the intrusions are more stable and thinner than the salt finger interfaces in the Arctic Ocean then indicates (1) that the buoyancy flux through the diffusive interface is larger than through the salt finger interface (this is in agreement with warm saline intrusions becoming more dense) and (2) the diffusive interface does not allow mass transfer between the layers and the convection from the interface will, at least initially, limit its thickening. The salt finger interface, by contrast, transfers mass between the layers and will spread out. This could explain the asymmetric “cog-like” appearance of the salinity and temperature profiles.
 However, it is important to note that none of mentioned above mechanisms can explain why the cog structures are typical for the Arctic Ocean only.
 For detailed evaluations of diffusivity in the upper layer an instability model of purely thermohaline front was used (section 4.1). Application of such a model is justified by the field observations: the upper layer front was almost purely thermohaline one with inessential baroclinicity. The model describes instability of a finite width front and, therefore, is more complete than instability models of an infinite width front because the latter are asymptotics of the former when the front width goes to infinity [see, e.g., Niino, 1986]. However, if models of the finite and infinite width front instability are used correctly, they will yield comparable results. Unfortunately, we did not take into account the influence of nonlinear equation of state of seawater on interleaving (see important model considerations by Walsh and Carmack ). To our mind, in the upper layer front we considered the temperature change in intrusive layers is hardly large enough to make cabbling effect essential. This issue deserves special examination which is outside of the scope of the paper.
 Some justification for the use of a linear model should be given. Nonlinear interactions can change the vertical scale of the most unstable mode, and some changes of the vertical scale can be expected during the quasi-stationary stage of intrusion evolution. However, drastic changes in initial intrusion thickness can only be caused by the instability of the intrusion itself. Since vertically regular, high-coherent intrusive layers are constantly present in the Arctic Ocean, we may consider them very stable features.
 This is the first time that the formula Kl = λ(d/2)2 is applied to estimate lateral exchange in the Arctic. The formula agrees well with our presentations of lateral exchange: the larger the amplitudes of thermohaline disturbances on vertical profiles, the higher the exchange. Indeed, it follows from the general case of instability described by nonlinear equations of hydrodynamics that the larger the linear approximation growth rate the larger the finite amplitude of disturbance in the stationary state. In a particular case of intrusive layering an empirical confirmation of a direct relation between the intrusion intensity and the growth rates of interleaving modeling is given, for example, in the paper by Kuzmina and Zhurbas .
 Our estimates of lateral diffusivity in the upper layer fronts (sections 3.1 and 4.1) are in a reasonable correspondence with the results by Walsh and Carmack [2002, 2003]. The latter were obtained for vertically large intrusive layers, structurally corresponding to our intrusions of type 2 (section 3.2), observed in the Makarov Basin. However, our mean estimate of vertical diffusivity was an order of magnitude larger than that of Walsh and Carmack . Such a discrepancy may be due to several reasons. Some of them are following. First, two different regions of the Arctic were considered. Second, there are, seemingly, some differences in the intensity of vertical diffusivity at the initial and stationary stages of intrusion evolution. Third, in our linear model of the upper layer intrusions a wide range of the mean lateral gradient of temperature was used to take into account that the lateral gradients are decreasing in the course of intrusive layering (Table 4). Thus, in accordance with Table 4 the vertical diffusivity can be much smaller than the mean value we found.
 In closing let us mark one circumstance. In a view of weak internal waves activity, the small beta effect and restricted interactions between ocean and atmosphere (due to ice cover) interleaving in the Arctic Ocean may be considered an important mechanism for water mass exchange and mixing. It is slow, but always present and therefore systematic.
 This work was supported by the Academy of Finland (grants 124008 and 108070), the Russian Foundation for Basic Research (grant 10-05-00467) and the EU 7th Framework Programme Priority Project THOR (contract 212643). We are grateful to anonymous reviewers for valuable remarks.