The statistical distributions for the elevation,velocity and acceleration of the surface of wind waves

Water surface elevations(t), vertical surface velocities and vertical surface acceleration of wind-generated waves have been measured in a laboratory wind wave channel by using resistance-type wave gauges combined with an electronic differentiation circuits. Probability distributions of the values of(t), , and have been determined from the wave records.In an initial stage of wave generation,i.e., when wind waves are generated at short fetches and low wind speeds, the observed distributions for(t), and are appreciately good fit to the distributions given by successive sum of a Gram-Charlier series, which has been derived following the formulation ofLonguet-Higgins (1963), by taking the weakly nonlinear effect into account.However, when wind waves develop with increasing wind speeds and fetches, the observed distributions deviate gradually from the Gram-Charlier series. Particularly, the deviations are remarkable for the distribution of .When the wind speed increases, the observed distributions of(t), and show the following characteristics: (i) the skewnesses of the distributions of(t) and decrease slightly, (ii) the skewness of changes, at some wind speed, from positive small values to relatively large negative values, (iii) the kurtosis of the distribution of(t) decreases slightly but that of increases slightly and these characteristics seem to depend not so much on fetches, (iv) the kurtosis of the distribution of increases rapidly.     

Nonlinear properties of laboratory wind waves at energy containing frequencies

Nonlinear properties of wind waves in a wind-wave tunnel are investigated by measuring the probability density distribution of surface elevation. The surface elevation distribution of raw records are found to have a positive skewness (K ₃=0.21 to 0.43) and a negative kurtosis (K ₄=–0.74 to –0.41) with magnitude depending of fetch and wind speed. The values of skewness are in qualitative agreement with a prediction of the weak interaction theory for a random wave field incorporating the effects of second harmonics (Tayfun, 1980), but the values of kurtosis are different in sign from the prediction.To examine the nonlinear properties of energy containing components, higher harmonic components are excluded from the wave records by using a kind of a band-pass filter. The surface elevation distributions of the filtered waves show a sharp decrease in skewness , but the distributions remain highly non-Gaussian with a large negative kurtosis almost independent of the fetch and wind speed . It is concluded that the negative kurtosis is due to the non-random character of the phase and amplitude among the energy containing components, and that nonlinear interactions occur amongst the energy containing frequencies.     

Temporal variation of the partial pressure of CO2 in surface seawater of Iyo Nada in the Seto Inland Sea,Japan

The temporal variation of the partial pressure of carbon dioxide in surface seawater of Iyo Nada in the western Seto Inland Sea was measured by infrared absorption of carbon dioxide (CO₂) in air equilibrated with seawater. The variation of from January to late May in 1994 was relatively small (from 270 to 340 atm). on the contrary, the measured in September 1993 ranged from 200 to 450 atm. It seems that the relative high observed in the north and the south of Iyo Nada in September were caused by destruction of a stratification owing to tidal currents at straits between Hiroshima Bay and Iyo Nada and Hayasui Straits, respectively. The low observed in the central Iyo Nada in September was ascribed to a tidal front where high concentrations of chlorophyll-a and a relation between and chlorophyll-a in negative sense were found. Except the observation in the north of Iyo Nada in September, the in the surface seawater of Iyo Nada were lowe than the atmospheric (about 367 atm). The results obtained by this work and Kimotoet al. (1993) lead to the conclusion that Iyo Nada acts as a sink of the atmospheric CO₂ on the average.     

In-water algorithms for ADEOS/OCTS

In-water algorithms for OCTS standard products were developed using in situ data and installed for operationally processing at NASDA/EOC. This paper describes the in-water algorithms Version 1.0 for chlorophylla concentration, pigment concentration, and attenuation coefficient at a wavelength of 490 nm. The selected OCTS standard algorithms (Ver. 1.0) are as follows:      

The separation of flow past a circular cylinder on aβ-plane

Effects of the Ekman friction on the prograde (eastward) flows past a cylinder on a-plane are investigated when (=R ²/U, whereR is the cylinder radius andU the freestream speed)O(1) and(=2E _k ^1/2/R ₀·O(1) where is the non-dimensional beta parameter and the ratio of the square root of the Ekman numberE _k multiplied by 2 to the Rossby numberRo multiplied by the aspect ratio(=H/R, whereH is the fluid depth). Previous studies without the Ekman friction have shown that the-effect inhibits flow separation for pragrade flows through the asymptotic boundary condition by shifting the region of the adverse pressure gradient toward the rear stagnation point. It is found that the Ekman friction alleviates this-effect on the exterior flow. In the E_k ^1/4-boundary layer, on the other hand, Ekman friction suppresses the vorticity advection along the wall, which tends to make the boundary layer thickness thin and delay the flow separation. The Ekman friction thus affects flow separation in a complicated manner. Details of the boundary layer structures and the separation angles are described for 0.3< <4.0 and 0.1<<1.5.     

The roughness height and drag law over the water surface based on the hypothesis of local equilibrium

A series of measurements of winds and wind-waves were carried out in wind-wave flumes. A data analysis based on the hypothesis of local equilibrium yielded a new empirical formula on the controversial quantity of roughness heightz ₀ over the water surface: , where the nondimensional roughness height is defined bygz ₀/u _* ² and the wave-wind parameterũ byω _p u _*/g, g being the gravitational acceleration,u _* the friction velocity of air,ω _p the peak frequency of wind-wave spectra. The obtained formula is compared with Charnock's (1955) and Toba's (1979) proposals; is constant in the former and inversely proportional toũ in the latter. As in Toba's, this formula immediately leads to a practically important conclusion that the drag coefficientC _d depends not merely on the usual variableU ₁₀ (wind velocity at 10m height over the water surface), but also on the surface state represented by wind-waves. An explicit expression is provided for the drag coefficient incorporating the wave-wind parameter; it covers the range ofC _d calculated from most of the previous drag formulas, by varying the wave-wind parameter.     

Relation between mean and variance in catch numbers of fish egg and larva

In each of six areas with various horizontal scale from 0.4 to 15.6 nautical miles, many surveys with vertical net hauls are made for sampling fish eggs and larvae. Though values ofC _A are widely spread in each area, the variances ² and the meanm of catch numbers calculated from each survey follow approximately the relation from a Poisson mixture model (PMM).

Estimation of spectral refractive index of colloidal sulfur at 20°C

In the marine environment, colloidal sulfurs often occur due to the redox reaction of sulfide ions and oxygen molecules. It is important to know the spectral refractive index of colloidal sulfurs for the discussion of the light scattering in the region where colloidal sulfurs are formed. We presented new methods to estimate the refractive index from the wave length of maximum absorbance (turbidity) of a nearly mono-dispersed colloidal solution. In these methods, the ripples in a first main maximum of the scattering efficiency,Q _sca , were taken into consideration. By virtue of these methods, we obtained the spectral refractive index of colloidal sulfurs,m _s (), at 20°C. The Cauchy's expression of it was given by

Measurements of east Tushima Current in winter and estimation of its seasonal variability

The Tushima Current in the east channel was measured in a site of the strong current between Tushima and Iki Islands for 43 days of the winter in 1986. The primary results are:First, it was highly barotropic and flowed northeastward with a mean speed of about 20 cm sec^–1. Second, it was decelerated by northeast winds rather than by northwest winds in a frequency range of 0.3 and 0.4 cpd. Third, the scale analysis showed that the Tushima Current is approximately in geostrophic balance. The best empirical relationship between the measured Tushima Current and cross-channel adjusted sea level difference is given by

Volume transport of the western boundary current penetrating into a marginal sea

The amount of penetration of a western boundary current into a marginal sea which is connected to an open ocean by two narrow straits is estimated from a linear, steady and barotropic theoretical model. In this model the western boundary current in the open ocean is driven by a wind stress imposed at the sea surface. The inflow of the water of the open ocean into the marginal sea is caused by the pressure difference between two straits produced by the wind-driven circulation in the open ocean.Main external parameters are combined into two non-dimensional parameters; and (the ratio of the depth of the marginal sea to that of the open ocean), whereb is the distance between north and south boundaries of the ocean,D ₀ is the depth of the open ocean, is the latitudinal variation of the Coriolis parameter andR is the coefficient of friction. The friction is assumed to be proportional to the flow velocity.In the limit of infinite the volume transport into the marginal sea is not affected by the width of two straits and . It is mainly controlled by the wind stress and the positions of two straits. For finite values of , however, the volume transport depends considerably on and the width of the straits.Guided by both this model and physical considerations, we obtained a relation between the volume transport into the marginal sea and the external parameters. This relation predicts that about 2 % of the volume transport of the Kuroshio penetrates into the Japan Sea.     

On Seasonal and Year to Year Variation in Flow of the Alaskan Stream in the Central North Pacific

The Alaskan Stream is the westward boundary current of the North Pacific subarctic gyre. In the central region of the North Pacific, the Alaskan Stream serves as a connection between the Alaskan gyre, Western subarctic gyre and Bering Sea gyre. Its volume transport is very important in estimating the magnitude of the subarctic circulation in the North Pacific. In order to clarify its seasonal and interannual variation, we conducted observations along a north-south section at 180° during June from 1990 to 1997. Moorings were deployed from 1995 to 1997. Hydrographic casts were made at intervals of 37 km to a depth of 3000 m. Moorings were set between CTD stations, with Moor1 (Moor2) at the center (southern edge) of the Alaskan Stream. Geostrophic volume transport (referred to 3000 m) revealed large interannual variability in the Alaskan Stream. Average volume transport over the 8 years was 27.5 × 10⁶ m³s^-1 with a standard deviation of 6.5 × 10⁶ m³s^-1. Maximum transport was 41.0 × 10⁶ m³s^-1 (1997) and minimum was 21.7 × 10⁶ m³s^-1 (1995). Stable westward flows were observed at Moor1 1500 m (259°, 11.7 cm s^-1) and 3000 m (240°, 3.7 cm s^-1, 1996–1997 year average). The ratio of eddy to mean kinetic energy (KE/ ) was very small (<0.6) throughout the year. A relatively weak and unstable westward flow was observed at Moor2 at 3000 m depth. Conversely, the average flow direction at Moor2 5000 m was eastward.     

Recent advances in ocean-circulation research on the Yellow Sea and East China Sea shelves

Recent advances in ocean-circulation research on the Yellow Sea and East China Sea shelves are summarized. Observations using acoustic Doppler current profilers (ADCPs) suggest that the connectivity of mean-volume-transports is incomplete between the Tsushima (2.6 Sverdrups; 1 Sv = 10⁶ m³/s) and Taiwan Straits (1.2 Sv). The remaining 1.4-Sv transport must be supplied by onshore Kuroshio intrusion across the East China Sea shelf break. The Yellow Sea Warm Current is not a persistent ocean current, but an episodic event forced by northerly winter monsoon winds. Nevertheless, the Cheju Warm Current is detected clearly regardless of season. In addition, the throughflow in the Taiwan Strait may be episodic in winter when northeasterly winds prevail. The throughflow strengthens (vanishes) under moderate (severe) northeasterly wind conditions. Using all published ADCP-derived estimates, the throughflow transport (V) in the Taiwan Strait is approximated as

The self-thinning exponent in overcrowded stands of the mangrove, Kandelia obovata, on Okinawa Island, Japan

Weller??s allometric model assumes that the allometric relationships of mean area occupied by a tree $ \bar{s} $ , i.e., the reciprocal of population density $ \rho $ , $ \bar{s}\left( { = {1 \mathord{\left/ {\vphantom {1 {\rho = g_{\varphi } \cdot \bar{w}^{\varphi } }}} \right. \kern-0em} {\rho = g_{\varphi } \cdot \bar{w}^{\varphi } }}} \right) $ , mean tree height $ \bar{H}\left( { = g_{\theta } \cdot \bar{w}^{\theta } } \right) $ , and mean aboveground mass density $ \bar{d}\left( { = g_{\delta } \cdot \bar{w}^{\delta } } \right) $ to mean aboveground mass $ \bar{w} $ hold. Using the model, the self-thinning line $ \left( {\bar{w} = K \cdot \rho^{ - \alpha } } \right) $ of overcrowded Kandelia obovata stands in Okinawa, Japan, was studied over 8?years. Mean tree height increased with increasing $ \bar{w} $ . The values of the allometric constant $ \theta $ and the multiplying factor $ g_{\theta } $ are 0.3857 and 2.157?m?kg^???, respectively. The allometric constant $ \delta $ and the multiplying factor $ g_{\delta } $ are ?0.01673 and 2.685?m^?3?kg^1???, respectively. The $ \delta $ value was not significantly different from zero, showing that $ \bar{d} $ remains constant regardless of any increase in $ \bar{w} $ . The average of $ \bar{d} $ , i.e., biomass density $ \left( {{{\bar{w} \cdot \rho } \mathord{\left/ {\vphantom {{\bar{w} \cdot \rho } {\bar{H}}}} \right. \kern-0em} {\bar{H}}}} \right) $ , was 2.641?±?0.022?kg?m^?3, which was considerably higher than 1.3?C1.5?kg?m^?3 of most terrestrial forests. The self-thinning exponent $ \alpha \left( { = {1 \mathord{\left/ {\vphantom {1 {\varphi = }}} \right. \kern-0em} {\varphi = }}{1 \mathord{\left/ {\vphantom {1 {\left\{ {1 - \left( {\theta + \delta } \right)} \right\}}}} \right. \kern-0em} {\left\{ {1 - \left( {\theta + \delta } \right)} \right\}}}} \right) $ and the multiplying factor $ K\left( { = \left( {g_{\theta } \cdot g_{\delta } } \right)^{\alpha } } \right) $ were estimated to be 1.585 and 16.18?kg?m^?2??, respectively. The estimators $ \theta $ and $ \delta $ are dependent on each other. Therefore, the observed value of $ \theta + \delta $ cannot be used for the test of the hypothesis that the expectation of the estimator $ \theta + \delta $ equals 1/3, i.e., $ \alpha = {3 \mathord{\left/ {\vphantom {3 2}} \right. \kern-0em} 2} $ , or 1/4, i.e., $ \alpha = {4 \mathord{\left/ {\vphantom {4 3}} \right. \kern-0em} 3} $ . The $ \varphi $ value was 0.6310, which is the same as the reciprocal of the self-thinning exponent of 1.585, and was not significantly different from 2/3 (t?=?1.860, df?=?191, p?=?0.06429), i.e., $ \alpha = {3 \mathord{\left/ {\vphantom {3 2}} \right. \kern-0em} 2} $ . Thus the self-thinning exponent is not significantly different from 3/2 based on the simple geometric model. On the other hand, the self-thinning exponent was significantly different from 3/4 (t?=?6.213, df?=?191, p?=?3.182?×?10^?9), i.e., $ \alpha = {4 \mathord{\left/ {\vphantom {4 3}} \right. \kern-0em} 3} $ . Therefore, the self-thinning exponent is significantly different from 4/3 based on the metabolic model.     

Improvement of sand activation depth prediction under conditions of oblique wave breaking

This study presents sand activation depth (SAD) measurements recently obtained on two contrasting beaches located along the Atlantic coast of France: the gently sloping, high-energy St Trojan beach where wave incidence is usually weak, and the steep, low-energy Arçay Sandspit beach where waves break at highly oblique angles. Comparisons between field measurements and predictions from existing formulae show good agreement for St Trojan beach but underestimate the SAD on the Arçay Sandspit beach by 40–60%. Such differences suggest a strong influence of wave obliquity on SAD. To verify this hypothesis, the relative influence of wave parameters was investigated by means of numerical modelling. A quasi-linear increase of SAD with wave height was confirmed for shore-normal and slightly oblique wave conditions, and a quasi-linear increase in SAD with wave obliquity was also revealed. Combining the numerical results with previously published relations, both a new semi-empirical and an empirical formula for the prediction of SAD were developed which showed good SAD predictions under conditions of oblique wave breaking. The new empirical formula for the prediction of SAD (Z ₀) takes into account the significant wave height (H _s), the beach face slope (β) and the wave angle at breaking (α), and is of the form $ Z_{0} = 1.6\tan {\left( \beta \right)}H^{{0.5}}_{{\text{s}}} {\sqrt {1 + \sin {\left( {2\alpha } \right)}} } This study presents sand activation depth (SAD) measurements recently obtained on two contrasting beaches located along the Atlantic coast of France: the gently sloping, high-energy St Trojan beach where wave incidence is usually weak, and the steep, low-energy Ar?ay Sandspit beach where waves break at highly oblique angles. Comparisons between field measurements and predictions from existing formulae show good agreement for St Trojan beach but underestimate the SAD on the Ar?ay Sandspit beach by 40–60%. Such differences suggest a strong influence of wave obliquity on SAD. To verify this hypothesis, the relative influence of wave parameters was investigated by means of numerical modelling. A quasi-linear increase of SAD with wave height was confirmed for shore-normal and slightly oblique wave conditions, and a quasi-linear increase in SAD with wave obliquity was also revealed. Combining the numerical results with previously published relations, both a new semi-empirical and an empirical formula for the prediction of SAD were developed which showed good SAD predictions under conditions of oblique wave breaking. The new empirical formula for the prediction of SAD (Z ₀) takes into account the significant wave height (H _s), the beach face slope (β) and the wave angle at breaking (α), and is of the form . The use of a dataset from the literature demonstrates the predictive skill of these new formulae for a wide range of wave heights, wave incidence and beach gradients.     

Environmental controls on phytoplankton community composition in the Thames plume, U.K.

The aim of this study was to investigate controls on the phytoplankton community composition and biogeochemistry of the estuarine plume zone of the River Thames, U.K. using an instrumented moored buoy for in situ measurements and preserved sample collection, and laboratory-based measurements from samples collected at the same site. Instrumentation on the moored buoy enabled high frequency measurements of a suite of environmental variables including in situ chlorophyll, water-column integrated irradiance, macronutrients throughout an annual cycle for 2001 e.g. nitrate and silicate, and phytoplankton biomass and species composition. The Thames plume region acts as a conduit for fluvial nutrients into the wider southern North Sea with typical winter concentrations of 45 μM nitrate, 17 μM silicate and 2 μM phosphate measured. The spring bloom resulted from water-column integrated irradiance increasing above 60 W h m^− 2 d^− 1 and was initially dominated by a diatom bloom mainly composed of Nitzschia sp. and Odontella sinesis. The spring bloom then switched after  30 days to become dominated by the flagellate Phaeocystis reaching a maximum chlorophyll concentration of 37.8 μg L^− 1. During the spring bloom there were high numbers of the heterotrophic dinoflagellates Gyrodinium spirale and Katodinium glaucum that potentially grazed the phytoplankton bloom. This diatom–flagellate switch was predicted to be due to a combination of further increasing water-column integrated irradiance > 100 W h m^− 2 d^− 1 and/or silicate reaching potentially limiting concentrations (< 1 μM). Post spring bloom, diatom dominance of the lower continuous summer phytoplankton biomass occurred despite the low silicate concentrations (Av. 0.7 μM from June–August). Summer diatom dominance, generally due to Guinardia delicatula, was expected to be as a result of microzooplankton grazing, dominated by the heterotrophic dinoflagellate Noctiluca scintillans, controlling 0.7–5.0 μm ‘flagellate’ fraction of the phytoplankton community with grazing rates up to 178% of ‘flagellate’ growth rate. The Thames plume region was therefore shown to be an active region of nutrient and phytoplankton processing and transport to the southern North Sea. The use of a combination of moorings and ship-based sampling was essential in understanding the factors influencing nutrient transport, phytoplankton biomass and species composition in this shelf sea plume region.     

Observed relationship between the drag coefficient,Cd, and stability parameter, (−z/L)

Momentum and heat flux were measured with a sonic anemometer at the Marine Observation Tower in the port of ItÔ. Under unstable conditions (T _w -T _a =3C4C), using the eddy correlation method, results show thatCd=(1.2±0.3)×10^–3 andCh=(1.5±0.3)×10^–3 at 5.5 m above mean sea level except for the case of weak winds.An unexpected relationship betweenCd and (–z/L) was observed, that is,Cd decreases as (–z/L) increases. If roughness variation over the sea is taken into account, we can explain the decrease in the range of (–z/L) less than 1, but not in the range greater than 1. This is due to a strong instability effect and the change of roughness class, from moderately rough to smooth.     

Seasonal survey of copper-complexing ligands and thiol compounds in a heavily utilized, urban estuary: Elizabeth River, Virginia

Concentrations of thiol compounds, copper-complexing ligands, and total dissolved copper were followed over the course of 1 year (October 2002 until September 2003) in the Elizabeth River, Virginia to evaluate seasonality. Copper-complexing ligand concentrations were determined by competitive ligand equilibration-adsorptive cathodic stripping voltammetry (CLE/ACSV). Thiol detection was carried out by high performance liquid chromatography (HPLC) and calibration using a suite of nine thiol compounds (cysteine, glutathione, mercaptoacetic acid, 2-mercaptoethanesulfonic acid, 2-mercaptoethanol, 2-mercaptopropionic acid, 3-mercaptopropionic acid, mercaptosuccinic acid, and monothioglycerol). Total dissolved copper concentrations reached a January low of 13.1 nM to a June high of 24.7 nM and were found to vary seasonally with higher concentrations occurring from June to September. With a low of 26 nM during April to a high of 56 nM in October, copper-complexing ligand (average log K′_CuL of 12.0 ± 0.2) concentrations displayed a similar seasonal pattern to that of total dissolved copper. Free cupric ion concentrations remained below 1.5 pM for a majority of the year except during March, April, and December when values reached pM levels greater than 1.5. Six of the nine thiol compounds surveyed were detected in the Elizabeth River samples and ranged in concentration from below detectable concentrations (< 5 nM) to individual highs ranging from 25.3 to168.5 nM. The thiol compound concentrations displayed a clear seasonality fluctuating at below detection limits during November to February then increasing with increasing surface water temperatures from March to July. CLE/ACSV was used to assess whether or not the suite of thiol compounds detected by HPLC could contribute to the copper-complexing ligand pool. Conditional stability constants for each one of six thiol standards (average log K′_CuL  12.1 ± 0.5) were found to be statistically equivalent to the naturally occurring copper-complexing ligands (average log K′_CuL  12.0 ± 0.2). This suggests that these thiol compounds could act as copper-complexing ligands in natural samples and could contribute to the copper-complexing ligand pool detected by CLE/ACSV. This study involving seasonality of copper-complexing ligands and thiols in an industrialized, urban estuary underscored several points that have to be substantiated in future research efforts including copper-complexing ligands sources and the role that thiol compounds as well as other unidentified organic compounds play in the copper-complexing ligand pool.     

Distribution, condition, and growth of newly settled southern flounder (Paralichthys lethostigma) in the Galveston Bay Estuary, TX

Several flatfish species, including southern flounder (Paralichthys lethostigma) recruit to estuaries during early life. Therefore, evaluation of estuarine sites and habitats that serve as nurseries is critical to conservation and management. The present study used density data in conjunction with biochemical condition and growth measurements to evaluate settlement sites used by southern flounder in the Galveston Bay Estuary (GBE). In 2005, beam-trawl collections were made in three major sections of the GBE (East Bay, Galveston Bay, West Bay). Three sites were sampled in each bay. Within each sampling site, replicate collections were taken from three habitats: 1) marsh edge (< 1 m depth), 2) intermediate zone (10–20 m from marsh interface;  1 m depth), and 3) bay zone (typically > 100 m from marsh interface; depth > 1 m). Average size of southern flounder collected was 12–19 mm standard length, and peak densities occurred in January and February. Catch data indicated that densities of southern flounder were significantly greater in East Bay (2.75 per 100 m²) than in Galveston Bay (0.91 per 100 m²) or in West Bay (0.45 per 100 m²). Densities were statistically similar among habitats. Otolith-based estimates of age indicated that the majority of southern flounder collected were 35–45 days old and derived from early December to early January hatch-dates. Growth rates were similar among bays and among habitats, with the average growth rate being 0.40 mm day^− 1 (range: 0.21–0.76 mm day^− 1). RNA:DNA was above the established baseline value for nutritional stress, indicating that newly settled southern flounder in the GBE were in relatively high condition. Habitat-specific differences in RNA:DNA ratios were not observed; however, ratios were significantly lower in West Bay (average 8.0) than in East Bay (average 9.5) or in Galveston Bay (average 9.8), suggesting the condition of new recruits may vary spatially within the GBE. Findings from the current study suggest density and condition of newly settled southern flounder vary at the bay scale, suggesting that parts of GBE do not function equally as nurseries.     

Mean Vertical Distribution of the Dissipation Rate of Turbulent Energy in the Black Sea. Comparison with the Existing Models

We compare the results obtained by using theoretical and semiempirical models developed for the evaluation of the dissipation rate of turbulent energy in a stratified ocean with independent distribution of this quantity established by the authors for the active layer of the Black Sea (50–300 m) by using a one-dimensional model taking into account the balance of heat, salt, and fluid inside the layer. It is shown that, in a layer with gradual variation of the Väisälä–Brunt frequency N as a function of depth, the predominant sink of the energy of motion into dissipation N ² is ensured by the flow of energy through the spectrum of internal waves toward low frequencies and small vertical scales. On the contrary, in layers with abrupt drops of density as a function of depth (layers with jumps of density), an important role is played by the interface-type waves and the dependence of on N transforms into N .