Vertical mixing in the bottom mixed layer near the continental shelf break in the East China Sea

The strength of the vertical mixing in the bottom mixed layer near the continental shelf break in the East China Sea was directly measured with the Micro-Scale Profiler (MSP). It has been shown that there is no significant statistical relation between the turbulent energy dissipation and the degree of the stratificationN ². It seems that the vigorous turbulence occurs not constantly but intermittently in the bottom mixed layer so that a large variation of is found depending on the time. In contrast to , the coefficient of the vertical eddy diffusivityK _z is mostly determined byN such thatK _z is large in the bottom mixed layer and small in the thermocline. Large value ofK _z in the bottom mixed layer is also found in the time series ofK _z estimated in terms of Richardson number calculated from the data obtained with electromagnetic current meters. The value ofK _z more than 10 cm²s^–1 frequently occur in the layer of 20–25 m thick just above the bottom.     

Vertical transport in the Black Sea

Investigations of the vertical exchange coefficientK _z , considering turbulent and advective transport, are summarized. The values ofK _z are determined from the climaticT, S characteristics, heat and salinity fluxes, and the rate of the low-Bosporus water transformation over the entire Black Sea water column; namely, in the upper mixed layer, the active layer, the cold intermediate layer, the halocline, and in the deep and near-bottom waters. A characteristic for annual fluctuations ofK _z in the active layer is given; it is noted that the coefficient tends to grow in transit from the centre of the cyclonic gyre toward its periphery.Translated by V. Puchkin.     

Dynamical structure of vertically two-dimensional estuary in steady state

The dynamical structure of a two-dimensional (depth and axial directions) estuary is studied analytically. A set of governing equations describing the time-averaged velocity and salinity in the estuary is used, where all of the external parameters (depth, width, freshwater discharge and horizontal and vertical coefficients of eddy viscosity and eddy diffusivity) are assumed to be constant along the estuary.Two dynamical relations are taken into consideration in the theory. One of them is the dependence of the longitudinal scaleL _d on the balance of longitudinal salt transport, and the other is the relation between the vertical stratification of salinity and the the Prandtl numberP _r=A_v/K_v, whereA _v andK _v denote the coeffcients of the vertical eddy viscosity and diffusivity, respectively. The two relations result in an extension of the parameter range in which the linear balance of momentum holds.A linear state of motion (LM-state) is defined as the state where the momentum balance is linear. The LM-state comprises the so-called vertically homogeneous and the so-called partially mixed state. Perturbation analysis is introduced and dynamical theory is developed in the LM-state. Since the LM-state covers a fairly wide regime with respect to the balance of salt transport, the state is subdivided into three stages: the diffusive, intermediate and advective stages. In the diffusive stage the upstream salt transport is mainly attributed to the horizontal diffusion, whereas in the advective stage it is attributed to advection caused by gravitational circulation. The salinity balance is also linear in the diffusive and intermediate stages, whereas the balance is nonlinear in the advective stage. The advective stage of the LM-state is regarded as a stage bordering the salt wedge state.The longitudinal distribution of depth-mean salinity is found to take an exponential form in the diffusive stage, a nearly linear form in the advective stage and an intermediate form between them in the intermediate stage.     

Three-dimensional structure of tidal current in the East China Sea and the Yellow Sea

A three-dimensional tidal current model is developed and applied to the East China Sea (ECS), the Yellow Sea and the Bohai Sea. The model well reproduces the major four tides, namely M₂, S₂, K₁ and O₁ tides, and their currents. The horizontal distributions of the major four tidal currents are the same as those calculated by the horizontal two-dimensional models. With its high resolutions in the horizontal (12.5 km) and the vertical (20 layers), the model is used to investigate the vertical distributions of tidal current. Four vertical eddy viscosity models are used in the numerical experiments. As the tidal current becomes strong, its vertical shear becomes large and its vertical profile becomes sensitive to the vertical eddy viscosity. As a conclusion, the HU (a) model (Davieset al., 1997), which relates the vertical eddy viscosity to the water depth and depth mean velocity, gives the closest results to the observed data. The reproduction of the amphidromic point of M₂ tide in Liaodong Bay is discussed and it is concluded that it depends on the bottom friction stress. The model reproduces a unique vertical profile of tidal current in the Yellow Sea, which is also found in the observed data. The reason for the reproduction of such a unique profile in the model is investigated.     

Characterization of vertical mixing at a tidal-front on Georges Bank

Studies of mixing were done at the northern flank of Georges Bank in the summer and autumn of 1988. Two time-series of the evolution and intensity of microstructure were examined over a tidal period in the context of tidal forcing and the evolution of the density and velocity field at the site. From the CTD, ADCP and microstructure observations (EPSONDE) on Georges Bank, several interesting features of the mixing processes were found. High dissipation and diffusivity regions appear near the bottom of the Bank. Turbulence near the bottom is highest in intensity and reaches farthest from the bottom at peak tidal flow and diminishes in intensity and vertical extent as the flow decreases. The thickness of the bottom turbulent layer has its maximum value when the flow is strongest and the stratification is weakest. Characterization of the dissipation rate and turbulent diffusivities in respect to buoyancy frequency N, current shear S, Richardson Number R_i and ε/νN² was done. Dissipation and χ_T showed little dependence on shear or N² but decreased at larger R_i. χ_t was found to be higher in regions of higher N² and increased as ε/νN² increased. K_T, K and K_ν, were all highest near the bottom in excess of 10⁻²m²s⁻¹ and decreased towards the surface. There was little suggestion of a dependence of mixing efficiency on S², R_i or ε/νN², but some indication that Γ decreases with decreasing N².     

Tidal Currents in the Tsushima Straits Estimated from ADCP Data by Ferryboat

Tidal currents in the Tsushima Straits have been analyzed using measurements obtained since February 1997 by an acoustic Doppler current profiler (ADCP) mounted on the ferryboat Camellia. Tidal current constituents (M ₂, S ₂, K ₁, O ₁) are dominant among the ten tidal current constituents (Q ₁, O ₁, P ₁, K ₁, N ₂, M ₂, S ₂, K ₂, MSf, Mf), and generally 1.4–2.1 times stronger at the western channel of the straits than those at the eastern channel. The ratio between amplitude of M ₂, S ₂, K ₁ and O ₁ averaged along the ferryboat track is 1:0.45:0.59:0.51. The major axis directions of tidal current ellipses are generally SW to NE, exceptionally in the vicinity of the Tsushima Islands. Approaching the Tsushima Islands from the Korean Peninsula side, the major axis gradually rotates clockwise. At the western channel, the M ₂ and K ₁ constituents change the rotation direction of current vectors from clockwise to counterclockwise at about 90–130 m depth. The contributions of the tidal currents to the mean kinetic energy and the mean eddy kinetic energy along the ferryboat track are, on average, 0.56 and 0.71, respectively. This suggests that tidal current activities are generally more dominant than the mean current activities and much more dominant than eddy activities. The only region where the eddy activities are comparable to the tidal current activities is located on the east side of the Tsushima Islands. This revised version was published online in July 2006 with corrections to the Cover Date.     

Barotropic instability of a viscous boundary jet

The barotropic instability of a boundary jet on a beta plane is considered with emphasis on the effect of internal viscosity. An eigenvalue problem for the disturbance equations and its inviscid version are solved by the aid of numerical methods, and instability characteristics are determined as functions of the Reynolds numberR for various values of the beta-parameter. Typical disturbance structures (eigenfunctions) are also computed. Numerical examples show that the minimum critical Reynolds numberR _cr for instability is smaller than 100. At a Reynolds number of the order of hundreds, there appears a second mode of instability in addition to the first unstable mode originating atR _cr ; a kind of ‘resonance’ between the first and second eigenvalues occurs at the particular value ofR. The neutral stability curves are accordingly multi-looped. Although each of the two unstable modes asymptotically approaches its inviscid counterpart asR→∞, the asymptotic approach to the inviscid limit is rather slow and the effect of varyingR is conspicuous even atR∼O (10⁴). It is thus demonstrated that the Reynolds number is an essential stability parameter for real boundary jets. The main part of the material contained in this paper was presented at 1981-Autumn Assembly of the Oceanographical Society of Japan.     

Validating a turbulence closure against estuarine microstructure measurements

A simple k–ε turbulence closure is introduced which has no stability functions but instead a Richardson number-dependent turbulent Prandtl number. Its free parameters are determined in a comparison with microstructure observations from a stratified and sheared tidal estuary and laboratory measurements. The closure is able to simulate observed turbulent dissipation rates (ε) and turbulent length scales (l_th) in regions of strong mean shear and small gradient Richardson number (R_g) to within factors of 2–3. It fails in regions of small shear and large R_g, presumably because of the dominance of internal wave-driven mixing. Additional simulations with a k–ε closure with stability functions taken from Canuto et al. [Canuto, V.M., Howard, A., Cheng, Y., Dubovikov, M.S., 2001. Ocean turbulence I: one-point closure model. Momentum and heat vertical diffusivities. J. Phys. Oceanogr. 31, 1413–1426] and with the closure of Baumert and Peters [Baumert, H., Peters, H., 2004. Turbulence closure, steady state, and collapse into waves. J. Phys. Oceanogr. 34, 505–512] show poor performance. Establishing a valid 1:1 comparison of simulated and observed ε and l_th requires nudging the model velocity and density toward observed values because free model integrations quickly diverge from the observations. Steady state gradient Richardson numbers are constrained to a range of 0.18–0.25, while flux Richardson numbers are constrained to the range of 0.1–0.22. The closure output is rather insensitive to such parameter variations. The simulations are sensitive, however, to the treatment of the observed velocity and density used to nudge the model. Good closure performance requires averaging the measured tidal flow over about an hour, a time scale for which conventional numerical models of estuarine circulations should be able to match observed shears. In the closure simulations the TKE balance stays close to a production–dissipation balance. The time rate of change and vertical diffusion of TKE are small, of the same order of magnitude, and vary in magnitude relative to each other systematically across the water column.     

Vertical distribution of the hydrogen sulphide sources in the Black Sea

Data on the diffusion coefficientK _zand the concentration of H₂S in the Black Sea are used to compute the depth distribution of the vertical flux, and the intensity of the H₂S sources and sinks. On average, the total production of H₂S in the Black Sea reaches 37×10⁶ t/year. The main bulk of H₂S is produced not at the bottom, but in the layer of 450–1300 m. Destruction of H₂S prevails above the 400 m layer. Dissolved oxygen penetrating the H₂S zone can oxidize only half of the hydrogen sulphide produced in the sea.Translated by Mikhail M. Trufanov.     

厦门湾海水中224Ra的深度分布特征及其应用

本文采用MnO₂-纤维富集、220Rn的连续射气闪烁法测定厦门湾海水中的224Ra,利用其垂直分布求出该海域的垂直涡动扩散系数(K_z),为该海域可溶性污染物扩散、迁移和海域自净能力的估算提供理论依据.该海域224Ra的垂直分布及由此得出的K_z使我们能够洞悉研究海域水体的垂直扩散特征及其时、空变化.     

The mixing efficiency and the processes of restratification in a stably stratified medium

The mechanism of the effect of a collapsing turbulent eddy on diapycnal transport in a stably stratified fluid is considered. It is shown that at small Richardson turbulent numbersRi ₀ the mixing efficiency increases asRi ₀, and at large numbers it decreases in proportion toRi ₀ ^–1/2 .Translated by Mikhail M. Trufanov. UDK 551.465.15.     

A quasi-three-dimensional numerical prediction model of salinity structure in Bohai Sea and Huanghai Sea

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Distribution of Overturn Induced by Internal Tides and Thorpe Scale in Uchiura Bay

The vertical mixing process induced by internal tides was investigated by repeated conductivity, temperature, and depth (CTD) measurements and bottom-mounted acoustic Doppler current profiler (ADCP) in Uchiura Bay from July 24 to 25, 2001. Internal tides were observed with a wave height of 40 m and a horizontal current of 0.3 ms⁻¹. Density inversions were found in the CTD data, and the method of Galbraith and Kelley (1996) was applied to the data to identify overturns and to calculate Thorpe scale. Most of the overturns distributed in the region of low Richardson number, so that they were considered to be caused by shear instability associated with the internal tides. Thorpe scale was calculated to be 0.48 m. From the Thorpe scale, the vertical eddy diffusivity due to internal tides in Uchiura Bay was estimated as K _ρ ∼ 10⁻⁴ m²s⁻¹. This revised version was published online in July 2006 with corrections to the Cover Date.     

The reliability of the thermodynamic constants for the dissociation of carbonic acid in seawater

Laboratory measurements of all four CO₂ parameters [f_CO2 ( = fugacity of CO₂), pH, TCO₂ ( = total dissolved inorganic carbon), and TA ( = total alkalinity)] were made on the same sample of Gulf Stream seawater (S = 35) as a function of temperature (5–35 °C) and the ratio of TA/TCO₂ (X) (1.0–1.2). Overall the measurements were consistent to ±8 μ atm in f_CO2, ± 0.004 in pH, ± 3 μ mol kg⁻¹ in TCO₂, and ± 3 μ mol kg⁻¹ in TA with the thermodynamic constants of Goyet and Poisson (1989), Roy et al. (1993), and Millero (1995). Deviations between the measured pH, TCO₂, TA and those calculated from various input combinations increase with increasing X when the same constants are used. This trend in the deviations indicates that the uncertainties in pK₂ become important with increasing X (surface waters), but are negligible for samples with the lower X (deep waters). This trend is < 5 μ mol kg⁻¹ when the pK₂ values of Lee and Millero (1995) are used.The overall probable error of the calculated f_CO2 due to uncertainties in the accuracy of the parameters (pH, TCO₂, TA, pK₀, pk₁, and pK₂) is ± 1.2%, which is similar to the differences between the measured values and those calculated using the thermodynamic constants of Millero (1995).The calculated values of pK₁, (from f_CO2-TCO₂-TA) agree to within ± 0.004 compared to the results of Dickson and Millero (1987), Goyet and Poisson (1989), Roy et al. (1993), and Millero (1995) over the same experimental conditions. The calculated values of pK₂ (from pH-TCO₂-TA) are in good agreement (± 0.004) with the results of Lee and Millero (1995) and also in reasonable agreement (± 0.008) with the results of Goyet and Poisson (1989), Roy et al. (1993), and Millero (1995). The salinity dependence of our derived values of pK₁ and pK₂, (S = 35) can be estimated using the equations determined by Millero (1995).     

Observations of turbulence under weakly and highly stratified conditions in the Ariake Sea

Observations of turbulence, stratification, and mean current were made using a microstructure profiler and an acoustic Doppler current profiler (ADCP) during four cruises at a central location in the Ariake Sea, under weakly and strongly stratified conditions. Continuous measurements of the dissipation rate of turbulent kinetic energy (TKE), ε, were made. These revealed that frictional bed turbulence with quarterdiurnal variation in the bottom boundary layer (BBL) was one of the most energetic sources of vertical mixing in the sea. Thickness of the BBL was strongly confined by the stable stratification. We investigate a relationship between the BBL height h and the Ozmidov scale. We present a systematic argument that describes the vertical structure and characteristic scales of velocity and turbulence inside the frictional BBL, where the stratification persisted. Considerable deviation of observed vertical shear from the law of the wall indicated a modification of turbulent scales by the stratification. Shear stress calculated from the velocity data using vertical integration of the equation of motion was found to decrease approximately linearly with height. The TKE production rate P, estimated using the shear stress, was highly correlated with the dissipation rate. The buoyancy contribution to TKE balance in the BBL was quantified in terms of the flux Richardson number R _f as R _f?=?0.12.     

Radium-228 in the Japan Sea

The distribution of²²⁸Ra in surface and subsurface waters in the Japan Sea was studied. The concentrations of²²⁸Ra in surface waters were around 100 dpm/1000l which were much higher than those reported for Pacific surface waters. The concentrations of²²⁸Ra decreased with increasing depth to less than 10 dpm/1000l in the Japan Sea Proper Water. Based on the comparison between observed values of²²⁸Ra and calculated profile through the near-surface water mass and the underlying main water mass in the Japan Sea, the apparent vertical eddy diffusion coefficient was estimated to be about 2 cm² s^–1.     

Effect of bottom slope in northeastern North Pacific on deep-water upwelling and overturning circulation

Hydrographic data show that the meridional deep current at 47°N is weak and southward in northeastern North Pacific; the strong northward current expected for an upwelling in a flat-bottom ocean is absent. This may imply that the eastward-rising bottom slope in the Northeast Pacific Basin contributes to the overturning circulation. After analysis of observational data, we examine the bottom-slope effect using models in which deep water enters the lower deep layer, upwells to the upper deep layer, and exits laterally. The analytical model is based on geostrophic hydrostatic balance, Sverdrup relation, and vertical advection–diffusion balance of density, and incorporates a small bottom slope and an eastward-increasing upwelling. Due to the sloping bottom, current in the lower deep layer intensifies bottomward, and the intensification is weaker for larger vertical eddy diffusivity (K _V), weaker stratification, and smaller eastward increase in upwelling. Varying the value of K _V changes the vertical structure and direction of the current; the current is more barotropic and flows further eastward as K _V increases. The eastward current is reproduced with the numerical model that incorporates the realistic bottom-slope gradient and includes boundary currents. The interior current flows eastward primarily, runs up the bottom slope, and produces an upwelling. The eastward current has a realistic volume transport that is similar to the net inflow, unlike the large northward current for a flat bottom. The upwelling water in the upper deep layer flows southward and then westward in the southern region, although it may partly upwell further into the intermediate layer.     

Does the Ulleung eddy owe its existence to β and nonlinearities?

A nonlinear theory for the generation of the Ulleung Warm Eddy (UWE) is proposed. Using the nonlinear reduced gravity (shallow water) equations, it is shown analytically that the eddy is established in order to balance the northward momentum flux (i.e., the flow force) exerted by the separating western boundary current (WBC). In this scenario, the presence of β produces a southward (eddy) force balancing the northward momentum flux imparted by the separating East Korean Warm Current (EKWC).It is found that, for a high Rossby number EKWC (i.e., highly nonlinear current), the eddy radius is roughly 2R_d/ε^1/6 (here ε≡βR_d/f₀, where R_d is the Rossby radius), implying that the UWE has a scale larger than that of most eddies (R_d). This solution suggests that, in contrast to the familiar idea attributing the formation of eddies to instabilities (i.e., the breakdown of a known steady solution), the UWE is an integral part of the steady stable solution. The solution also suggests that a weak WBC does not produce an eddy (due to the absence of nonlinearity).A reduced gravity numerical model is used to further analyze the relationship between β, nonlinearity and the eddy formation. First, we show that a high Rossby number WBC which is forced to separate from the wall on an f plane does not produce an eddy near the separation. To balance the northward momentum force imparted by the nonlinear boundary current, the f plane system moves constantly offshore, producing a southward Coriolis force. We then show that, as β is introduced to the problem, an anticyclonic eddy is formed. The numerical balance of forces shows that, as suggested by the analytical reasoning, the southward force produced by the eddy balances the northward flow force imparted by the boundary current. We also found that the observed eddy scale in the Japan/East Sea agrees with the analytical estimate for a nonlinear current.     

Ecological and physiological features of the mesopelagic mysid,Meterythrops microphthalma,in the Japan Sea

The abundance and vertical distribution pattern of a mysidMeterythrops microphthalma were investigated in the Japan Sea. Results from vertical hauls from 602–982 m depth to the surface around Yamato Rise in April 1987 indicated that the dominance (by biomass) ofM. microphthalma was third to fifth of major zooplankton taxa. Vertical distribution investigated at a single station in Toyama Bay in June, September and December 1986 showed that the most part of population of this mysid inhabited consistently below 250 m depth. No marked diurnal vertical migration was evident. Data on body composition and oxygen consumption rate ofM. microphthalma are presented. Water content of the body was 75.6–83.8% of wet weight, and ash was 11.4–20.4% of dry weight. Carbon, hydrogen and nitrogen were 37.9–47.5%, 6.2–7.4% and 9.4–10.1%, respectively, of dry weight. Oxygen consumption rates were 2.2–11.0µl O₂ individual^–1 hr^–1 at 0.5°C, and were directly proportional to body mass. From the comparison with the published data on epipelagic and bathypelagic mysids it is revealed that both body nitrogen composition and oxygen consumption rate expressed as adjusted metabolic rate [AMR₀₂,µl O₂ (mg body N)^–0.85 hr^–1] ofM. microphthalma are intermediate between high epipelagic and low bathypelagic levels, indicating typical mesopelagic features.     

Vertical diffusion and oxygen consumption during stagnation periods in the deep North Aegean

Ventilation of the deep basins of the North Aegean Sea takes place during relatively scarce events of massive dense water formation in that region. In the time intervals between such events, the bottom waters of each sub-basin are excluded from interaction with other water masses through advection or isopycnal mixing and the only process that changes their properties is diapycnal mixing with overlying waters. In this work we utilize a simple one-dimensional model in order to estimate the vertical eddy diffusion coefficient K_ρ based on the observed rate of change of density and stratification. Vertical diffusivity is estimated for each of three sub-basins of the North Aegean, one of convex shape of the seabed and the other two of concave topography. It is noteworthy that the convex sub-basin exhibited much higher vertical diffusivity than the two concave sub-basins, a fact consistent with theoretical predictions that internal-wave-induced mixing is higher over the former shape of seabed. Furthermore, the estimates of K_ρ are exploited in computing the vertical transport of dissolved oxygen through diffusion and the rate of oxygen consumption by decaying organic matter. The different levels of the estimated diffusion and oxygen consumption rates testify to the dynamical and biogeochemical characteristics of each basin.