On the turbulent prandtl number in a stably stratified atmospheric boundary layer

The results obtained from both atmospheric and laboratory measurements and from LES data show that, in the stably stratified flows of the atmospheric boundary layer, turbulent mixing occurs at gradient Richardson numbers Ri _g that significantly exceed one: the inverse turbulent Prandtl number Pr _t ⁻¹ decreases with an increase in the thermal flow stability. The decreasing trend of the inverse turbulent Ptandtl number is reproduced in a stably stratified atmospheric boundary layer in agreement with measurement data with the aid of an improved three-parameter turbulence model. In this model, a modified model that takes into account the effect of stratification in the expression for the time scale of the scalar field is used for the pressure-scalar correlation.     

瓯江河口盐度层化数值研究

瓯江口是一个径流量变化剧烈的强潮河口。本文基于非结构网格FVCOM模型,建立瓯江口海域大范围三维数学模型,研究不同时间尺度（潮周期、大-小潮）的盐度变化,并利用势能异常动力方程对数值模拟结果分析了瓯江口层化过程的动力机制。同时,利用河口R_i数和层化参数△s/<s>研究了不同时间尺度的层化稳定性及其空间变化,得出决定层化状态的潮差和径流量的阈值。结果显示：瓯江北口上段、中段和口门在潮差分别超过3.8m、4.0m和4.6m时呈完全混合状态。当径流量小于280 m³/s或大于510 m³/s,北口上段持续完全混合;而在口门附近,完全混合和层化的临界径流量约为280 m³/s。研究认为瓯江河口北口存在周期性的层化,北口下段在落潮和涨潮初期呈部分混合状态,而其它时段为完全混合。上段只在落潮初期存在层化。层化增强主要是纵向对流与横向速度剪切导致,而湍混合和纵向潮应力是层化减弱的主要因素。     

Turbulent perturbations of velocity in the conwy estuary

Field measurements of the vertical and horizontal components of fluid velocity 0·43 m above the bed have been made with an electromagnetic flowmeter in a partially mixed reach of the Conwy estuary for parts of a flood and an ebb tide. The turbulent mean velocity and density fields showed different effects for flood and ebb tides caused by the interaction of shear and the longitudinal density gradient. The turbulent velocity parameters were generally dominated by bed-generated turbulence effects, but significant longer period contributions attributed to the shear-density interactions were detected. The shear-stress measurements made by two independent methods showed good agreement. The results generally show good agreement with previous less complete data. The use of the Richardson number to quantify vertical stability needs further consideration for partially mixed estuarine flows.     

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.     

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.     

Field studies of velocity,salinity and suspended solids concentration in a shallow tidal channel near tidal flap gates

The design and operation of mathematical models of solute mixing and sediment transport in estuaries rely heavily on the provision of good-quality field data. We present some observations of salinity, suspended sediment concentration and velocity at one of the tidal limits of a semi-enclosed tidal lagoon in Southern England (Pagham Harbour, West Sussex, UK) where the natural processes of tidal incursion and solute mixing have been heavily modified as a result of the construction of sea walls dating back to the 18th Century. These observations, made immediately downstream of two parallel tidal flap gates by conductivity-temperature-depth (CTD) profiler, and also using bed-mounted sensor frames to measure velocity at 2 fixed depths, have yielded a set of results covering 11 tidal cycles over the period 2002–04. It is clear from the results obtained that over a typical tidal cycle, the greatest vertical salinity gradients occur in the 1–2 h immediately after the onset of the flood tide, and that subsequently, energetic mixing acts to rapidly break down this stratification. Under moderate-to-high fresh water flows (>0.5 m³/s), the break-down in vertical salinity gradient is more gradual, while under low fresh water flows (<0.2 m³/s), the vertical salinity gradient is generally less pronounced. Estimates of Richardson number during the early flood-tide period reveal values that vary rapidly between <1 and about 20, with lower values occurring after around 1.5–2 h after low water. Observations of suspended sediment concentration vary widely even for similar tidal and fresh water flow conditions, revealing the possible influence of wind speed, the storage effects of the water in the lagoon downstream of the observation site, and the complexity of the hydrodynamics downstream of tidal flap gates. The data also show that most of the sediment transport is landward, and occurs during flood tides, with estimated total tidal landward flood tide flux of fine sediment of the order of 50–120 kg under low fresh water flow conditions. These observations, which reinforce the results presented in Warner et al. (2004) and elsewhere, can help to provide information about the appropriate techniques for managing sediments and pollutants, including nutrients from sewage effluent waters, in estuaries where hydraulic flap gates are used to control the entry of fresh water over the tidal cycle.     

Some consequences of a flood tide front in Loch Creran

Loch Creran is a small Scottish sea loch with two basins which are connected by a shallow narrows. A sharp front that forms just inside the narrows during flood tides producing a simple mechanism for flushing the top brackish layer of the inner basin. The mechanism is shown to be consistent with temperature and velocity data. Conservation equations are used with salinity data to estimate mixing and entrainment rates and thus the energy used. A bottom drag coefficient for the narrows is estimated from the tidal signals of velocity and pressure gradient, and the turbulent kinetic energy entering the inner loch from the narrows is calculated, so that finally a value for the flux Richardson number (the fraction of available energy used by mixing and entrainment) can be given.     

Quantitative evaluation of turbulent mixing in the Central Equatorial Pacific

Turbulent mixing in the central equatorial Pacific has been quantitatively evaluated by analyzing data from microstructure measurements and conductivity temperature depth profiler (CTD) observations in a meridionally and vertically large region. The result that strong turbulent mixing with dissipation rate ε (>O(10^?7) W kg^?1), continuing from sea-surface mixed layer to low Richardson number region below, in the area within 1° of the equator, shows that turbulent mixing has a close relationship to shear instability. ε > O(10^?7) W kg^?1 and turbulent diffusivity K _ρ  > O(10^?3) m² s^?1 were obtained from near-surface to 85 db at stations even southwardly beyond 3°S, where it is already far from the southern boundary (~2°S) of the Equatorial Undercurrent. Turbulence-induced heat flux and salinity flux were calculated, and both had their maxima in the equatorial upwelling region, though the former was downward and the latter was upward. Accordingly, vertical velocity in the upwelling region was estimated to be similar to the results derived by other methods. These fluxes and the vertical velocity suggest the critical importance of turbulent mixing in maintaining the well-mixed upper layer. Secondly, in the intermediate region (>500 db), turbulent eddies were investigated by applying Thorpe’s method to the CTD data. A large number of overturns were detected, with spatial-averaged K _ρ (700–1,000 db) being 3.3 × 10^?6 m² s^?1, and the corresponding K _ρ-max reaching to O(10^?4) m² s^?1 in the north (3°–13°N). The results suggest that, in the intermediate region, considerable turbulent mixing occurs and moderates the properties of the water masses.     

Turbulent mixing in stably stratified flows of the environment: The current state of the problem (Review)

Specific features of the turbulent transfer of the momentum and heat in stably stratified geophysical flows, as well as possibilities for including them into RANS turbulence models, are analyzed. The momentum (but not heat) transfer by internal gravity waves under conditions of strong stability is, for example, one such feature. Laboratory data and measurements in the atmosphere fix a clear dropping trend of the inverse turbulent Prandtl number with an increasing gradient Richardson number, which must be reproduced by turbulence models. Ignoring this feature can cause a false diffusion of heat under conditions of strong stability and lead, in particular, to noticeable errors in calculations of the temperature in the atmospheric boundary layer. Therefore, models of turbulent transfer must include the effect of the action of buoyancy and internal gravity waves on turbulent flows of the momentum. Such a strategy of modeling the stratified turbulence is presented in the review by a concrete RANS model and original results obtained during the modeling of stratified flows in the environment. Semiempirical turbulence models used for calculations of complex turbulent flows in deep stratified bodies of water are also analyzed. This part of the review is based on the data of investigations within the framework of the large international scientific Comparative Analysis and Rationalization of Second-Moment Turbulence Models (CARTUM) project and other publications of leading specialists. The most economical and effective approach associated with modified two-parameter turbulence models is a real alternative to classical variants of these models. A class of test problems and laboratory and full-scale experiments used by the participants of the CARTUM project for the approbation of numerical models are considered.     

A two-fluid model of turbulent two-phase flow for simulating turbulent stratified flows

In this paper, a two-fluid model of turbulent two-phase flow is used to simulate turbulent stratified flows. This is a unified multi-fluid model for the motion of each phase in the flow, whose turbulent transport is closed by a two-phase k– model. The exchanges of mass, momentum and energy between the two phases are fully accounted for in the simulation. For illustration, a case of turbulent stratified flow with strong buoyancy effects, for which extensive experimental data are available, is selected for examination. It is shown that the numerical results agree well with the experimental data.     

Three-dimensional instability of shear flows with inflection-free velocity profiles in stratified media with a high Prandtl number

In stably stratified media with a Prandtl number Pr ≫ 1, vertical scales of the density (ℓ) and horizontal velocity variation (L) are quite different, ℓ/L = O(Pr^−1/2) ≪ 1, and this influences the flow stability. In particular, shear flows without inflection points on the velocity profile are unstable even in an ideal incompressible fluid. The maximum instability growth rate for sufficiently small ℓ/L is of the same order as in homogeneous mixing layers, with mainly three-dimensional rather than two-dimensional oscillations increasing in a wide range of parameters. This paper focuses on the three-dimensional instability of such flows. It is shown that the spectrum of unstable oscillations is essentially anisotropic in the case of a relatively weak stratification when the bulk Richardson number J ≤ O[(ℓ/L)^3/2]. The results of the asymptotic analysis are illustrated by calculations for a model flow in a two-layer medium (ℓ = 0) as well as for flows with values of ℓ/L corresponding to a temperature or salinity stratification of the water.     

A model for Meddy formation

A particular feature of “Meddies” is that the water within them has stable gradients of salinity and temperature. In this paper a model for a dense turbulent plume falling in a stationary, linearly-stratified environment is described. The density of the plume is assumed to be a linear function of two components, while the ambient density gradient is due to a gradient in only one of these components (labelled component one). The ratio of the contributions to the source buoyancy flux of the two components within the plume is identified as the important parameter for this type of flow. After deriving the steady equations for the plume, a simplified model for the filling process which creates the Meddy is described, which shows how a layer of fluid may be formed with stable gradients in both components in the lower part of the intrusion. The intrusion is shown to be less stratified than the surrounding fluid, with relatively weak gradients in component one (identified with temperature in the Meddy) that vary from unstable at the top to stable at the bottom of the intrusion and a fairly constant (stable) gradient in the second component (salinity for a Meddy). If the stable gradients in a Meddy are due solely to the filling process then, during formation, the top of the Meddy must become cooler than the surrounding water at the same level. The observed stable temperature gradient in Meddies is likely to be due to mixing processes after their formation, whereas the stable salanity gradient is mainly due to the filling process during formation.     

Shear stress statistics and wall similarity analysis in turbulentboundary layers using a high-resolution 3-D ADVP

Three-dimensional (3-D) quasi-instantaneous acoustic Doppler velocity profiles at the center of uniform, turbulent open-channel flow over smooth and rough beds have been analyzed for the dynamics of coherent structures. The qualitative aspects of simultaneously measured Eulerian velocity and shear stress signatures identify coherent structures in the water column. A cumulant discard method is applied to describe the statistical properties of the covariance terms u'w' along the mean flow and v'w' across the mean flow relative to their time means. Conditional statistics and conditional sampling are used to compare the theoretical and experimental relative covariance contributions from the four quadrants in the longitudinal and transverse planes. The results in the (u', w') plane show the dominance of ejections (quadrant 2; u'<0, w'>0) and sweeps (quadrant 4; u'>0, w'<0). In contrast, the distribution of fractional v'w' events in the transverse plane is quasi-uniform over the four quadrants. Based on these experimentally determined statistical properties of the covariance terms in different flow conditions, a simplified form of the vertical turbulent energy flux in the intermediate flow region is given and the concept of wall similarity in turbulent boundary layers is validated. Since the validity of the wall similarity concept over a wide range of bed roughness has been shown, it is proposed to determine the mean bed friction velocity from the evaluation of the vertical turbulent energy flux     

Study of the Neutral Ekman Flow Using an Algebraic Reynolds Stress Model

A recently developed fully explicit algebraic model of Reynolds stress and turbulent heat flux in a thermally stratified planetary atmospheric boundary layer without stratification has been used for a numerical study of the Ekman turbulent boundary layer over a homogeneous rough surface for different dimensionless surface Rossby numbers. A comparative analysis has been conducted for a closure model of the transport term in the prognostic equation of turbulent kinetic energy dissipation including third-order moments. Dependences of the total wind rotation angle on the Rossby number have been obtained. The calculated vertical profiles of mean velocity, turbulent stress, turbulent kinetic energy, surface-friction velocity, and boundary-layer height agree satisfactorily with observational and earlier obtained LES data.     

Mixing caused by lateral internal seiching within a partially mixed estuary

The salinity fluctuations at an STD near the halocline in Southampton Water have been spectrally analysed. Mixing is shown to commence at a layer Richardson number of about 20. The predominant energy inputs have periods of 7–9 and 3·5–4·5 min. These motions arise from lateral internal seiching and it is considered that they are produced by interaction of the surface seiche with the shallow side of the estuary. The wavelengths of the standing wave are calculated to be about 120 and 60 m respectively, and these compare well with echo-sounding surveys of the elevation of the halocline.     

Nutrient exchange across the sediment-water interface in the Potomac River estuary

The flux of ammonia, phosphate, silica and radon-222 from Potomac tidal river and estuary sediments is controlled by processes occurring at the sediment-water interface and within surficial sediment. Calculated diffusive fluxes range between 0·6 and 6·5 mmol m^?2 day^?1 for ammonia, 0·020 and 0·30 mmol m^?2 day^?1 for phosphate, and 1·3 and 3·8 mmol m^?2 day^?1 for silica. Measured in situ fluxes range between 1 and 21 mmol m^?2 day^?1 for ammonia, 0·1 and 2·0 mmol m^?2 day^?1 for phosphate, and 2 and 19 mmol m^?2 day^?1 for silica. The ratio of in situ fluxes to diffusive fluxes (flux enhancement) varied between 1·6 and 5·2 in the tidal river, between 2·0 and 20 in the transition zone, and from 1·3 to 5·1 in the lower estuary. The large flux enhancements from transition zone sediments are attributed to macrofaunal irrigation. Nutrient flux enhancements are correlated with radon flux enhancements, suggesting that fluxes may originate from a common region and that nutrients are regenerated within the upper 10–20 cm of the sediment column.The low fluxes of phosphate from tidal viver sediments reflect the control benthic sediment exerts on phosphorus through sorption by sedimentary iron oxyhydroxides. In the tidal river, benthic fluxes of ammonia and phosphate equal one-half and one-third of the nutrient input of the Blue Plains sewage treatment plant. In the tidal Potomac River, benthic sediment regeneration supplies a significant fraction of the nutrients utilized by primary producers in the water column during the summer months.     

Layered Structure of Stably Stratified Turbulent Shear Flows

Izvestiya, Atmospheric and Oceanic Physics - Data of a numerical simulation of a stably stratified turbulent Couette flow are analyzed for various values of the Richardson number. Two different...     

The effect of salinity on the microbial mineralization of two polycyclic aromatic hydrocarbons in estuarine sediments

Sediments from the lower Hudson River estuary and two other coastal environments were examined experimentally for their ability to mineralize (convert to CO₂) the polycyclic aromatic hydrocarbons (PAHs) naphthalene and anthracene over a range of salinities. Routine assays employed 1:1 (vol fresh sed:vol water) sediment slurrys in order to overcome natural variability in mineralization rates among replicates. Mineralization rates were stimulated by about 2·5 fold, compared to unslurried controls, while the coefficient of variation fell from 13% to 3·5%.Rates of naphthalene mineralization in surface sediments from along the mainstem of the Hudson River (salinities from 2 to 27%) ranged from 0·011 to 1·5 nmol cm⁻³ day⁻¹ (pool turnover [T_n] from 60 to 2040 days) with no discernible trends along the estuarine gradient. For two stations examined experimentally (mile point 5, salinity 23%; mile point 26, salinity 5%), microbial assemblages appeared acclimated to broad salinity variations as alter rates of mineralization compared to controls.Sediments from two upstream marshes of the Hudson (mile points 36 and 45) showed rates of naphthalene mineralization from 0·007 to 0·15 nmol cm⁻³ day⁻¹ (T_n from 14 to 368 days), while sediments from a third marsh in freshwater (mile point 76) had high rates (66 nmol cm⁻³ day⁻¹; T_n 40 days). For the two upstream marsh stations which rarely experienced salt intrusion, there was a substantial decrease in mineralization of naphthalene and anthracene with increasing salinity.Consistently high rates of naphthalene mineralization (780 to 1600 nmol cm⁻³ day⁻¹; T_n 5 to 6 days) were observed in petroleum contaminated sediments from Port Jefferson Harbor (PJH) on the north shore of Long Island. PJH has a relatively constant salinity regime (about 27%) and imposed decreases in salinity effected decreases in rates of naphthalene and anthracene mineralization. Lowest rates of naphthalene mineralization (0·003 to 0·004 nmol cm⁻³ day⁻¹; T_n from 714 days to 833 days) were found in sediments from two stations in the relatively pristine Carmans River estuary on the south shore of Long Island.The ability of increases or decreases in salinity to affect the rate of model PAH mineralization appeared to be dependent on the natural variation in the salinity regime from which a sample was obtained. Data from all the environments studied indicated a strong positive correlation between PAH concentration and the rates of mineralization of naphthalene. Rates of PAH mineralization in all environments examined appear to be primarily controlled by the extent of pollutant loading and not by natural variations in the salinity regime.     

Nutrient transport from an artificial upwelling of deep sea water

The transport of nutrient-rich, deep sea water from an artificial upwelling pipe has been simulated. A numerical model has been built within a commercial Computational Fluid Dynamics (CFD) package. The model considers the flow of the deep sea water after it is ejected from the pipe outlet in a negatively buoyant plume (densimetric Froude number = −2.6), within a stably stratified ocean environment subject to strong ocean current cross flow. Two cross-flow profiles were tested with momentum flux ratios equal to 0.92 and 3.7. The standard k-ε turbulence model has been employed and a range of turbulent Schmidt and Prandtl numbers tested. In all cases the results show that the rapid diffusion of heat and salinity at the pipe outlet causes the plume to attain neutral buoyancy very rapidly, preventing strong fountain-like behavior. At the higher momentum flux ratio fountain-like behavior is more pronounced close to the pipe outlet. The strong cross-current makes horizontal advection the dominant transport process downstream. The nutrient plume trajectory remains largely within one relatively thin stratified layer, making any ocean cross-flow profile less important. Very little unsteady behavior was observed. The results show that the nutrient is reduced to less than 2% of its inlet concentration 10 meters downstream of the inlet and this result is largely independent of turbulent Prandtl or Schmidt number. Initial results would suggest that if such an artificial upwelling were to be viable for an ocean farming project, a large number of upwelling pipes would be necessary. Further work will have to determine the minimum nutrient concentration required to sustain a viable phytoplankton population and the required spacing between upwelling pipes.