Estimation of TKE dissipation rates in dense bottom plumes using a Pulse Coherent Acoustic Doppler Profiler (PC-ADP) — Structure function approach

During a hydrographic survey in January 2006 the spreading of inflowing saline water was observed in the Arkona Basin (Western Baltic Sea). Two bottom mounted ‘pulse coherent’ acoustic Doppler profilers (PC-ADP) were used to measure the near-bottom current field of the dense plume with a high temporal (1 s) and spatial resolution (5 cm). In order to estimate the dissipation rate of turbulent kinetic energy () a structure function approach was applied to the beam velocity data. Simultaneous measurements with a microstructure shear profiler (MSS) and an acoustic Doppler velocimeter (ADV) supplied independent data for the verification of the structure function method. Additional measurements with standard CTD, near-bottom towed and vessel mounted acoustic Doppler current profilers (ADCP) completed the data set.The estimated dissipation rates from the structure function approach fit well with the values derived from the ADV and the MSS probe. It is shown that the structure function approach is a reliable and easily applicable method to derive estimates of TKE dissipation rates from PC-ADP beam velocities. The observed dissipation rates ranged between 5 · 10^− 6 and 1 · 10^− 8 W kg^− 1 depending on the hydrographic conditions. Inside the plume the dissipation rates exceeded that of the overlaying brackish water by two orders of magnitude. Since the noise level of velocity data in pulse coherent mode is considerably lower than in the Doppler mode the PC-ADP can also be used for estimates in marine environments with low turbulence level. Reynolds stresses estimated from the PC-ADP and the ADV agreed well at the same depth level. TKE production derived from PC-ADP measurements compared reasonably well with the dissipation rate of TKE in a varying environment.     

The interaction of tidal advection, diffusion and mussel filtration in a tidal channel

Time series measurements of flow and pigment concentrations (Chl) in the Menai Strait have revealed that the strong residual flow in a tidal channel ( 500 m³ s^− 1) transports phytoplankton from the open sea into the channel where much of it is consumed by suspension feeders, mainly in commercial beds of Mytilus edulis. The progressive depletion of phytoplankton along the channel results in a strong horizontal gradient of plankton and hence Chl. Tidal displacement of this gradient causes large (± 50% of mean) oscillations of Chl in the vicinity of the mussel beds. Vertical mixing by the strong tidal flows is sufficiently vigorous for most of the tidal cycle to ensure that downward diffusion can resupply the near-bed layer although there are indications of some transient depletion around slack water.This paradigm of the interaction of advection, diffusion and filtration determining the distribution of plankton and its supply to mussels has been encapsulated in a series of simple models forced only by boundary values. In the first, a 1-D model of tidal flow in the channel reproduces the principal features of the observed currents including the unusually large spatial change in phase of the currents and the variation of the residual transport with tidal range. The flow field from this physical model is used to drive a second model based on the advection diffusion equation for Chl with a source at the Irish Sea boundary and a sink over the mussel bed. This model illustrates the formation of a strong Chl gradient along the channel and simulates the amplitude and phase of the M₂ oscillations of Chl and the development of the M₄ variation apparent in the observations. This second model has been extended to 2-D over the mussel beds to allow investigation of the effects of water column mixing. The model indicates that only for a short period ( 30 min), close to slack water, is mixing sufficiently reduced to permit the development of a depletion boundary layer and then only within  1 m from the bottom, a result which is consistent with the observations.     

Mixing in the surface boundary layer of a tropical freshwater reservoir

A combined observational-modeling study was conducted to investigate turbulence mixing, and the relation to surface forcing, in the surface boundary layer (SBL) of a tropical, high-altitude, freshwater reservoir. A suite of vertical profiles of temperature microstructure, collected at three different stations of one-day duration each, provided estimates of dissipation rates of turbulence kinetic energy, , and temperature variance, χ. Numerical simulations of and χ, using state-of-the-art, public domain, two-equation turbulence closure models, compared favorably with the observations and reproduced the dynamics of daytime wind mixing as well as the vertical and temporal turbulence structure during nighttime convective conditions.Two independent estimates of vertical eddy diffusivities in the stably stratified (daytime) SBL, computed from the microstructure measurements, agreed closely, and the near surface heat and buoyancy fluxes, computed from the diffusivities, were similar to those computed independently from surface meteorology. Model generated eddy diffusivities agreed closely with the observed values, except those generated by K profile parameterization (KPP) model simulations. The good agreement provides confidence that nutrient fluxes in the SBL may be accurately computed from the models when forced with regularly measured surface meteorological parameters. The consequences are important for estimation of daily primary productivity rates in the euphotic zone and the ability to predict algal blooms such as those observed in the present reservoir.     

Modelling physical processes of haline stratification in ROFIs with application to the Rhine outflow region

A physical and numerical study is made of the processes governing the stratification and circulation in ROFIs (Regions of Freshwater Influence) where there is an important impact of wind and tides. Observations in the Rhine ROFI showed that the salinity field consists of a mean and a tidally oscillating part. The physical processes are first analysed using the analytical solutions from a one-dimensional two-layer model. A justification is given for the neglection of non-linear advective terms in the equations of momentum and salinity. The dimensionless forms of the solutions can be expressed in terms of a series of dimensionless numbers. It is shown in particular that stratification and cross-shore circulation largely depend on the balance between rotation and turbulent diffusion, which depends in turn on parameters such as the Ekman number, the bottom friction coefficient, the eddy viscosity ratio and the depth of the layer interface. Surface winds either enhance or destroy stratification depending on the wind angle. The response to wind forcing is discussed using classical Ekman theory. To verify the analytical theory numerical tests are performed with a point model including an advanced turbulence closure scheme. Differences arise due to the non-linear interaction between turbulence on the one hand and current shear and stratification on the other hand. It is shown in particular that the amplitude of the tidal forcing and the off-shore horizontal salinity gradient strongly affect the semi-diurnal and semi-monthly variation of stratification. The effect of the wind is found to be in good agreement with the analysis of the two-layer model. Finally, the numerical model is compared with existing observational data in the Rhine ROFI for October 1990.     

One-dimensional modelling of the plankton ecosystem of the north-western Corsican coastal area in relation to meteorological constraints

In order to study the influence of wind mixing on the spring variability of the plankton production of the north western Corsican coastal area, a one-dimensional (1D), vertical, coupled hydrodynamic/biological model (ECOHYDROMV) is used. A hydrodynamic 1D model of the water column with a k–l turbulent closure is applied. The biological model comprises six state variables, representing the plankton ecosystem in the spring period: phytoplankton, copepods, nitrate, ammonium, particulate organic matter of phytoplanktonic origin and particulate organic matter of zooplanktonic origin. The system is influenced by turbulence (expressed by the vertical eddy diffusivity), temperature and irradiance. The model takes into account momentum and heat surface fluxes computed from meteorological data in order to simulate a typical spring atmospheric forcing for the considered area. Results show that primary production vertical structure is characterised by a subsurface maximum which deepens with time and is regulated by the opposite gradients of nitrate concentration and irradiance. Surface plankton productivity is mainly controlled by turbulent vertical transport of nutrients into the mixed layer. The short time scale variability of turbulent mixing generated by the wind appears to be responsible for the plurimodal shape of plankton blooms, observed in the considered area. Furthermore, the model is applied to the study of the spring evolution of the plankton communities off the bay of Calvi (Corsica) for the years 1986 and 1988. In order to initiate and validate the model, time series of hydrological, chemical and biological data have been used. The model reproduces accurately the spring evolution of the phytoplankton biomass measured in situ and illustrates that its strong variability in those years was in close relation to the variability of the wind intensity.     

Effects of small-scale turbulence on the growth of two diatoms of different size in a phosphorus-limited medium

The effect of turbulence on the nutrient flux towards osmotrophic cells is predicted to be size dependent. This should translate into growth. We experimentally followed and modelled the growth of two marine diatoms of different size (Thalassiosira pseudonana, 6 μm in diameter and Coscinodiscus sp., ca. 109 μm in diameter) under still water and turbulent conditions, using a shaker table. Experiments were done with phosphorus-limited cultures and lasted for ca. 5 days. Turbulence enhanced the growth of Coscinodiscus sp. in agreement with theory but not the growth of T. pseudonana, which was actually slightly lower under turbulence. At the end of the experiments there were about 1.7 times as many Coscinodiscus sp. cells in the turbulent treatment than in the still treatment, while for T. pseudonana almost the same cell concentration was found in both conditions. In addition, the Coscinodiscus sp. cells growing under still conditions presented a higher specific alkaline phosphatase activity than those growing in turbulence which indicates a higher need for phosphorus in the still cultures. A simple dynamic model, based on Michaelis–Menten nutrient uptake kinetics, needed nearly no optimisation other than using observed initial conditions of phosphate and cell concentrations. The model showed how an increased nutrient flux towards the cells translates non-linearly into cell growth, most likely by affecting the half-saturation constant (K_M). However, since Coscinodiscus sp. experienced significant mortality and cells partially settled to the bottom of the containers, unequivocal support for the size-dependent effect of turbulence on nutrient uptake will require further experiments and more sophisticated modelling. The mechanisms to connect an increased nutrient flux towards cells with population growth and whether this process is size dependent are important in parameterizing the effects of turbulence on marine plankton in coupled physical–biological models.     

An approach to estimation of near-surface turbulence and CO2 transfer velocity from remote sensing data

The air–sea CO₂ exchange is primarily determined by the boundary-layer processes in the near-surface layer of the ocean since it is a water-side limited gas. As a consequence, the interfacial component of the CO₂ transfer velocity can be linked to parameters of turbulence in the near-surface layer of the ocean. The development of remote sensing techniques provides a possibility to quantify the dissipation of the turbulent kinetic energy in the near-surface layer of the ocean and the air–sea CO₂ transfer velocity on a global scale. In this work, the dissipation rate of the turbulent kinetic energy in the near-surface layer of the ocean and its patchiness has been linked to the air–sea CO₂ transfer velocity with a boundary-layer type model. Field observations of upper ocean turbulence, laboratory studies, and the direct CO₂ flux measurements are used to validate the model. The model is then forced with the TOPEX POSEIDON wind speed and significant wave height to demonstrate its applicability for estimating the distribution of the near-surface turbulence dissipation rate and gas transfer velocity for an extended (decadal) time period. A future version of this remote sensing algorithm will incorporate directional wind/wave data being available from QUIKSCAT, a now-cast wave model, and satellite heat fluxes. The inclusion of microwave imagery from the Special Sensor Microwave Imager (SSM/I) and the Synthetic Aperture Radar (SAR) will provide additional information on the fractional whitecap coverage and sea surface turbulence patchiness.     

Using high sampling-rate ADCP for observing vigorous processes above sloping [deep] ocean bottoms

Above sloping bottoms in the ocean mixing processes are not predominantly generated by shear-induced turbulence via bottom friction. Instead, the restratifying buoyancy forces and internal waves create a highly non-linearly varying environment including ‘stratified turbulence’. Most of the resulting vigorous mixing processes that dominate sediment resuspension occur during the passage of frontal bores or solitary boluses, ‘solibores’. Here, the observed evolution of different forms of highly non-linear strictly upslope moving ‘waves’, bores or boluses are reviewed from various NIOZ projects at deep sloping bottom sites ranging from 500 to 3000 m.Such fronts pass a fixed site within a few minutes, extending some 60 ± 30 m above the bottom and occurring over much larger periods at once per subinertial or meso-scale period or approximately, but not exactly, once per tidal harmonic period. In order to observe the details of such solibore one needs specific, high-sampling rate equipment. A suitable piece of equipment is a bottom-mounted 4-beam 300 kHz acoustic Doppler current profiler (ADCP), provided it samples at a rate of about once per second over a period of at least several weeks. Not just the three components of current velocity [u,v,w] are monitored over a range of some 80 m at 1 m intervals, but also the relative ‘echo intensity’ dI, which is a measure for suspended matter and stratified turbulence. Such ADCP-observations are combined and compared with high-resolution temperature measurements. Fine details show a turbulent inner core with more or less laminar streamlines outside it. Whether a front or a bolus, the bore is never observed as a completely closed contour, as swept up turbulent material is sucked into the core at the rear end.     

Late summer stratification, internal waves, and turbulence in the Yellow Sea

Microstructure profiling measurements at two locations in the Yellow Sea (a deeper central basin and a local shelf break) were analyzed focusing on tidal and internal-wave induced turbulence near the bottom and in the pycnocline. A classical three-layer density structure consisting of weakly stratified surface and bottom boundary layers and a narrow sharp pycnocline is developed by the end of warm season. Turbulence in the surface layer was not influenced by the tidal forcing but by the diurnal cycle of buoyancy flux and wind forcing at the sea surface. The enhanced dissipation and diffusivity generated by the shear stress at the seafloor was found in the water interior at heights 10–15 m above the bottom with a phase shift of ~ 5–6 m/h. No internal waves, turbulence, or mixing were detected in the pycnocline in the central basin, in contrast to the pycnocline near the local shelf break wherein internal waves of various frequencies were observed all the time. The thickness of the surface layer near the local shelf break slightly exceeded that of the bottom layer (20 vs. 18 m). A 5–6 m high vertical displacement of the pycnocline, which emerged during the low tide, was arguably caused by the passage of an internal soliton of elevation. During this episode, the gradient Richardson number decreased below 0.25 due to enhanced vertical shear, leading to local generation of turbulence with dissipation rates exceeding the background level by an order of magnitude.     

Distribution of void fraction in bubbly flow through a horizontal channel: Bubbly boundary layer flow, 2nd report

A method of enveloping the hull with a sheet of microbubbles is discussed. It forms part of a study on means of reducing the skin friction acting on a ship's hull. In this report, a bubble traveling through a horizontal channel is regarded as a diffusive particle. Based on this assumption, an equation based on flow flux balance is derived for determining the void fraction in approximation. The equation thus derived is used for calculation, and the calculation results are compared with reported experimental data. The equation is further manipulated to make it compatible with a mixing length model that takes into account the presence of bubbles in the liquid stream. Among the factors contained in the equation thus derived, those affected by the presence of bubbles are the change of mixing length and the difference in the ratio of skin friction between cases with and without bubbles. These factors can be calculated using the mean void fraction in the boundary layer determined by the rate of air supply into the flow field. It is suggested that the ratio between boundary layer thickness and bubble diameter could constitute a significant parameter to replace the scale effect in estimating values applicable to actual ships from corresponding data obtained in model experiments.List of symbols a ₁ proportionality constant indicating directionality of turbulence - B law-of-the-wall constant - C _f local skin-friction coefficient in the presence of bubbles - C _f0 local skin-friction coefficient in the absence of bubbles - d _b bubble diameter (m) - g acceleration of gravity (m/s²) - j _g flow flux of gas phase accountable to buoyancy (m/s) - j _t flow flux of gas phase accountable to turbulence (m/s) - k ₄ constant relating reduction of liquid shear stress by bubble presence to decrease of force imparted to bubble by its displacement due to turbulence - l _b mixing length of gas phase (m) - l _m mixing length of liquid phase (m) - l _mb diminution of liquid phase mixing length by bubble presence (m) - Q _G rate of air supply to liquid stream (l/min) - q _/g velocity of bubble rise (m/s) - 2R height of horizontal channel (m) - T _* integral time scale (s) - U _m mean stream velocity in channel (m/s) - U friction velocity in channel (m/s) - V volume of a bubble (m³) - u, ¯ v time-averaged stream velocities inx- andy-directions, respectively (m/s) - u, v turbulent velocity components inx- andy-directions, respectively (m/s) - v root mean square of turbulence component in they-direction (m/s) - root mean square of bubble displacement iny-direction with reference to turbulent liquid phase velocity (m) - y displacement from ceiling (m) - local void fraction - _m mean void fraction in boundary layer - _m constant relating local void fraction to law-of-the-wall constant - _t reduction of turbulent stress (N/m²) - law-of-the-wall constant in turbulent liquid region in absence of bubbles - ₁ law-of-the-wall constant in turbulent liquid region in presence of bubbles - ₂ law-of-the-wall constant in gas phase - _m constant indicating representative turbulence scale (m) - viscosity (Pa × s) - v kinematic viscosity (m²/s) - density (kg/m³) Suffixes G gas - L liquid - 0 absence of bubbles     

The influence of different turbulence schemes on modelling primary production in a 1D coupled physical–biological model

A one-dimensional (1D) coupled physical–microbiological model has been applied to a site in the central North Sea. The impact of the choice of the turbulence closure scheme on the modelling the primary production has been investigated.The model was run with four different parameterisations of vertical mixing of heat, momentum and dissolved and suspended matters, using M2 tidal forcing and the hourly mean meteorological forcing of 1989 to reproduce the annual thermal structure and primary production. The four mixing parameterisations are: Level 2 turbulence closure scheme [Mellor, G.L., Yamada, T., 1974. A hierarchy of turbulence closure models for planetary boundary layers. J. Atmos. Sci. 31, 1791–1806; Mellor, G.L., Yamada, T., 1982. Development of a turbulence closure model for geophysical Fluid problems. Rev. Geophys. Space Phys. 20 (4) 851–875] using an explicit numerical scheme [Sharples, J., Tett, P., 1994. Modelling the effect of physical variability on the midwater chlorophyll maximum. J. Mar. Res. 52, 219–238]; a version of the Level 2.5 turbulence closure scheme [Galperin, B., Kantha, L.H., Hassid, S., Rosati, A., 1988. A quasi-equilibrium turbulent energy model for geophysical flows. J. Atmos. Sci. 45, 55–62; Ruddick, K.G., Deleersnijder, E., Luyten, P.J., Ozer, J., 1995. Haline stratification in the rhine/meuse freshwater plume: a 3D model sensitivity analysis. Cont. Shelf Res. 15 (13) 1597–1630] simplified to use an algebraic mixing length by Sharples and Simpson [Sharples, J., Simpson, J.H., 1995. Semidiurnal and longer period stability cycles in the Liverpool Bay region of freshwater influence. Cont. Shelf Res. 15, 295–313], also solved explicitly; the same simplified L2.5 scheme with an implicit numerical solution and modified vertical discretisation scheme [Annan, J.D., 1999. Numerical methods for the solution of the turbulence energy equations in the shelf seas. Int. J. Numer. Methods Fluids 29, 193–206]; and another version of the same scheme (but using a different algebraic mixing length) as described by Xing and Davies [Xing, J., Davies, A.M., 1996a. Application of turbulence energy models to the computation of tidal currents and mixing intensities in the shelf edge regions. J. Phys. Oceanogr. 26, 417–447; Xing, J., Davies, A.M., 1996b. Application of a range of turbulence models to the computation of tidal currents and mixing intensities in shelf edge regions. Cont. Shelf. Res. 16, 517–547; Xing, J., Davies, A.M., 1998. Application of a range of turbulence energy models to the computation of the internal tide. Int. J. Numer. Methods Fluids 26, 1055–1084]. Various model outputs at the sea surface and in depth profiles have been compared with data collected in 1989 as part of the North Sea Project [Huthnance, J.M., 1990. Progress on North Sea Project. NERC News, vol. 12, pp. 25–29, UK]. It is shown that the biological results are extremely sensitive to the small changes in the physical conditions, which arise due to the different turbulence schemes tested. The timing of the spring bloom and the maintenance of the midwater chlorophyll maximum all differ greatly between model runs, and the gross primary production varies by a factor of two from the highest to lowest results. The simplified Level 2.5 scheme, implemented using the numerical methods of Annan [Annan, J.D., 1999. Numerical methods for the solution of the turbulence energy equations in the shelf seas. Int. J. Numer. Methods Fluids 29, 193–206], produces results, which give the best agreement with the available data.     

A pseudofield model approach to simulate compartment-fire phenomena for marine fire safety design

In order to prevent the spread of marine compartment fires, it is necessary to understand the governing factors or characteristics of fire-spread phenomena. We present a pseudofield model approach to this problem. We first described a field model of turbulent heat convection based on a standard k – turbulence model. Two-dimensional numerical simulations of a two-linked compartment fire were carried out in order to predict the turbulent convection flow induced by the heat released from the fire. Then a more complicated fire-spread problem of multilinked compartment fires was analyzed by means of a zone model, in which the amounts of oxygen consumption and gas generation were solved by a gas-balance equations system. The effect of threshold conditions on fire propagation and the effect of the thickness of the heat insulation were investigated with numerical simulations.     

Quantifying copepod kinematics in a laboratory turbulence apparatus

We describe application of a new apparatus that permits simultaneous detailed observations of plankton behavior and turbulent velocities. We are able to acquire 3D trajectories amenable to statistical analyses for comparisons of copepod responses to well-quantified turbulence intensities that match those found in the coastal ocean environment. The turbulence characteristics consist of nearly isotropic and homogeneous velocity fluctuation statistics in the observation region. In the apparatus, three species of copepods, Acartia hudsonica, Temora longicornis, and Calanus finmarchicus were exposed separately to stagnant water plus four sequentially increasing levels of turbulence intensity. Copepod kinematics were quantified via several measures, including transport speed, motility number, net-to-gross displacement ratio, number of escape events, and number of animals phototactically aggregating per minute. The results suggest that these copepods could control their position and movements at low turbulence intensity. At higher turbulence intensity, the copepods movement was dominated by the water motion, although species-specific modifications due to size and swimming mode of the copepod influenced the results. Several trends support a dome-shaped variation of copepod kinematics with increasing turbulence. These species-specific trends and threshold quantities provide a data set for future comparative analyses of copepod responses to turbulence of varying duration as well as intensity.     

航道清礁对西江鱼类保护区紊流体的影响

河底裸露的礁石增加水体紊动,有助于鱼卵正常形成,大量存在礁石的河段往往是鱼类栖息和产卵的重要场所。礁石也存在碍航的可能,航道清礁一定程度上影响水体紊动强度,改变鱼类栖息环境。为此,在重要鱼类栖息河段进行航道清礁需充分论证。以紊动动能作为评价水体紊动强度指标,开展西江中游珍稀鱼类保护区河段三维紊流数值模拟,计算并统计航道清礁工程前后水体紊动动能及不同强度的紊流水体体积,分析其变化规律及原因。研究结果表明,断面中紊动动能强度与水深成正相关关系;清礁工程导致河段中弱紊动动能的紊流水体体积增加,强紊动动能的紊流体积减小;底层水体紊动动能的变化量高于表层;强紊动动能水体体积减少的变化率大于弱紊动动能水体体积增加的变化率。     

航道整治工程软体排压载体的水力特性

软体排是航道整治工程中的基础结构,其水力特性直接影响航道整治工程的护滩效果。通过建立水槽模型,研究软体排压载体附近流场结构、回流区长度、近底流速、紊动流场、切应力等水力特性。结果表明,设置软体排压载体后,近底流速和回流区流速减小,上层流速和水流纵向紊动强度增加,近底层的切应力则明显减小。压载体的设置有利于调节近底水流流态、促进泥沙落淤,提高工程边滩守护效果。     

A numerical investigation of the impact of turbulence on the feeding rates of Oithona davisae

Individual based numerical simulations of the copepod, Oithona davisae, feeding on motile prey, Oxyrrhis marina, under variable turbulent conditions are performed. These simulations correspond to laboratory observations conducted by Saiz et al. [Saiz, E., Calbet, A., and Broglio, E., 2003. Effects of small-scale turbulence on copepods: the case of Oithona Davisae. Limnol. Oceanogr., 48:1304–1311.].The flow field in the simulation is reconstructed by a kinematic simulation whose characteristic scales are derived from the grid mesh and the dissipation rates of the laboratory experiments. The kinematic simulation provides a simplified model, which while not fully realistic, captures the basic relevant feature of turbulence. A hop and sink swimming behaviour is prescribed for O. davisae, while O. marina moves along helical paths with random changes of directions.Three possible effects are tested: the existence of a time threshold in the duration of the contacts between predator and prey, a progressive reduction of the perceptive distance with increasing turbulence level and an abrupt reduction in feeding of O. davisae when the flow speed, in relation to the copepod position, is higher than a prescribed threshold. This last approach introduces an intermittency in the feeding which depends on the variations of velocity both in space and time within the numerical box.The introduction of the time threshold causes a dome-shaped relationship between the simulated enhancement factor and the dissipation rate, while with the other two effects, a monotonic decrease in the enhancement factor is observed, with values reasonably close to the ones observed in the laboratory experiment. In all the cases, the use of realistic values of biological parameters (e.g. swimming behaviour) reproduces response curves in the range of the observations.     

Simple Lagrangian formulation of bubbly flow in a turbulent boundary layer (bubbly boundary layer flow)

For the theoretical consideration of a system for reducing skin friction, a mathematical model was derived to represent, in a two-phase field, the effect on skin friction of the injection of micro air bubbles into the turbulent boundary layer of a liquid stream. Based on the Lagrangian method, the equation of motion governing a single bubble was derived. The random motion of bubbles in a field initially devoid of bubbles was then traced in three dimensions to estimate void fraction distributions across sections of the flow channel, and to determine local bubble behavior. The liquid phase was modeled on the principle of mixing length. Assuming that the force exerted on the liquid phase was equal to the fluid drag generated by bubble slip, an equation was derived to express the reduction in turbulent shear stress. Corroborating experimental data were obtained from tests using a cavitation tunnel equipped with a slit in the ceiling from which bubbly water was injected. The measurement data provided qualitative substantiation of the trend shown by the calculated results with regard to the skin friction ratio between cases with and without bubble injection as function of the distance downstream from the point of bubble injection.List of symbols B law of wall constant - C _f local coefficient of skin friction - C _f0 local coefficient of skin friction in the absence of bubbles - d _b bubble diameter [m] - g acceleration of gravity [m/s²] - k ₁ k₄ proportional coefficient - k _L turbulent energy of the liquid phase [m²/s²] - L representative length [m] - l _b mean free path of a bubble [m] - m _A added mass of a single bubble [kg] - m _b mass of a single bubble [kg] - N _x ,N _y ,N _z force perpendicular to the wall or ceiling exerted on a bubble adhering to that wall or ceiling [N] - P absolute pressure [Pa] - Q _G rate of air supply [/min] - q _L ⁽ⁱ⁾ turbulent velocity at the ith time increment [m/s] - R> _ex Reynolds number defined by Eq. 32 - T _*L integral time scale of the liquid phase [s] - U velocity of the main stream [m/s] - ,¯v,¯w time-averaged velocity components [m/s] - u,v,w turbulent velocity components [m/s] - û _L ,v_L root mean square values of liquid phase turbulence components in thex- and y-directions [m/s] - V volume of a single bubble [m³] - X,Y,Z components of bubble displacement [m] - x _s ,y _s ,z _s coordinate of a random point on a sphere of unit diameter centered at the coordinate origin - root mean square of bubble displacement in they-direction in reference to the turbulent liquid phase velocity [m] - local void fraction - _m mean void fraction in a turbulent region - regular random number - R _v increment of the horizontal component of the force acting on a single bubble, defined by Eq. 22 [N] - t time increment [s] - ₁ reduction of turbulent stress [N/m²] - _L rate of liquid energy dissipation [m²/s³] - _m coefficient defined by Eq. 30 - law of wall constant in the turbulent region in absence of bubbles - ₁ law of wall constant in the turbulent region in presence of bubbles     

PIV velocity field measurements of flow around a KRISO 3600TEU container ship model

The main purpose of this investigation was to demonstrate a useful application of the particle image velocimetry (PIV) method to analyze the complex flow characteristics around a ship. For a sample illustration, the KRISO 3600TEU container ship model was chosen. The flow structure in the stern and near-wake region of the model has been investigated experimentally in a circulating water channel. Instantaneous velocity fields measured by the PIV velocity field measurement technique have been ensemble-averaged to give details of flow structures such as the spatial distributions of the local mean velocity, vorticity, and turbulent kinetic energy. The free-stream velocity was fixed at U _o = 0.6m/s, and the corresponding Reynolds number based on the length between perpendiculars was about 9.0 × 10⁵. The container ship model shows a complicated three-dimensional flow structure in the stern and near-wake regions. The PIV results clearly revealed the formation of large-scale bilge vortices in the stern region and their effect on the flow in the near-wake. The results shown here provide valuable information for hull form design and the validation of viscous ship flow codes and of turbulence models.     

Estimates of vertical mixing during a Lagrangian experiment off the Galician coast

An adjoint 1-D model was used to determine vertical diffusivity coefficients from temperature profiles collected within a filament escaping from the Galician coast following an upwelling event. The optimisation scheme ended with relatively high diffusivity values within the thermocline (9×10⁻⁵ m² s⁻¹). Such high values are relevant for biogeochemical exchanges between surface and deep waters in stratified areas.The optimised values were several orders of magnitude higher than the bulk of diffusivity measurements recorded with a free-falling device; however, the optimisation solution was consistent with the arithmetic mean of the measurements in the thermocline (7.7×10⁻⁵ m² s⁻¹), giving more weight to the few largest values. Below the thermocline, the data assimilation method failed because of the three-dimensional nature of the advective field of the upwelling system. Ignoring this advective forcing in the model led to estimates that were two orders of magnitude too high.The results suggest that turbulent mixing is a random process where a few intense events determine the average mixing that drives the long-term evolution of the water column structure. This statistical property is very important when one wants to use instantaneous diffusivity measurements for modelling purposes.