Entrainment Depth Research Articles

Second-order turbulence closure models for geophysical boundary layers. A review of recent work

Recent contributions to second-order turbulence modelling are reviewed with an emphasis on models of the coastal ocean. Classical and recent turbulence models are reformulated using a unifying notation, making differences in model structure and model parameters more transparent. The essential characteristics of a number of models are compared. It is further demonstrated that the mathematical stability and realisability of the models is crucial for practical applications. The parameter constraints to insure stable computations are discussed. Model performance is evaluated for a number of idealised entrainment scenarios that are typical for shelf seas: entrainment in linearly stratified and two-layer fluids caused by (a) surface wind stress (b) bottom stress due to water motion driven by a barotropic pressure gradient (c) bottom stress due to water motion in a bottom jet. It is shown that the predicted entrainment velocities are in good agreement with available laboratory data, provided the models have been calibrated according to a theoretical constraint. In addition, model behaviour in free convection is re-analysed with the help of recent data from large eddy simulations (LES). It is shown that even the most simple models, which do not solve a differential equation for the turbulent kinetic energy (TKE), can approximately reproduce the entrainment depth, however, they fail completely in reproducing the correct budget of the TKE-balance. In contrast, second-order models solving transport equations for the TKE and a length scale determining variable are in reasonable agreement with the TKE-budgets from LES.

Friction and mixing in the Faroe Bank Channel outflow

Three hydrographic sections made during RRS Discovery cruise 242, from 7 September to 6 October 1999, are used to study the Faroe Bank Channel overflow. Each section, made perpendicular to the plume direction, comprised 10–14 stations measuring the outflow properties and velocity. The overflow defined as water with potential temperatures below 3 °C has densities greater than 28.1 kg m –3, salinities between 34.9 and 35.1, with velocities as high as 80 cm s –1 approximately 20 km downstream from the sill. We use these measurements to describe the characteristics of the outflow and to estimate the amount of friction and mixing as the plume travels along the continental slope into the Iceland Basin. From Lowered Acoustic Doppler Current Profiler (LADCP) measurements we estimate stress in the bottom Ekman layer. Our stress results are best related to the overflow velocity with a drag coefficient of 0.5 × 10 –3 and to the height of the bottom Ekman layer with a von Karman constant of 0.75. Below a potential temperature of 8 °C, the isotherms sink with distance downstream. Calculating transport below different isotherms, we make an estimate for the amount of entrainment. In the region downstream of the sill, entrainment is initially maximum near the 0 °C isotherm just above the cold dense outflow and turbulent diffusivities reach as high as 500 cm 2 s –1. Fifty kilometre downstream of the sill the depth of maximum entrainment has moved upwards to the 2 °C isotherm and turbulent diffusivity has decreased to 50 cm 2 s –1. Froude numbers are found to exceed one in the centre of the overflow on all three sections. Calculating Richardson numbers we see evidence that mixing takes place above the fast flowing outflow core.

Seasonal variation of average phytoplankton concentration in the Kattegat—a periodical point model

Seasonal variations in primary production, phytoplankton biomass, chlorophyll-a, dissolved inorganic phosphorus and nitrogen concentrations in the upper 10 m of the Kattegat were analysed by means of monitoring data from 1993–1997. Spatial optimal analysis, based on a stochastic model, was used to reconstruct weekly constituent fields onto a spatial grid. The reconstructed fields were spatially integrated, resulting in a relatively smooth seasonal variability of the average variables. A simple dynamical model, set up as a periodical boundary problem, is suggested for the average phytoplankton concentration, dissolved inorganic nitrogen and entrainment depth as state variables. The model is forced by the solar radiation, nitrogen load from the land sources and atmosphere as well as by nitrogen supply from the lower nutrient-rich layer. The latter process is modelled proportional to the water entrainment into the upper euphotic layer and is driven by atmospheric forcing, river runoff and the Baltic water inflow. Four model coefficient values were fitted by minimising the root mean square difference between the integrated monitoring data and the model output. The suggested diagnostic model reflects the main features in seasonal variability of phytoplankton and nitrogen concentrations by average values, including the magnitude and timing of such dynamic events as the spring and late summer phytoplankton blooms. The importance of different forcing factors is quantified and estimates of unobserved components such as new primary production can be computed.

「岡山県荒戸山のアルカリ玄武岩中のざくろ石を含むハルツバージャイト捕獲岩（山元ら，１９９９）」に対するコメント

Yamamoto et al. (1999) obtained a low-temperature geotherm typical of continental shield from a “garnet peridotite” xenolith in the Arato-yama alkali basalt. Their geotherm is, however, possibly erroneous. Their data of the “garnet peridotite” suggest discrepancies from the chemical equilibration of minerals, and the pressure obtained is too large for the depth of xenolith entrainment by alkali basalt magma. The lack of thin section descriptions is also a cause of uncertainty.

SALMONID SMOLT SURVIVAL RELATIVE TO TURBINE EFFICIENCY AND ENTRAINMENT DEPTH IN HYDROELECTRIC POWER GENERATION

ABSTRACT: The hypotheses that fish survival probabilities may be lower (1) at less than peak operating turbine efficiency; (2) at deeper entrainment depth; and (3) with the deployment of extended-length intake guidance screens, are not supported by results on yearling chinook salmon smolts (Oncorhynchus tshawytscha) at Lower Granite Dam, Snake River, Washington. Estimated 96 h survival probabilities for the six test conditions ranged from 0.937 to 0.972, with the highest survival at turbine operating towards the lower end of its efficiency. A blanket recommendation to operate all Kaplan type turbines within ± 1 percent of their peak efficiency appears too restrictive. Cavitation mode survival (0.946) was comparable to that at peak operating efficiency mode (0.937), as was the survival between upper (0.947) and mid depths (0.937). Survival differed only slightly among three turbine intake bays at the same depth (0.937 to 0.954), most likely due to differential flow distribution. Extended-length intake fish guidance screens did not reduce survival. However, the sources of injury somewhat differed with depth; probable pressure and shear-related injuries were common on fish entrained at mid-depth, and mechanically-induced injuries were common at upper depth. Operating conditions that reduce turbulence within the turbine environment may enhance fish survival; however, controlled experiments that integrate turbine flow physics and geometry and the path entrained fish traverse are needed to develop specific guidance to further enhance fish passage survival.

Multi-stage magma ascent beneath the Canary Islands: evidence from fluid inclusions

Gabbroic and ultramafic xenoliths and olivine and clinopyroxene phenocrysts in basaltic rocks from Gran Canaria, La Palma, El Hierro, Lanzarote and La Gomera (Canary Islands) contain abundant CO2-dominated fluid inclusions. Inclusion densities are strikingly similar on a regional scale. Histogram maxima correspond to one or more of the following pressures: (1) minimum 0.55 to 1.0 GPa (within the upper mantle); (2) between 0.2 and 0.4 GPa (the Moho or the lower crust); (3) at about 0.1 GPa (upper crust). Fluid inclusions in several rocks show a bimodal density distribution, the lower-density maximum comprising both texturally early and late inclusions. This is taken as evidence for an incomplete resetting of inclusion densities, and simultaneous formation of young inclusions, at well-defined magma stagnation levels. For Gran Canaria, pressure estimates for early inclusions in harzburgite and dunite xenoliths and olivine phenocrysts in the host basanites overlap at 0.9 to 1.0 GPa, indicating that such magma reservoir depths coincide with levels of xenolith entrainment into the magmas. Magma chamber pressures within the mantle, inferred to represent levels of mantle xenolith entrainment, are 0.65–0.95 GPa for El Hierro, 0.60–0.68 GPa for La Palma, and 0.55–0.75 GPa for Lanzarote. The highest-density fluid inclusions in many Canary Island mantle xenoliths have probably survived in-situ near-isobaric heating at the depth of xenolith entrainment. Inclusion data from all islands indicate ponding of basaltic magmas at Moho or lower crustal depths, and possibly at an additional higher level, strongly suggestive of two main crustal accumulation levels beneath each island. We emphasize that repeated magmatic underplating of primitive magmas, and therefore intrusive accretion, are important growth mechanisms for the Canary Islands, and by analogy, for other ocean islands. Comparable fluid inclusion data from primitive rocks in other tectonic settings, including Iceland, Etna and continental rift systems (Hungary, South Norway), indicate that magma accumulation close to Moho depths shortly before eruption is not, however, restricted to oceanic intraplate volcanoes. Lower crustal ponding and crystallization prior to eruption may be the rule rather than the exception, independent of the tectonic setting.

Bubbles entrained by mechanically generated breaking waves

A photographic technique was used to make measurements of the size distributions of large bubbles entrained by mechanically generated breaking waves in freshwater and saltwater. Digital video images of the region immediately beneath and behind the breaking wave crest were analyzed. This imaging technique was accurate for bubble radii, r ≥ 0.8 mm. The magnitude and shape of the bubble size distributions were approximately the same in freshwater and saltwater. The bubble size distributions are well represented by an exponential equation of the form N ∼ e−1.5r or by a power law equation of the form N ∼ r−3.7. There were no significant differences observed between the depth distribution of the bubbles in saltwater and freshwater. In both cases the data can be represented by N = No e−z/h, where z is the distance below the free surface, h is the entrainment depth, and No is the total bubble concentration at the free surface. No and h were found to be 4 × 105 m−3 and 1.0 cm, respectively. The fact that significant numbers of large bubbles are entrained by relatively small breaking waves (wavelength ∼ 1.5 m) suggests that gas transfer due to large entrained bubbles may be important even at low wind speeds.

On bubble clouds produced by breaking waves: An event analysis of ocean acoustic measurements

A field experiment was carried out to measure the time‐varying properties of bubble clouds as they evolve from ocean breaking waves. The experiment was conducted from the floating instrument platform Flip and consisted of simultaneous, colocated acoustic measurements of subsurface bubbles and video recordings of the sea surface. Details of two breaking wave events are presented. The results of the acoustic measurements of bubble density and their entrainment depth are reported for the time t/Tc ≳ 3, where t is the time from breaking and Tc is a characteristic timescale based on the speed of the breaking wave crest as estimated from the video recordings. Order of magnitude values for the air‐void fraction β, vertical eddy diffusivity kν, and kinetic energy dissipation ε associated with breaking waves are presented. The wind speed dependence of average acoustic backscattering properties over the course of the experiment is also given.

Temperature Effects on Generation and Entrainment of Bubbles Induced by a Water Jet

A simple experiment simulating the jet feature of breaking waves is conducted to study quantitative effects of the water temperature on the generation of bubbles at the air–water interface and their entrainment into the water column. The results indicate that there is a critical water temperature for the inception of bubbles. Such a critical temperature can be attributed to changes of the surface tension and viscosity, both of which decrease as water temperature increases. Field measurements of the bubble entrainment depth, bubble size spectrum, and whitecap coverage are shown to have similar temperature dependencies as our observations.

Tectonics and hydrogeology of accretionary prisms: role of the décollement zone

At convergent margins the décollement zone comprises the plate boundary and is marked by profound structural disharmony, by changes in stress orientation and by a discontinuity in plate velocity. The décollement zone initiates in a weak sediment layer, typically a low-permeability hemipelagic mud lying below a more rapidly deposited, stronger, more permeable trench turbidite sequence. At the deformation front, trench turbidites tend to be offscraped, whereas the finer-grained hemipelagic and pelagic sediments are more likely to be underthrust. Offscraped materials may undergo only limited burial whereas underthrust deposits can be deeply buried, undergo high-pressure metamorphism, and are more likely to be preserved in the stratigraphic record. Burial rates associated with underthrusting are high, exceeding 20 km/my. With high rates of underthrusting, sediment descending below the décollement zone is probably buried faster than it can dewater, resulting in emplacement of relatively high porosity deposits at depth. Fluids flowing from modern décollement zones have migrated substantial distances laterally and tapped deep sources. The episodicity of flow suggests pumping of fluid by cycles of dilation and flow to the décollement zone followed by failure and fluid expansion along the décollement zone. Possible pressure gradients below the décollement zone allow flow upward into it while maintaining minimum effective stress along it. The thickness of sediment underthrust beneath the décollement zone determines whether these deposits are emplaced by diffusive underplating with stratal disruption and efficient dewatering, or by coherent underplating with the formation of macroscopic duplexes and transfer of fluid to the base of the accretionary prism. Deformation mechanisms affecting accreted sediment depend on depth of entrainment into the décollement zone and duration of residence.

Ceiling Jet-Driven Wall Flows in Compartment Fires

Abstract Analytic estimates are developed for depth of penetration and lateral entrainment of negatively buoyant, ceiling jet-driven wall flows during early times of compartment fire scenarios. When walls are not too far from the fire source of the order of the fire-to-ceiling distance, it is found that the penetration of these downward wall flows is a large fraction of the fire-to-ceiling distance, and that this Traction is relatively independent of the details of fire size and fire-to-wall spacing. Also, net rate of entrainment into the wall flow as it is buoyed back upward to the ceiling elevation is found to be several times larger than the Row rate of the driving ceiling jet flow immediately upstream of wall impingement. Data from five studies reported in the literature are reviewed relative to the analytic results obtained. One of these involved a field model simulation of the flow generated by a buoyant source in an enclosure. Two experimental laboratory studies involved fires in enclosures with ch...