Ambient Stratification Research Articles

Product water mass formation by turbulent density currents from a high-order nonhydrostatic spectral element model

In light of the pressing need for development of parameterizations of gravity current entrainment in ocean general circulation models, the behavior of turbulent gravity currents in the presence of ambient stratification is studied via numerical simulation, for cases in which equilibrated product water masses are formed. The main objective is to explore how the ambient stratification impacts entrainment and the properties of product water masses, which are of ultimate interest to ocean and climate modelers. Numerical experiments are conducted by employing the high-order nonhydrostatic spectral element model Nek5000. It is investigated how the separation level of the current from the bottom, the propagation speed, the salinity of the product water masses, and the transport and entrainment of the gravity current are affected as a function of the strength of the ambient stratification and the slope angle. Results show that, for the case of constant slope angle and linear ambient stratification, the gravity current separates from the bottom such that the entrained mass flux is independent of the slope angle. The entrainment mass transport, product mass transport, and product salinity then depend only on the ambient stratification, and these quantities are approximated as simple algebraic functions of the ambient stratification parameter that modify the source properties.

The stratified Boycott effect

We present the results of an experimental investigation of the flows generated by monodisperse particles settling at low Reynolds number in a stably stratified ambient with an inclined sidewall. In this configuration, upwelling beneath the inclined wall associated with the Boycott effect is opposed by the ambient density stratification. The evolution of the system is determined by the relative magnitudes of the container depth, ; subsequently, smaller overlying layers develop. Within each layer, convection erodes the initially linear density gradient, generating a step-like density profile throughout the system that persists after all the particles have settled. Particles are transported across the discrete density jumps between layers by plumes of particle-laden fluid.

Katabatic Flow Mechanisms on a Low-Angle Slope

Abstract Momentum and heat budget equations for katabatic flows on sloping surfaces are revisited. Terms in these equations are evaluated using wind and potential temperature data from four tethered-balloon data collection systems on a 3-km line running down a 1.6° slope at the foot of the Oquirrh Mountains in Utah’s Great Salt Lake valley. The analyses focus on the development with downslope distance of the katabatic flow and the associated negatively buoyant layer under synoptically undisturbed conditions. With strong ambient stratification, the katabatic flow shows little variation between sites, suggesting a state close to local equilibrium. When the ambient stratification is weaker, the acceleration of the katabatic flow between two tethersonde sites is systematically larger than what would be predicted based on observed buoyancy. Comparison of observed flow direction with the local topographic gradient indicates that slope curvature, associated with small deviations from the basically planar slope, may be responsible for the anomalous increase. It is concluded that the cross-slope homogeneity of the flow, which is assumed in simplified katabatic flow models, may be significantly disturbed even on slopes that appear to be planar to the observer.

Decaying grid turbulence in a strongly stratified fluid

Grid turbulence experiments have been carried out in a stably stratified fluid at moderately large Reynolds numbers (160 based on the Taylor microscale). A scanning particle image velocimetry technique is used to provide time-resolved velocity fields in a relatively large volume. For late times, in the low-Froude-number regime, the flow consists of quasi-horizontal motion in a sea of weak internal gravity waves. In this regime the dynamics of the flow is found to be independent of the ambient stratification. Fundamental differences with two-dimensional turbulence, due to the strong vertical shearing of horizontal velocity, are observed. In this regime, a self-similar scaling law for the energy decay and the length-scale evolution are observed. This behaviour reflects a process of adjustment of the eddy aspect ratio based on a balance between the horizontal advective motion which tends to vertically decorrelate the flow and the dissipation due to the strong vertical shear. The characteristic vertical size of the eddies grows according to a diffusion law and is found to be independent of the turbulence generation. The organization of the flow into horizontal layers of eddies separated by intense shear leads to a strong anisotropy of the dissipation: this has been checked by direct measurement of the different tensorial components of the viscous dissipation.

A Simple Criterion to Determine the Transition from a Localized Convection to a Distributed Convection Regime*

Abstract A recent numerical study by Noh et al. of open-ocean deep convection in the presence of a single geostrophic eddy showed that two possible regimes exist: 1) the localized convection regime in which baroclinic instability of the eddy dominates, with slantwise fluxes and restratification, and 2) the distributed convection regime in which vertical mixing dominates. Noh et al. found that localized convection dominates for relatively small buoyancy forcing, strong eddies, and strong surface ambient stratification. Here it is shown that this regime transition can be expressed in terms of a ratio of time scales: the localized convection regime appears when the time scale for lateral fluxes from eddy interior to exterior tL is short in comparison with the time scale for convective erosion of the exterior stratification tc. Scaling arguments give this ratio of time scales as tL/tc ∼ f β2R2B/(A2γ) where f is the Coriolis parameter, R is the radius of the eddy, B is the buoyancy forcing, 1/β is the depth scale of the exponentially decaying surface-intensified stratification, γ is the relative amplitude of the eddy, and Aβ is the value of the surface stratification N20. Comparison with the numerical simulations of Noh et al. shows that this parameter does indeed separate the localized and distributed convection regimes, with the transition occurring at tL/tc ≈ 0.05–0.1.

Marine Wastewater Discharges from Multiport Diffusers. III: Stratified Stationary Water

Experiments on the near-field mixing of wastewater discharged from multiport diffusers into a stationary density-stratified environment are reported for conditions typical of ocean sewage outfalls. Dilutions were measured with a microconductivity probe in which the test tank was stratified with a nonconducting solution; geometrical characteristics such as rise height and layer thickness were measured by planar laser-induced fluorescence in which the test tank was stratified with refractive-index matched fluids. The port spacing was varied over a wide range encompassing rapidly merging to nonmerging plumes. The end of the near-field occurs at a distance of order one plume rise height from the diffuser. At this point the turbulence and mixing induced by the discharge is effectively damped by the ambient stratification, and little near-field mixing occurs beyond it. The results were analyzed in terms of line and point-source parameters to deduce the ranges of port spacings for which line and point plume solutions apply. Equations to predict the near-field characteristics are presented.

Parameterization of a surface drag coefficient in conventionally neutral planetary boundary layer

Abstract. Modern large-scale models (LSMs) rely on surface drag coefficients to parameterize turbulent exchange between surface and the first computational level in the atmosphere. A classical parameterization in an Ekman boundary layer is rather simple. It is based on a robust concept of a layer of constant fluxes. In such a layer (log-layer), the mean velocity profile is logarithmic. It results in an universal dependence of the surface drag coefficient on a single internal non-dimensional parameter, namely the ratio of a height within this layer to a surface roughness length scale. A realistic near-neutral planetary boundary layer (PBL) is usually much more shallow than the idealized Ekman layer. The reason is that the PBL is developing against a stably stratified free atmosphere. The ambient atmospheric stratification reduces the PBL depth and simultaneously the depth of the log-layer. Therefore, the first computational level in the LSMs may be placed above the log-layer. In such a case, the classical parameterization is unjustified and inaccurate. The paper proposes several ways to improve the classical parameterization of the surface drag coefficient for momentum. The discussion is focused on a conventionally neutral PBL, i.e. on the neutrally stratified PBL under the stably stratified free atmosphere. The analysis is based on large eddy simulation (LES) data. This data reveals that discrepancy between drag coefficients predicted by the classical parameterization and the actual drag coefficients can be very large in the shallow PBL. The improved parameterizations provide a more accurate prediction. The inaccuracy is reduced to one-tenth of the actual values of the coefficients.

Hydrostatic and non-hydrostatic studies of gravitational adjustment over a slope

In many numerical ocean models, the hydrostatic approximation is made. This approximation causes a considerable saving in computing time. However, for phenomena involving large vertical speeds, for many small scale phenomena, and in areas with weak stratification, the approximation becomes questionable. In this report, a σ -coordinate hydrostatic C-grid model is extended to include non-hydrostatic dynamics. The test cases involve gravitational adjustment of a downslope flow. The first test case has a simplified slope profile and no ambient stratification in the deep basin. The second test case has ambient stratification and more realistic topography. The differences between hydrostatic and non-hydrostatic simulations are described and discussed. It is shown that the shapes of the head and the body of density driven plumes are better preserved in the non-hydrostatic experiments. The wave propagation away from the plume head is considerably reduced when including non-hydrostatic effects.

Kelvin–Helmholtz Instability of Potential Vorticity Layers: A Route to Mixing

The linear and nonlinear dynamics of layers of anomalously high potential vorticity (PV) are studied in detail. It is well known that PV layers are subject to slow, balanced, mixed barotropic‐baroclinic instabilities. In this paper, it is shown that, in addition, PV layers are subject to a Kelvin‐Helmholtz instability, operating on much smaller spatial and faster temporal scales. For simplicity, spatially infinite layers of uniform anomalous PV are considered. Such layers are characterized by two key parameters: the ratio Dq of their anomalous PV to the background PV, and the angle a between the layer and the direction of the ambient stratification gradient (in suitably scaled coordinates). It is found that Kelvin‐Helmholtz appears, for certain values of a, whenever Dq . 8. Of notable interest is the case of an initially vertical PV layer embedded in a weak ambient shear flow: for sufficiently large Dq, once the PV layer is tilted past a critical angle, Kelvin‐Helmholtz instability becomes possible. It is argued that the breakdown of PV layers due to a Kelvin‐Helmholtz instability induced by ambient shear might be an important systematic mechanism leading to irreversible mixing during stratosphere‐troposphere exchange events. This is discussed in the context of an example of Kelvin‐Helmholtz instability observed near a tropopause fold.

Sedimentation from buoyant fine-grained suspensions

Laboratory experiments were performed to observe the sedimentation of natural sediment in buoyant turbulent suspensions. A series of experiments were conducted in a flume modified to investigate sedimentation from a steady, stratified shear layer. Ambient salinity stratification in the lower fluid allowed the upper layer to remain buoyant, while turbulence induced by free shear in the water column produced instabilities between the two fluids. These experiments showed that convective plumes dominated sedimentation. These convective plumes had vortex tips and vertical velocities of 1–2 cm/s. The velocities observed are two orders of magnitude larger than those predicted by Stokes settling of the constituent particles. Surface plume concentrations as low as 380 mg/l were documented to support robust mixing-induced convective sedimentation. At high concentrations (>6000 mg/l), the experiments produced a divergent plume with a considerable amount of the sediment-laden fluid being diverted along the bottom of the flume. Our observed vertical sediment fluxes demonstrated a 50% increase as compared to previous studies of double-diffusive sedimentation. A simple scaling analysis using the dissipation rate of turbulent energy and the surface plume sediment concentration was able to collapse the experimental data and indicated a positive correlation between turbulent energy and sedimentation. The empirical scaling relationship accurately predicted effective settling velocities measured on the Eel River margin in 1997–1998. The quality of the agreement between the laboratory and field measurements provides strong evidence that sedimentation by mixing-induced convection may be the dominant mode of sediment removal from energetic, highly concentrated, buoyant river plumes.

Behavior of Oil and Gas from Deepwater Blowouts

This paper presents a detailed analysis of different deepwater blowout scenarios using the Clarkson deepwater oil and gas model (CDOG). In CDOG, hydrate formation, hydrate decomposition, gas dissolution, nonideal behavior of gas, and possible gas separation from the main plume due to strong cross-currents, are integrated with the jet/plume hydrodynamics and thermodynamics. CDOG takes into account unsteady-state three-dimensional variation of ambient currents and density stratification. Detailed comparisons between CDOG simulations and deepspill field experiments have been published. The model is used to simulate 30 deepwater blowout scenarios based on realistic cases and the results are analyzed in this paper. The scenarios demonstrate the differences in plume behavior due to different ambient conditions, different types of gas, possible hydrate formation, and variations in gas-to-oil ratio. Some key findings of these analyses follow. Oil droplet sizes affect the oil surfacing time significantly. For oil-only blowouts, the ambient conditions do not affect the oil surfacing time significantly, but the location and the size of the slick are affected. For oil and gas mixes, the surfacing time is not sensitive to the type of gas in the mix, but is somewhat dependent on the ambient conditions. In none of the cases simulated here, did free gas reach the water surface. While changing the release temperature had only an insignificant effect on the model results, changing oil type or gas-to-oil ratio did affect the model results. The analyses are useful to engineers/scientists and administrators.

The Boycott effect in magma chambers

We investigate the plausibility of the stratified Boycott effect as a source of layering in magma chambers. Crystal settling within the magma chamber will generate buoyant fluid near the sloping sidewalls whose vertical ascent may be limited by the ambient stratification associated with vertical gradients in SiO2. The resulting flow may be marked by a layered structure, each layer taking the form of a convection cell spanning the lateral extent of the magma chamber. Using parameters relevant to magma chambers, we estimate that such convection cells would be established over a timescale of a month and have a depth on the order of 4m, which is roughly consistent with field observations of strata within solidified chambers.

New experimental techniques for validation of marine discharge models

A new three-dimensional Laser-Induced Fluorescence (3DLIF) system was applied to study the mixing of a produced water outfall discharge typical of that used in offshore production operations. The outfall consists of a pipeline terminating in a multiport diffuser discharging into water about 12 m deep. Scaled laboratory experiments were done using conditions based on measured oceanographic conditions near the site. The current was perpendicular to the diffuser, and the receiving water was linearly stratified. The model was undistorted and the jet densimetric Froude number was the same as in the prototype. This scaling results in correct modeling of the source volume, momentum, and buoyancy fluxes, and equality of other line source dimensionless parameters. The experiments were conducted in a constant refractive-index environment which enabled detailed three-dimensional concentration measurements in the near field mixing zone to be obtained despite the density variations in the flow field. The mixing processes were found to be complex. The jets discharging upstream were quickly swept downstream, where they began merging with the downstream jets. Lateral mixing caused the concentration profiles to quickly become laterally homogeneous. Initially, dilution increased rapidly with distance from the diffuser, but farther away the rate of increase of dilution slowed as the turbulence became affected by the ambient density stratification. The dilution eventually becomes approximately constant; the location where this occurs defines the end of the near field, where mixing is primarily due to turbulence and other processes induced by the discharge itself. The end of the near field is marked by collapse of the self-induced turbulence under the influence of the ambient stratification. The results were compared to predictions of commonly used mathematical models of marine mixing zones: RSB, UM3, and CORMIX. The best predictions of the near field dilution and the length of the near field were by RSB. UM3 gave good predictions of the near field dilution, but CORMIX overestimated the dilution and rise height substantially. It is believed that this overestimation by CORMIX is due to its approximation of the diffuser as a row of vertically discharging jets of equivalent total momentum flux; this is clearly a poor approximation to the diffuser conditions modeled here. 3DLIF is an exciting new technique that can give unprecedented insight into the complex hydrodynamics and processes occurring in buoyancy-modified mixing zones and to improvement of near field mathematical models. Experiments on other discharge configurations are continuing.

Horizontal Variability of 2-m Temperature at Night during CASES-97

Abstract Surface-station, radiosonde, and Doppler minisodar data from the Cooperative Atmosphere–Surface Exchange Study-1997 (CASES-97) field project, collected in a 60-km-wide array in the lower Walnut River watershed (terrain variation ∼150 m) southeast of Wichita, Kansas, are used to study the relationship of the change of the 2-m potential temperature Θ2m with station elevation ze, ∂Θ2m/∂ze ≡ Θ,ze to the ambient wind and thermal stratification ∂Θ/∂z ≡ Θ,z during fair-weather nights. As in many previous studies, predawn Θ2m varies linearly with ze, and Θ,ze ∼ Θ,z over a depth h that represents the maximum elevation range of the stations. Departures from the linear Θ2m–elevation relationship (Θ,ze line) are related to vegetation (cool for vegetation, warm for bare ground), local terrain (drainage flows from nearby hills, although a causal relationship is not established), and the formation of a cold pool at lower elevations on some days. The near-surface flow and its evolution are functions of the Froud...

Model study of the cross‐frontal water exchange on Georges Bank: A three‐dimensional Lagrangian experiment

Characteristics of the cross‐frontal water exchange over Georges Bank are investigated through a sequence of numerical model experiments featuring realistic three‐dimensional (3‐D) bathmetry, bi‐monthly averaged climatological stratification, tidal forcing, and mean and observed wind‐forcing. The model used in this study is the ECOM‐si version of the Blumberg and Mellor [1987] primitive equation model with Mellor‐Yamada [1982] level 2.5 turbulence closure. The model domain includes Georges Bank and the Gulf of Maine, and is forced at the open ocean boundary by the semidurnal M2 tide. Fluid particles were tracked in the 3‐D, time‐dependent Eulerian flow field to examine the Lagrangian flow field, and passive tracer experiments were conducted to investigate the relative roles of advection and turbulent diffusion on cross‐frontal exchange. Two distinct paths for the on‐bank water movement were detected on Georges Bank: one is over the northwestern flank of the bank where the bottom topography changes sharply in both along‐ and cross‐bank directions, and the other is near the bottom around the bank where the tidal mixing front is located. Over the northern flank, the cross‐bank component of the Lagrangian residual current is generally opposite in direction to that of the Eulerian residual current, resulting in an on‐bank, cross‐frontal water transport near the bottom. Over the southern flank, the near‐bottom water tends to converge toward the tidal mixing and shelf‐break fronts, so that the near‐bottom flow over the shelf between these two fronts is divergent. The response to wind‐forcing varied with ambient stratification and water depth. In winter, strong winds can drive a significant off‐bank water transport, tending to “wash out” the bank. In summer, winds are generally too weak to alter the general pattern of tidal‐driven particle motion within the mixed region on the crest of the bank and the surrounding tidal mixing front. Some wind‐driven off‐bank transport occurs near the surface in the stratified region on the outer southern flank, but this has little influence on water movement near the bottom. Passive tracer experiments reveal that the net cross‐frontal water flux near the bottom is caused primarily by advection and horizontal diffusion. Tidal‐induced vertical diffusion tends to make the tracer mix rapidly upward, thus reducing the percent of the cross‐frontal flux due to advection. Our new model results are consistent with previous model studies of Georges Bank, and agree in general with drifter and dye patches observed in the U.S. GLOBEC NW Atlantic/Georges Bank program.

Weak fountains in a stratified fluid.

The behavior of weak axisymmetric and plane fountains resulting from the injection of denser fluid upwards into large containers containing a stably stratified fluid has been explored using dimensional analysis, scaling analysis, and direct numerical simulation. For weak fountains, with Froude number Fr approximately 1.0, dimensional and scaling analyses have been used to derive scaling relations for the dimensionless fountain height, width, thickness of the temperature layer, and development times in terms of the Froude number Fr, Reynolds number Re, Prandtl number Pr, and ambient stratification number s. Numerical simulations have been carried out for a series of Fr, Re, Pr, and s for both axisymmetric and plane fountains to validate and quantify the scaling relations obtained by the dimensional and scaling analyses. The numerical results have been found to agree well with the analytical scaling relations.

Natural convection on a vertical cylinder embedded in a thermally stratified high-porosity medium

The laminar natural convection boundary layer flow on an isothermal vertical thin cylinder embedded in a thermally stratified high porosity medium has been studied. The non-Darcy effects including convective, boundary and inertial effects are included in this analysis. The non-linear coupled partial differential equations governing the flow are solved by using an implicit finite-difference scheme. For small and moderate values of the axial distance, these equations are also solved by a perturbation technique in combination with the Shanks transformation. It is observed that for certain values of the ambient stratification parameter, the skin friction vanishes and the direction of the heat transfer changes. The skin friction and heat transfer decrease with increasing ambient stratification, curvature and inertia parameters, but they increase with the permeability parameter.

Modeling dense water production and salt transport from Alaskan coastal polynyas

The main significance of this paper is that a realistic, three-dimensional, high-resolution primitive equation model has been developed to study the effects of dense water formation in Arctic coastal polynyas. The model includes realistic ambient stratification, realistic bottom topography, and is forced by time-variant surface heat flux, surface salt flux, and time-dependent coastal flow. The salt and heat fluxes, and the surface ice drift, are derived from satellite observations (SSM/I and NSCAT sensors). The model is used to study the stratification, salt transport, and circulation in the vicinity of Barrow Canyon during the 1996/97 winter season. The coastal flow (Alaska coastal current), which is an extension of the Bering Sea throughflow, is formulated in the model using the wind-transport regression. The results show that for the 1996/97 winter the northeastward coastal current exports 13% to 26% of the salt produced by coastal polynyas upstream of Barrow Canyon in 20 to 30 days. The salt export occurs more rapidly during less persistent polynyas. The inclusion of ice-water stress in the model makes the coastal current slightly weaker and much wider due to the combined effects of surface drag and offshore Ekman transport.

Two‐basin filling boxes

The convection induced by turbulent buoyant plumes in a rectangular “filling box” (Baines and Turner, 1969) is extended to situations where the lower depths of the box are divided into two basins by a vertical barrier. The barrier restricts horizontal spreading and allows the interbasin exchange of water to occur only in the common region above the barrier height. One‐and two‐plume systems are considered; in the two‐plume case, it is assumed that each of the plumes arises from an independent buoyancy source above each basin. The resulting two‐basin circulation is characterized by different stratifications in each basin and by an overflow from one basin into the other. The spreading depths of the plumes and ambient stratification depend on the barrier height, relative basin sizes, and, in the two‐plume case, the relative strengths of the two buoyancy fluxes. These results may be of relevance to multibasin seas and oceans where the circulation produced by near‐surface sources of intermediate and deep water is influenced by underwater ridges.

Ventilation of Black Sea pycnocline by the Mediterranean plume

We present here results of numerical simulations with reduced gravity model of the Mediterranean plume intruding into the Black Sea. The model has horizontal resolution of 600 m. The scenarios analyzed in the paper aim at quantifying the sensitivity of the plume to the ambient stratification and the fluxes of mass, momentum and buoyancy through the Bosphorus Straits. The simulated plume characteristics are compared against observations. It is found that the mixing of Mediterranean and Black Sea water, as well as the termination depth of the plume, are very sensitive to specific combinations of the governing parameters. The behavior of gravity currents on the shelf and on the continental slope is also studied and the role of topographic control is demonstrated. The relatively large entrainment rate (∼10–12) compared to the one in the Atlantic ocean (∼2–3), shallow penetration and small deflection to the right caused by the earth rotation are explained as a result of the specific combination of governing parameters, topography routing and ambient stratification. A simple two-component chemical model for the interaction between H 2S and O 2 is coupled with the dynamical model in order to investigate the impact of the Bosphorus plume (rich in O 2) on the oxidation of anoxic water.