Local Gradient Richardson Number Research Articles

Long-wave instabilities of sloping stratified exchange flows

We investigate the linear instability of two-layer stratified shear flows in a sloping two-dimensional channel, subject to non-zero longitudinal gravitational forces. We reveal three previously unknown instabilities, distinct from the well-known Kelvin–Helmholtz instability and Holmboe wave instability, in that they have longer wavelengths (of the order of 10 to $10^3$ shear-layer depths) and often slower growth rates. Importantly, they can grow in background flows with gradient Richardson number $\gg 1$ , which offers a new mechanism to sustain turbulence and mixing in strongly stratified flows. These instabilities are shown to be generic and relatively insensitive to Reynolds number, Prandtl number, base flow profile and boundary conditions. The nonlinear evolution of these instabilities is investigated through a forced direct numerical simulation, in which the background momentum and density are sustained. The growth of long unstable waves in background flows initially stable to short wave causes a decrease in the local gradient Richardson number. This leads to local nonlinear processes that result in small-scale overturns resembling Kelvin–Helmholtz billows. Our results establish a new energy exchange pathway, where the mean kinetic energy of a strongly stratified flow is extracted by primary unstable long waves and secondary short waves, and subsequently dissipated into internal energy.

Threshold behavior of local gradient Richardson number in strongly stratified nonequilibrium turbulence

A nonequilibrium, strongly stratified turbulent flow is examined with a numerically simulated data set. We find self-organization of the flow around a critical state with a local gradient Richardson number (Ri) of about 1/4. The turbulence spontaneously organizes into layered, anisotropic flow structures within which the local Ri probability density function peaks around 1/4 for regions with the most significant dissipation rates and eddy viscosities. The results suggest that self-organization of the flow around Ri = 1/4 could be a property of layered anisotropic stratified turbulence and may not require the specific external forcing mechanisms previously reported.

Growth laws and self-similarity in the confined mixing zone of unstratified and strongly stably stratified isokinetic mixing-layers past a splitter plate

The velocity U and the mixing scalar field Θ of turbulent wake flows developing downstream of a slender splitter plate were studied experimentally for unstratified and strongly stably stratified conditions in a square channel with water as fluid. The experimental program comprises five different Reynolds numbers spanning Re0=10 000–60 000 for u0=u1=u2 (isokinetic conditions) between the two planar, initially separated streams and five relative density stratifications from Δρ=0 to 10%, since mixing studies for these stratification strengths are rather limited. This full-channel Reynolds number uses the hydraulic diameter dh=50 mm of the mixing section as the characteristic length scale. These experiments challenge the corresponding numerical calculations based on Reynolds-averaged Navier–Stokes approaches relying on the Boussinesq approximations of the first and second kind. The development of the mixing scalar field Θ was measured by two fundamentally different approaches: laser induced fluorescence (LIF) in the downstream x–y mid-plane and wire-mesh sensors (WMSs) in discrete lateral y–z planes. This allows for a direct comparison of both sensing techniques at locations where both planes intersect. For the unstratified conditions, it is shown that the downstream developing wake velocity deficit decay agrees well with the theoretical approach. The concentration fields based on LIF and WMS profiles of the mean and fluctuating (root mean square, RMS) data confirm self-similarity by introducing a mixing scalar Θ for both techniques. In the approximate limit, it is shown that the mean concentration field can be well described by an error function and the corresponding RMS data by a Gaussian profile in self-similar coordinates. By using the momentum thickness θm at the splitter plate as the normalization parameter, the downstream developing width of the mixing zone δ(x) becomes independent for Re0≥30 000. The mean and the RMS values of the concentration field Θ for the stably stratified experiments show self-similarity in the core of the concentration field but also a departure from the error function and Gaussian profile in the outer parts. Introducing a local gradient Richardson number Rig, it is shown that both the growth and growth-suppression of the mixing zone are well described by the Miles–Howard criterion for all the stratified experiments considered, even though this criterion was originally developed for shear layers.

Supporting data for: Numerical Study of Near-Surface Jet in the Atmospheric Surface Layer over Oceanic Fronts

Simulation data used for figures in Numerical study of near-surface jet in the atmospheric surface layer over oceanic fronts including the mean velocity profiles, the turbulent variance profiles, the vortex structures, the streamwise momentum flux, the surface shear stress, and the local gradient Richardson number, etc. The data was generated and written by our in-house codes. Its format matches the requirement of the software Tecplot, and hence users can open the data using Tecplot.

Investigation of LES models for a stratified shear layer

The performance of three large-eddy simulation (LES) models in predicting the evolution of a shear layer at moderate Reynolds number in a linearly stratified background is investigated. Results of the Dynamic Smagorinsky, Ducros, and Wall-Adapting Local Eddy Viscosity (WALE) models are compared against those of direct numerical simulation (DNS). Two levels of grid refinement are employed to assess the change in the models’ capabilities with varying resolution. Of particular interest is the ability of the models to capture the evolution of instabilities as well as accurately quantify turbulence statistics. Evolution of momentum thickness, local buoyancy flux, shear, and gradient Richardson number show good agreement of the LES models with the DNS. A comparison of the turbulent kinetic energy (TKE) and its budget indicates good capture of turbulence evolution in the LES models. There is a moderate over prediction of spatially integrated TKE during a short period when the integrated TKE is at its maximum. This feature is traced to the underestimate of turbulent dissipation rate in the LES. Coarsening grid resolution significantly increases the discrepancy in dissipation between the WALE model and the DNS while defects due to the coarser grid resolution are mild in the case of the Ducros model. All of the LES models overestimate the peak values of eddy viscosity and eddy diffusivity although the Ducros model produces the closest agreement with the DNS. Furthermore, the Ducros model is found to require fewer CPU hours than the DNS or other LES models.

Physical Modeling of Hydrodynamic and Heat Transfer Processes in Liquid-Metal Cooled Nuclear Power Facilities

The article presents the results from analyzing the application conditions of the thermophysical processes similarity theory as applied to modeling the hydrodynamics and heat transfer in liquid-metal cooled nuclear power facilities, namely, in channels, in the reactor core rod systems, and in the reactor pressure vessel under different operating conditions. It is shown that direct modeling can be used without limitations only for processes whose determined similarity numbers (criteria) are functions of only the system’s geometrical simplexes and one determining criterion. The availability of two determining criteria in the heat transfer description, e.g., the Reynolds and Prandtl numbers, noticeably complicates the modeling. With three determining criteria, direct modeling is impracticable as a rule. In such cases, systematic multivariate experiments must be set up. The aim of such experiments is to reveal the effects that are allowed by the general mathematical model but which cannot be simulated—either analytically or numerically—using state-of-the-art mathematical technologies. It has been shown from numerical and theoretical investigations and from generalization of experiments, including data on temperature distribution patterns in a liquid-metal flow, that the thermal resistance at the coolant–heat-transfer surface interface boundary is essentially zero if the concentration of impurities in the coolant does not exceed their solubility at the circulating metal temperature. In the case of using liquid metals and alloys (Pb, Pb–Bi, Hg, Na, Na–K, Li, etc.), the heat transfer is described under such conditions by a unified dimensionless dependence on the Peclet number. The transfer of heat in fuel assemblies takes place mainly by convective heat transfer, and the temperature field is governed by the increase in liquid-metal temperature. The temperature distribution depends on the classical similarity criteria, including the Reynolds, Peclet (Prandtl), and Grashof criteria, and on the design and thermophysical characteristics of fuel elements and fuel assemblies (the latter serve as the fuel element approximate similarity criterion). Forced circulation in the reactor vessel is simulated in small-scale water models using the Froude and Peclet numbers, and natural circulation is simulated using the Euler number. The similarity of currents in stably stratified coolant zones is determined by the Froude and Peclet numbers and by the local-gradient Richardson number.

Vertical dispersion of Lagrangian tracers in fully developed stably stratified turbulence

We study the effect of different forcing functions and of the local gradient Richardson number Rig on the vertical mixing of Lagrangian tracers in stably stratified turbulence under the Boussinesq approximation, and present a wave and continuous-time random walk model for single- and two- particle vertical dispersion. The model consists of a random superposition of linear waves with their amplitude based on the observed Lagrangian spectrum of vertical velocity, and a random walk process to capture overturning that depends on the statistics of Rig among other Eulerian quantities. The model is in good agreement with direct numerical simulations of stratified turbulence, where single- and two-particle dispersion differs from the homogeneous and isotropic case. Moreover, the model gives insight into the mixture of linear and non-linear physics in the problem, as well as on the different processes responsible for vertical turbulent dispersion.

Turbulent Transport by Diffusive Stratified Shear Flows: From Local to Global Models. II. Limitations of Local Models

This paper continues the systematic investigation of diffusive shear instabilities initiated in Part I of this series. In this work, we primarily focus on quantifying the impact of non-local mixing, which is not taken into account in Zahn's mixing model \citep{Zahn92}. We present the results of direct numerical simulations in a new model setup designed to contain coexisting laminar and turbulent shear layers. As in Part I, we use the Low P\'eclet Number approximation of \citet{Lign1999} to model the evolution of the perturbations. Our main findings are twofold. First, turbulence is not necessarily generated whenever Zahn's nonlinear criterion \citep{Zahn1974} $J{\rm Pr} < (J{\rm Pr})_c$ is satisfied, where $J=N^2/S^2$ is the local gradient Richardson number, ${\rm Pr} = \nu/ \kappa_T$ is the Prandtl number, and $(J{\rm Pr})_c \simeq 0.007$. We have demonstrated that the presence or absence of turbulent mixing in this limit hysteretically depends on the history of the shear layer. Second, Zahn's nonlinear instability criterion only approximately locates the edge of the turbulent layer, and mixing beyond the region where $J{\rm Pr} < (J{\rm Pr})_c$ can also take place in a manner analogous to convective overshoot. We found that the turbulent kinetic energy decays roughly exponentially beyond the edge of the shear-unstable region, on a lengthscale $\delta$ that is directly proportional to the scale of the turbulent eddies, which are themselves of the order of the Zahn scale (see Part I). Our results suggest that mixing by diffusive shear instabilities should be modeled with more care than is currently standard in stellar evolution codes.

Entrainment across a sheared density interface in a cavity flow

The entrainment of fluid across a sheared density interface has been examined experimentally in a purging cavity flow. In this flow, a long straight cavity with sloped entry and exit boundaries is located in the base of a straight open channel. Dense cavity fluid is entrained from the cavity into the turbulent overflow. The cavity geometry has been designed to ensure there is no separation of the overflow in the cavity region, with the goal of avoiding cavity-specific entrainment mechanisms as have been encountered in most previous experiments using similar arrangements. Results are obtained over a bulk Richardson number range $Ri_{b}=g\unicode[STIX]{x0394}\unicode[STIX]{x1D70C}D/\unicode[STIX]{x1D70C}_{0}U_{b}^{2}=1$ to 19, where $D$ and $U_{b}$ are the depth of the mixed layer and bulk velocity in the cavity, respectively. The experiments cover the Reynolds number range $Re=U_{b}D/\unicode[STIX]{x1D708}=7100$ to 15 100 and interface length to mixed layer depth ratios of 2.4 to 16. Particle image velocimetry and laser induced fluorescence measurements indicate the flow regime over this entire range is one dominated by the Holmboe wave instability. The non-dimensional entrainment rate, $E=u_{e}/U_{b}$, is shown to scale with the bulk Richardson number. We find that the entrainment scaling $E=CRi_{b}^{-1.38}$ applies over the entire experimental range, with no apparent dependence on interface length. The exponent in the scaling is similar to previous non-cavity-based sheared interface flows, however, the constant $C$ is up to an order of magnitude smaller. Close agreement is, however, obtained by instead correlating entrainment with the local gradient Richardson number centred on the interface, rather than bulk quantities. We obtain $E=0.0021Ri_{g}^{-0.63}$ for data over $10&lt;Ri_{g}&lt;50$, where $Ri_{g}=\langle g\unicode[STIX]{x2202}\unicode[STIX]{x1D70C}/\unicode[STIX]{x1D70C}_{0}\unicode[STIX]{x2202}z\rangle /\langle (\unicode[STIX]{x2202}U/\unicode[STIX]{x2202}z)^{2}\rangle$. The density interface is much thinner and therefore more stable in the present flow configuration compared with other published results for the same bulk Richardson number. We suggest that our configuration ensures a sharp mixing layer profile at the upstream end of the cavity even at relatively low bulk Richardson numbers of $Ri_{b}=1$ and that the reduced mixing in the Holmboe wave regime allows the interface to retain its sharp character over the cavity length, resulting in weak sensitivity to cavity length.

Seasonality of Deep Cycle Turbulence in the Eastern Equatorial Pacific

AbstractThe seasonal cycles of the various oceanic and atmospheric factors influencing the deep cycle of turbulence in the eastern Pacific cold tongue are explored. Moored observations at 140°W have shown seasonal variability in the stratification, velocity shear, and turbulence above the Pacific Equatorial Undercurrent (EUC). In boreal spring, the thermocline and EUC shoal and turbulence decreases. Marginal instability (clustering of the local gradient Richardson number around the critical value of 1/4), evident throughout the rest of the year, has not been detected during spring. While the daily averaged turbulent energy dissipation in the EUC is weakest during the spring, it is not clear whether the diurnal fluctuations that define the deep cycle cease. Large-eddy simulations are performed using climatological initial and boundary conditions representative of January, April, July, and October. Deep cycle turbulence is evident in all cases; the mechanism remains the same, and the maximum turbulence levels are similar. In the April simulation, however, the deep cycle is confined to the uppermost ~30 m, explaining why it has not been detected in moored microstructure observations.

Diapycnal mixing in layered stratified plane Couette flow quantified in a tracer-based coordinate

The mixing properties of statically stable density interfaces subject to imposed vertical shear are studied using direct numerical simulations of stratified plane Couette flow. The simulations are designed to investigate possible self-maintaining mechanisms of sharp density interfaces motivated by Phillips’ argument (Deep-Sea Res., vol. 19, 1972, pp. 79–81) by which layers and interfaces can spontaneously form due to vertical variations of diapycnal flux. At the start of each simulation, a sharp density interface with the same initial thickness is introduced at the midplane between two flat, horizontal walls counter-moving at velocities$\pm U_{w}$. Particular attention is paid to the effects of varying Prandtl number$\mathit{Pr}\equiv \unicode[STIX]{x1D708}/\unicode[STIX]{x1D705}$, where$\unicode[STIX]{x1D708}$and$\unicode[STIX]{x1D705}$are the molecular kinematic viscosity and diffusivity respectively, over two orders of magnitude from 0.7, 7 and 70. Varying$\mathit{Pr}$enables the system to access a considerable range of characteristic turbulent Péclet numbers$\mathit{Pe}_{\ast }\equiv {\mathcal{U}}_{\ast }{\mathcal{L}}_{\ast }/\unicode[STIX]{x1D705}$, where${\mathcal{U}}_{\ast }$and${\mathcal{L}}_{\ast }$are characteristic velocity and length scales, respectively, of the motion which acts to ‘scour’ the density interface. The dynamics of the interface varies with the stability of the interface which is characterised by a bulk Richardson number$\mathit{Ri}\,\equiv \,b_{0}h/U_{w}^{2}$, where$b_{0}$is half the initial buoyancy difference across the interface and$h$is the half-height of the channel. Shear-induced turbulence occurs at small$\mathit{Ri}$, whereas internal waves propagating on the interface dominate at large$\mathit{Ri}$. For a highly stable (i.e. large$\mathit{Ri}$) interface at sufficiently large$\mathit{Pe}_{\ast }$, the complex interfacial dynamics allows the interface to remain sharp. This ‘self-sharpening’ is due to the combined effects of the ‘scouring’ induced by the turbulence external to the interface and comparatively weak molecular diffusion across the core region of the interface. The effective diapycnal diffusivity and irreversible buoyancy flux are quantified in the tracer-based reference coordinate proposed by Winters &amp; D’Asaro (J. Fluid Mech., vol. 317, 1996, pp. 179–193) and Nakamura (J. Atmos. Sci., vol. 53, 1996, pp. 1524–1537), which enables a detailed investigation of the self-sharpening process by analysing the local budget of buoyancy gradient in the reference coordinate. We further discuss the dependence of the effective diffusivity and overall mixing efficiency on the characteristic parameters of the flow, such as the buoyancy Reynolds number and the local gradient Richardson number, and highlight the possible role of the molecular properties of fluids on diapycnal mixing.

The effect of stable thermal stratification on turbulent boundary layer statistics

The effects of stable thermal stratification on turbulent boundary layers are experimentally investigated for smooth and rough walls. For weak to moderate stability, the turbulent stresses are seen to scale with the wall shear stress, compensating for changes in fluid density in the same manner as done for compressible flows. This suggests little change in turbulent structure within this regime. At higher levels of stratification turbulence no longer scales with the wall shear stress and turbulent production by mean shear collapses, but without the preferential damping of near-wall motions observed in previous studies. We suggest that the weakly stable and strongly stable (collapsed) regimes are delineated by the point where the turbulence no longer scales with the local wall shear stress, a significant departure from previous definitions. The critical stratification separating these two regimes closely follows the linear stability analysis of Schlichting (Z. Angew. Math. Mech., vol. 15 (6), 1935, pp. 313–338) for both smooth and rough surfaces, indicating that a good predictor of critical stratification is the gradient Richardson number evaluated at the wall. Wall-normal and shear stresses follow atmospheric trends in the local gradient Richardson number scaling of Sorbjan (Q. J. R. Meteorol. Soc., vol. 136, 2010, pp. 1243–1254), suggesting that much can be learned about stratified atmospheric flows from the study of laboratory scale boundary layers at relatively low Reynolds numbers.

Poincaré wave–induced mixing in a large lake

A 10,000‐km2 hypoxic ‘dead zone’ forms, during most years, in the central basin of Lake Erie. To investigate the processes driving the hypoxia, we conducted a 2‐yr field campaign where the mixing in the lake interior during the stratification period was examined using current meters and temperature‐loggers data, as well as &gt; 600 temperature microstructure profiles, from which turbulent mixing was computed. Near‐inertial Poincaré waves drive shear instability, generating ∼ 1‐m amplitude and 10‐m wavelength high‐frequency internal waves with ∼ 1‐mdensity overturns that lead to an increase in turbulent dissipation by one order of magnitude. The instabilities are associated with enhanced vertical shear at the crests and troughs of the Poincaré waves and may be correlated with the local gradient Richardson number. Poincaré wave–induced mixing should be an important factor when the Burger number &lt; 0.25. The strong diapycnal mixing induced by the Poincaré wave activity will also significantly modify the energy‐flux paths. For example, we estimate that, in Lake Erie, 0.85% of the wind energy is transferred to the lake interior (below the surface layer); of this, 40% is dissipated in the interior metalimnion and 60% is dissipated at the bottom boundary. In smaller lakes, 0.42% of wind energy is transferred to the deeper water, with 90% dissipated in the boundary and 10% in the interior metalimnion.

Turbulence Regimes and Turbulence Intermittency in the Stable Boundary Layer during CASES-99

Abstract An investigation of nocturnal intermittent turbulence during the Cooperative Atmosphere–Surface Exchange Study in 1999 (CASES-99) revealed three turbulence regimes at each observation height: 1) regime 1, a weak turbulence regime when the wind speed is less than a threshold value; 2) regime 2, a strong turbulence regime when the wind speed exceeds the threshold value; and 3) regime 3, a moderate turbulence regime when top-down turbulence sporadically bursts into the otherwise weak turbulence regime. For regime 1, the strength of small turbulence eddies is correlated with local shear and weakly related to local stratification. For regime 2, the turbulence strength increases systematically with wind speed as a result of turbulence generation by the bulk shear, which scales with the observation height. The threshold wind speed marks the transition above which the boundary layer approaches near-neutral conditions, where the turbulent mixing substantially reduces the stratification and temperature fluctuations. The preference of the turbulence regimes during CASES-99 is closely related to the existence and the strength of low-level jets. Because of the different roles of the bulk and local shear with regard to turbulence generation under different wind conditions, the relationship between turbulence strength and the local gradient Richardson number varies for the different turbulence regimes. Turbulence intermittency at any observation height was categorized in three ways: turbulence magnitude oscillations between regimes 1 and 2 as wind speed varies back and forth across its threshold value, episodic turbulence enhancements within regime 1 as a result of local instability, and downbursts of turbulence in regime 3.

Breaking of Progressive Internal Gravity Waves: Convective Instability and Shear Instability*

Abstract The breaking of a monochromatic two-dimensional internal gravity wave is studied using a newly developed spectral/pseudospectral model. The model features vertical nonperiodic boundary conditions that ensure a realistic simulation of wave breaking during the wave propagation. Isopycnal overturning is induced at a local wave steepness of sc = 0.75–0.79, which is below the conventional threshold of s = 1. Isopycnal overturning is a sufficient condition for subsequent wave breaking by convective instability. When s = sc, little primary wave energy is being transferred to high-mode harmonics. Beyond s = 1, high-mode harmonics grow rapidly. Primary wave energy is more efficiently transferred by waves of lower frequency. A local gradient Richardson number is defined as Ri = −(g/ρ0)(dρ/dz)/ζ2 to isolate convective instability (Ri ≤ 0) and wave-induced shear instability (0 &amp;lt; Ri &amp;lt; 0.25), where dρ/dz is the local vertical density gradient and ζ is the horizontal vorticity. Consistent with linear wave theory, the probability density function (PDF) for occurrence of convective instability has a maximum at wave phase ϕ = π/2, where the wave-induced density perturbations to the background stratification are the greatest, whereas the wave-induced shear instability has maxima around ϕ = 0 (wave trough) and ϕ = π (wave crest). Nonlinearities in the wave-induced flow broaden the phase span in PDFs of both instabilities. Diapycnal mixing in numerical simulations may be compared with that in realistic oceanic flows in terms of the Cox number. In the numerical simulations, the Cox numbers increase from 1.5 (s = 0.78) to 21.5 (s = 1.1), and the latter is in the lower range of reported values for the ocean.

The breaking of interfacial waves at a submerged bathymetric ridge

The breaking of periodic progressive two-layer interfacial waves at a Gaussian ridge is investigated through laboratory experiments. Length scales of the incident wave and topography are used to parameterize when and how breaking occurs. Qualitative observations suggest both shear and convection play a role in the instability of waves breaking at the ridge. Simultaneous particle image velocimetry (PIV) and planar laser-induced fluorescence (PLIF) measurements are used to calculate high resolution, two-dimensional velocity and density fields from which the local gradient Richardson number Rig is calculated. The transition to breaking occurred when 0.2 ≤ Rig ≤ 0.4. In these wave-ridge breaking events, the destabilizing effects of waves steepening in shallow layers may be responsible for breaking at higher Rig than for similar waves breaking through shear instability in deep water (Troy &amp; Koseff, J. Fluid Mech., vol. 543, 2005b, p. 107). Due to the effects of unsteadiness, nonlinear shoaling and flow separation, the canonical Rig &gt; 0.25 is not sufficient to predict the stability of interfacial waves. A simple model is developed to estimate Rig in waves between finite depth layers using scales of the incident wave scale and topography. The observed breaking transition corresponds with a constant estimated value of Rig from the model, suggesting that interfacial shear plays an important role in initial wave instability. For wave amplitudes above the initial breaking transition, convective breaking events are also observed.

A numerical investigation of entrainment and transport within a stratocumulus‐topped boundary layer

AbstractEntrainment into the stratocumulus‐topped boundary layer (STBL) is investigated by means of large‐eddy simulations. Set‐up of the numerical experiment is based on the research flight RF‐01 in the DYCOMS‐II field campaign. We focus on the stability of the flow in the cloud‐top region known as the Entrainment Interface Layer (EIL). We calculate the local gradient Richardson number, Ri, at the surface of maximum static stability and at the material top of the STBL defined by a threshold of the total water content. We found that regions in which updraughts impinge upon the inversion and diverge horizontally are characterized by small values of Ri. Resulting turbulence is responsible for entrainment and formation of the EIL. Volumes of the STBL air and the free‐tropospheric air from above it, mixed in proportion resulting in negative buoyancy and typically void of cloud water, form ‘cloud holes’ ‐‐ trenches of descending cloud‐free air which surround updraught areas.The entrainment process is further analyzed using a passive scalar introduced after three hours of the simulation above the layer of maximum static stability. The mixing fraction of this scalar in the air within the cloud holes falls within the range corresponding to the buoyancy reversal. Some of the negatively buoyant mixtures sinking through the cloud holes are wrapped around the edge of cloudy regions and recirculated into the cloud, which causes a local increase of the cloud‐base height. The rest of the entrained free‐tropospheric air sinks slowly into the STBL and leads to its gradual dilution. Copyright © 2008 Royal Meteorological Society

Numerical Simulation of Flushing of Trapped Salt Water from a Bar-Blocked Estuary

Results of a numerical simulation investigating the complicated flushing process of an isolated trapped volume of salt water from a bar-blocked estuary are presented. A multiphase model, a part of the commercial code FLUENT 6.2, is applied. The governing equations together with initial and boundary conditions and the numerical scheme are described. The time-dependent salt-wedge position, vertical-density distribution, and proportion of total input kinetic energy converted into potential energy are examined for various incoming flow densimetric Froude number and estuary bed slope. The vertical position and thickness of the interfacial mixed layer between freshwater and salt water as well as the local gradient Richardson number are determined from simulated density profiles and velocity fields. The good agreement between the simulated and measured results indicates that the numerical model can be successfully applied to investigate the complex flushing process involving stratified flow.

Intermittent Bursting of Turbulence in a Stable Boundary Layer with Low-level Jet

The atmospheric stable boundary layer (SBL) with a low-level jet is simulated experimentally using a thermally stratified wind tunnel. The turbulence structure and flow characteristics are investigated by simultaneous measurements of velocity and temperature fluctuations and by flow visualization. Attention is focused on the effect of strong wind shear due to a low-level jet on stratified boundary layers with strong stability. Occasional bursting of turbulence in the lower portion of the boundary layer can be found in the SBL with strong stability. This bursting originates aloft away from the surface and transports fluid with relatively low velocity and temperature upward and fluid with relatively high velocity and temperature downward. Furthermore, the relationship between the occurrence of turbulence bursting and the local gradient Richardson number (Ri) is investigated. The Ri becomes larger than the critical Ri, Ricr = 0.25, in quiescent periods. On the other hand, the Ri number becomes smaller than Ricr during bursting events.

Simultaneous synthetic schlieren and PIV measurements for internal solitary waves

Large-amplitude internal solitary waves in a stratification comprising a thick, lower, homogeneous layer separated from a thin, upper, homogeneous layer by a broad gradient region are studied using simultaneous measurements of the density and velocity fields. Density field measurements are achieved through synthetic schlieren, operating in an absolute mode to allow efficient and accurate measurements of density in systems with strong curvatures and large perturbations to the density field. The images used for these density measurements are interleaved with images used for particle image velocimetry by phase locking two video cameras (one configured for the density measurements and the other for the velocity measurements) with a computer-driven LCD monitor, allowing the background texture required for synthetic schlieren to be turned off for the particle image velocimetry measurements on the mid-plane of the experimental tank. The simultaneous measurements of both density and velocity fields not only allow greater insight into the internal wave dynamics, but also allow the velocity measurements to be corrected for the normal errors associated with the refractive index variations. As an illustration of the power of this technique, we determine for the first time in an internal solitary wave the spatial structure of the local gradient Richardson number, finding regions where this falls below the limit for linear stability.