Large Ri Research Articles

Impact of size and location of outflow opening vent on mixed convective heat transfer induced by two aligned heated cylinders immersed in a partially open channel

AbstractThe current work deals with the numerical investigation of mixed convection occurring from two hot cylinders placed inside vented ducts under different sizes of inflow and locations of outflow opening vents. The mathematical formulation is solved based on the finite volume approach. The location of the outflow section is changed to left, center, and right of enclosure. Impacts of inflow section sizes (1 = 0.125 and 1 = 0.25), locations of outflow section ( = ), space between cylinders (), Reynolds number (), and Richardson number () are implemented. Findings display that the average Nusselt number (Nu) is exceeded by 20% for low due to the effect of nonsymmetrical inflow and outflow sections as compared with the case of equal opening vents. For large Ri, a higher Nu is obtained for nonequal opening vents in comparison with the case of equal opening vents by 10%. The difference in the average Nu between left and right cylinders is about 11%. Findings display that the enhancement in Nu due to the large spacing size between cylinders as compared with those of low spacing size is about 35%. The variations of Nu display the opening vents ratio, Re, , and have an extreme action on the characteristics of flow and temperature fields.

Hydrogen-enriched methane combustion in a swirl vortex-tube combustor

The hydrogen-enrichment combustion performance was investigated numerically by employing methane mixed with different volume proportions of hydrogen, wherein a vortex-tube combustor was employed to achieve a steady combustion process. Results show that this combustion technique indicates good adaptability to hydrogen-enrichment combustion together with an ultra-steady combustion process. The lean stability limit is always within 0.15, which decreases further with the increase of hydrogen content, whilst the amplitude of pressure fluctuation △p is always within 500 Pa with a uniform flame front. The generated non-premixed property flame structure can guarantee a high concentration of components in the reaction zone, which improves the local concentration of species and yields a large stability limit. The strong vortex flow can decrease the local flow velocity to inhibit flame blow-out and yield a large tangential velocity component. The high combustion intensity generates a large density gradient. The large density gradient and large tangential velocity promote the laminarization of the flow, resulting in a large Richardson number Ri* that is always much greater than 1.0. The laminarization of the flow field provides good aero-dynamic and thermo-dynamic stability. Further, the thermo-acoustic coupling is ultra-weak as well, and therein the Ra(x) is always smaller than 0.0024, indicating good flame-dynamic stability. In summary, the resultant good aero-dynamic, thermo-dynamic, and flame-dynamic stabilities of this vortex-tube combustor are the principal reasons for the super-steady hydrogen-enrichment combustion.

Mixed convection characteristics in a baffled U-shaped lid-driven cavity in the presence of magnetic field

The lattice Boltzmann method is utilized to investigate the mixed convection of a CuO/water nanofluid by magnetic field’s effect in a lid-driven U-shaped enclosure filled with a baffle. The bottom wall’s temperature is high. The Koo–Kleinstreuer–Li model, which considering the Brownian motion of nanoparticles, is adopted to obtain the thermophysical properties of the nanofluid. How the Hartmann number (Ha), Richardson number (Ri), Reynolds number (Re), and nanoparticle concentration (ϕ) affect streamlines, isotherms, and average Nusselt number (Nuave) is also examined. The results reveal that, at Re = 100 and for a large Ri, the nanofluid strategy degrades the Nu. The favorable effect of increasing the Re on the average Nu and adverse trends of the increment in the Ha on the heat transfer are the main highlights in this study. In addition, the increase in the Re more strongly affects the heat transfer rate at higher Ri.

Combining data from multiple agencies to assess benthic macroinvertebrate communities in a large gravel-bed river

AbstractGovernment agencies frequently conduct benthic macroinvertebrate surveys for bioassessment at large spatial scales in a variety of aquatic habitats, including large rivers. However, these data are rarely used by investigators outside the specific regulatory agency. We used data from 150 benthic macroinvertebrate samples collected over a period of 20 y from 10 locations in a large, shallow river system (the Susquehanna River and 2 major tributaries) by personnel in 4 government agencies to explore broad spatial and temporal patterns in benthic assemblages. We standardized sample size and taxonomy to account for differences in sampling, processing, and identification methods among agencies. Invertebrate assemblages were dominated by mayflies and caddisflies (46–83%). Percent Ephemeroptera, Plecoptera, Trichoptera (EPT) and standard diversity measures were inversely correlated, indicating that traditional macroinvertebrate Index of Biotic Integrity (IBI) approaches might not be applicable to large ri...

An explanation for salinity- and SPM-induced vertical countergradient buoyancy fluxes

Measurements of turbulent fluctuations of velocity, salinity, and suspended particulate matter (SPM) are presented. The data show persistent countergradient buoyancy fluxes. These countergradient fluxes are controlled by the ratio of vertical turbulent kinetic energy (VKE) and available potential energy (APE) terms in the buoyancy flux equation. The onset of countergradient fluxes is found to approximately coincide with larger APE than VKE. It is shown here that the ratio of VKE to APE can be written as the square of a vertical Froude number. This number signifies the onset of the dynamical significance of buoyancy in the transport of mass. That is when motions driven by buoyancy begin to actively determine the vertical turbulent transport of mass. Spectral and quadrant analyses show that the occurrence of countergradient fluxes coincides with a change in the relative importance of turbulent energetic structures and buoyancy-driven motions in the transport of mass. Furthermore, these analyses show that with increasing salinity-induced Richardson number (Ri), countergradient contributions expand to the larger scales of motions and the relative importance of outward and inward interactions increases. At the smaller scales, at moderate Ri, the countergradient buoyancy fluxes are physically associated with an asymmetry in transport of fluid parcels by energetic turbulent motions. At the large scales, at large Ri, the countergradient buoyancy fluxes are physically associated with convective motions induced by buoyancy of incompletely dispersed fluid parcels which have been transported by energetic motions in the past. Moreover, these convective motions induce restratification and enhanced settling of SPM. The latter is generally the result of salinity-induced convective motions, but SPM-induced buoyancy is also found to play a role.

On the Velocity Gradient in Stably Stratified Sheared Flows. Part 1: Asymptotic Analysis and Applications

We give a new derivation of the familiar linear relation for the dimensionless velocity gradient in the stably stratified surface layer and provide physical and empirical grounds for its universal applicability in stationary homogeneous turbulence over the whole range of static stabilities from Ri = 0 to very large Ri. Combining this relation with the budget equation for the turbulent kinetic energy we obtain the “equilibrium formulation” of the turbulent dissipation length scale, and recommend it for use in turbulence closure models.

Explicit algebraic Reynolds stresses and scalar fluxes for density-stratified shear flows

An explicit algebraic model for Reynolds stresses and active scalar turbulent fluxes is proposed for simply stratified, stable shear flows such as atmospheric boundary layers of estuaries, including buoyant effects due to density variations (temperature, salinity). Under equilibrium assumptions, these models lead to explicit functions of the gradient Richardson number Ri that model the damping of the eddy viscosity and eddy diffusivity coefficients. The present model is compared to other existing theoretical approaches, as well as experimental observations, with satisfactory agreement. The evolution of the turbulent Prandtl number as a function of Ri is correctly predicted and its neutral value is consistent with existing values in the literature. The behavior of the model predicts that internal waves are responsible for momentum diffusion at large Ri, consistently with recent publications. The properties of turbulence anisotropy are briefly investigated.

Vertical Shearing Instabilities in Radially Shearing Disks: The Dustiest Layers of the Protoplanetary Nebula

Gravitational instability of a vertically thin, dusty sheet near the midplane of a protoplanetary disk has long been proposed as a way of forming planetesimals. Before Roche densities can be achieved, however, the dust-rich layer, sandwiched from above and below by more slowly rotating dust-poor gas, threatens to overturn and mix by the Kelvin-Helmholtz instability (KHI). Whether such a threat is real has never been demonstrated: the Richardson criterion for the KHI is derived for two-dimensional Cartesian shear flow and does not account for rotational forces. Here we present three-dimensional numerical simulations of gas-dust mixtures in a shearing box, accounting for the full suite of disk-related forces: the Coriolis and centrifugal forces, and radial tidal gravity. Dust particles are assumed small enough to be perfectly entrained in gas; the two fluids share the same velocity field but obey separate continuity equations. We find that the Richardson number Ri does not alone determine stability. The critical value of Ri below which the dust layer overturns and mixes depends on the height-integrated metallicity Σd/Σg (surface density ratio of dust to gas). Nevertheless, for Σd/Σg between 1 and 5 times solar, the critical Ri maintains a nearly constant value of ~0.1. Keplerian radial shear stabilizes those modes that would otherwise disrupt the layer at large Ri. If the height-integrated metallicity is at least ~5 times greater than the solar value of 0.01, then midplane dust densities can approach Roche densities. Such a metal-rich environment might be expected to produce gas giant planets having similarly supersolar metallicities.

Observations of Stably Stratified Shear-Driven Atmospheric Turbulence at Low and High Richardson Numbers

Abstract Stably stratified shear-driven turbulence is analyzed using the gradient Richardson number, Ri, as the stability parameter. The method overcomes the statistical problems associated with the widely used Monin–Obukhov stability parameter. The results of the Ri-based scaling confirm the presence of three regimes: the weakly and the very stable regimes and the transition in between them. In the weakly stable regime, fluxes scale in proportion with variance, while in the very stable regime, stress and scalar fluxes behave differently. At large Ri, the velocity field becomes highly anisotropic and the turbulent potential energy becomes approximately equal to half of the turbulent kinetic energy. It appears that even in the strongly stable regime, beyond what is known as the critical gradient Richardson number, turbulent motions are present.

A quasi-normal scale elimination model of turbulence and its application to stably stratified flows

Abstract. Models of planetary, atmospheric and oceanic circulation involve eddy viscosity and eddy diffusivity, KM and KH, that account for unresolved turbulent mixing and diffusion. The most sophisticated turbulent closure models used today for geophysical applications belong in the family of the Reynolds stress models. These models are formulated for the physical space variables; they consider a hierarchy of turbulent correlations and employ a rational way of its truncation. In the process, unknown correlations are related to the known ones via "closure assumptions'' that are based upon physical plausibility, preservation of tensorial properties, and the principle of the invariant modeling according to which the constants in the closure relationships are universal. Although a great deal of progress has been achieved with Reynolds stress closure models over the years, there are still situations in which these models fail. The most difficult flows for the Reynolds stress modeling are those with anisotropy and waves because these processes are scale-dependent and cannot be included in the closure assumptions that pertain to ensemble-averaged quantities. Here, we develop an alternative approach of deriving expressions for KM and KH using the spectral space representation and employing a self-consistent, quasi-normal scale elimination (QNSE) algorithm. More specifically, the QNSE procedure is based upon the quasi-Gaussian mapping of the velocity and temperature fields using the Langevin equations. Turbulence and waves are treated as one entity and the effect of the internal waves is easily identifiable. This model implies partial averaging and, thus, is scale-dependent; it allows one to easily introduce into consideration such parameters as the grid resolution, the degree of the anisotropy, and spectral characteristics, among others. Applied to turbulent flows affected by anisotropy and waves, the method traces turbulence anisotropization and shows how the dispersion relationships for linear waves are modified by turbulence. In addition, one can derive the internal wave frequency shift and the threshold criterion of internal wave generation in the presence of turbulence. The spectral method enables one to derive analytically various one-dimensional and three-dimensional spectra that reflect the effects of waves and anisotropy. When averaging is extended to all scales, the method yields a Reynolds-averaged, Navier-Stokes equations based model (RANS). This RANS model shows that there exists a range of Ri, approximately between 0.1 and 1, in which turbulence undergoes remarkable anisotropization; the vertical mixing becomes suppressed while the horizontal mixing is enhanced. Although KH decreases at large Ri and tends to its molecular value, KM remains finite and larger than its molecular value. This behavior is attributable to the effect of internal waves that mix the momentum but do not mix a scalar. In the Reynolds stress models, this feature is not replicated; instead, all Reynolds stress models predict KM→0 at some value of Ri≤1 which varies from one model to another. The presented spectral model indicates that there is no a single-valued critical Richardson number Ri at which turbulence is fully suppressed by stable stratification. This result is in agreement with large volume of atmospheric, oceanic and laboratory data. The new spectral model has been implemented in the K-ε format and tested in simulations of the stably stratified atmospheric boundary layers. The results of these simulations are in good agreement with the data collected in BASE, SHEBA and CASES99 campaigns. Implementation of the QNSE-derived KM and KH in the high-resolution weather prediction system HIRLAM results in significant improvement of its predictive skills.

Convection regimes and heat transfer characteristics along a continuously moving heated vertical plate

The steady laminar flow and thermal characteristics of a continuously moving vertical sheet of extruded material are studied close to and far downstream from the extrusion slot. The velocity and temperature variations, obtained by a finite volume method, are used to map out the entire forced, mixed and natural convection regimes. The effects of the Prandtl number ( Pr) and the buoyancy force parameter ( B) on the friction and heat transfer coefficients are investigated. Comparisons with experimental measurements and solutions by others in the pure forced and pure natural convection regions are made. In the mixed convection region, the results are compared with available finite-difference solutions of the boundary layer equations showing excellent agreement. The region close to the extrusion slot is characterized as a non-similar forced-convection dominated region in which Nu x Re x −1/2 drops sharply with increasing Richardson number ( Ri x ). This is followed by a self-similar forced-convection dominated region in which Nu x Re x −1/2 levels off with increasing Ri x until the buoyancy effect sets in. The existence and extent of the latter region depend upon the value of B. A non-similar mixed convection region where increasing buoyancy effect enhances the heat transfer rate follows. Finally, this region is followed downstream by a self-similar natural-convection dominated region in which Nu x Re x −1/2 approaches the pure natural convection asymptote at large Ri x . Critical values of Ri x to distinguish the various convection regimes are determined for different Pr and B.

Effects of Critical Levels on Two-Dimensional Back-Sheared Flow over an Isolated Mountain Ridge on anfPlane

It is well known that there exist three singular points, U 2 c 56 f/k and U 5 c, where the corresponding levels will be called inertia critical levels (ICLs) and the classic critical level (CCL), in the equation governing a two-dimensional, rotating, continuously stratified, hydrostatic, back-sheared Boussinesq flow. Here U and c are basic wind and phase speed, respectively; f is the Coriolis force; and k is the wavenumber. The effects of these critical levels on flows over an isolated mountain ridge are investigated both analytically and numerically, based on a broad range of Rossby numbers (Ro) and Richardson numbers (Ri). Each wave mode generated from the isolated mountain with a continuous spectrum has its own ICL. To indicate the net effects of all ICLs, the authors define the effective ICL as the height above which the amplitude of the inertia-gravity wave mode is very small. The findings for linear flows are summarized as follows. Regime I is inertia-gravity waves. The flow behaves like unsheared inertia-gravity waves and the effective lower ICL plays a similar role as the CCL does in a nonrotating flow. Regime II is combined inertia-gravity waves and baroclinic lee waves. These waves behave like those in regime I below the lower effective ICL, and like baroclinic lee waves near the CCL. In this regime, the horizontal warm advection by the baroclinic lee wave plays an important role in the formation of the lee pressure trough. On the other hand, near the downslope of the mountain, both the warm advection by the inertia gravity and the adiabatic warming also contribute significantly to the lee trough. Therefore, Smith’s quasigeostrophic theory of lee cyclogenesis is extended to a nongeostrophic regime. Regime III is combined evanescent and baroclinic lee waves. These waves still behave like baroclinic lee waves near the CCL, but they are trapped near the surface. Regime IV is transient waves. Nongeostrophic baroclinic instability exists, as evidenced by the positive domain-averaged north‐south heat flux. There exists no steady state. At earlier times, the flow behaves like trapped baroclinic lee waves. For a relatively large Ri (e.g., Ri . 25), the flow falls into regime I when Ro is relatively large (e.g., Ro $ 2). It then shifts to regime II, and finally to regime III as Ro decreases. For a relatively small Ri (e.g., Ri , 25), the flow shifts from regime I to II, and then finally to regime IV when both Ro and Ri decrease.

Diapycnal mixing in western boundary currents

In a previous study (Pelegrí and Csanady, 1991) we found upward entrainment and two‐way exchange between the upper thermocline and surface layers of the Gulf Stream. Here we use isopycnic coordinates to analyze the mechanism of diapycnal shear‐induced mixing in western boundary currents. A hydrographic section across the Gulf Stream off the Mid‐Atlantic Bight is used for a case study. It shows that the upper thermocline layers of the Gulf Stream are characterized by relatively small (16 m averaged) gradient Richardson numbers, Ri. Analysis of the Jacobian, J = ∂z/∂p (with z the depth and p the potential density), total vorticity and potential vorticity fields shows that this region has low Jacobian values associated with high values of potential vorticity, as required theoretically for the case of dominant diapycnal mixing. The density tendency, wp = Dp/Dt, is calculated from the vertical gradient of the Reynolds density flux, the latter parameterized as density eddy diffusivity divided by the Jacobian. We use Munk and Anderson's (1948) expression for the eddy diffusivity coefficient, modified to conform to data of Ueda et al. (1981), maintaining a Ri−3/2 dependence for large Ri. From this we obtain an explicit expression for wp in terms of the Ri and J distributions. The distributions of wp, its diapycnal gradient, ∂wp/∂p, and the diapycnal velocity, wd = Jwp, are then calculated. Regions of high diapycnal convergence (large negative ∂wp/∂p values) coincide with the location of anomalously low Jacobians, in agreement with the idea that diapycnal mixing is the consequence of anomalies produced during frontogenesis in some phase of the meanders. We suggest that this process, taking place intermittently in space and time, is responsible for two‐way exchange in western boundary currents.

THE INFLUENCE OF SIDE-WALL FRICTION ON SHEAR-STRESS DRIVEN ENTRAPMENT EXPERIMENTS

Laboratory experiments on mixed-layer deepening in a density-stratified fluid are known to be affected by side-wall friction, in particular when the overall Richardson number Ri* = B/u* 2 is large where B is the total mixed-layer buoyancy and u* the friction velocity. Finite aspect (depth to width)-ratio effects are calculated starting from a simple mathematical model based on the gradienttransport hypothesis. An asymptotic expansion for large Ri*, which covers almost the whole range of practical interest, yields good agreement with the entrainment rates observed by Kantha, Phillips and Azad (1977) and Deardorff and Willis (1982). At zero aspect-ratio the dimensionless entrainment rate E* = We/u*, where we is the entrainment rate, is found to vary as Ri* -1/2 for both two-layer fluid and an initial density distribution according to a power law, which result is in agreement with the Pollard, Rhines and Thompson (1973) model. A similar analysis of the experiments of Moore and Long (1971) shows that most of these experiments were controlled by side-wall friction.

Soot emission, thermal radiation, and laminar instability of acetylene diffusion flames

Soot emission and radiant heat loss from turbulent or largely turbulent vertical free diffusion flames of acetylene in still air have been studied over a broad range of the buoyancy Richardson ratio Ri L . Soot emission reaches a peak equal in mass to 12% of the fuel carbon around Ri L = 600. The radiant heat loss there reaches 75% of the theoretical combustion heat release. The flames at large Ri L were initially laminar, and a predominantly sinuous instability was observed in the transition to turbulent flow. The instability was studied stroboscopically, utilizing soot-scattered light. The Strouhal ratio based on burner exit conditions is independent of the exit Reynolds ratio but proportional to the cube of the diameter.

Turbulent Transport Near the Ground in Stable Conditions

Abstract The variation of the nondimensional transfer coefficients, k* and K*, and the Monin-Obukhov function ϕ in strong stability, are examined. The exchange coefficients for heat, water vapor and momentum are shown to be approximately equal even at large Ri. The relationships suggest that the decay of turbulent motion in the lower atmosphere begins at Ri=0.1, and completely ceases at Ri>0.3. In these nonturbulent conditions the profiles of wind and water vapor show very little variation with height, but the temperature profile reflects the increasing importance of infrared radiation.

Instability of Frontal Waves

Abstract The stability of the classical Norwegian polar front model is investigated, using a numerical technique to supplement the more precise conclusions which are possible in the limiting cases of zero density difference or zero wavenumber. The feasibility of the numerical technique depends on a careful formulation of boundary conditions at the limits of the frontal zone. The numerical results cover the region of Rossby number (Ro) ≤ 3 and Richardson number(Ri) ≤ 5, but their interpretation is unclear at Ri > 2 and Ro > 1. Unstable waves exist at all wavelengths; Rayleigh shear instability at small Ri, Helmholtz shear instability at large Ro and small Ri, shear instability and geostrophic baroclinic instability simultaneously at small Ro and Ri > 2, and a combination of geostrophic and Helmholtz instability when Ri > 2 and Ro < l (but not too small). The previous conclusion of Kotschin that this frontal model is stable for Ri < 2 is therefore incorrect.