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At least 19 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2015

Sensitivity of a global climate model to the critical Richardson number in the boundary layer parameterization

The critical bulk Richardson number (Ri cr ) is an important parameter in planetary boundary layer (PBL) parameterization schemes used in many climate models. This paper examines the sensitivity of a Global Climate Model, the Beijing Climate Center Atmospheric General Circulation Model, BCC_AGCM to Ri cr . The results show that the simulated global average of PBL height increases nearly linearly with Ri cr , with a change of about 114 m for a change of 0.5 in Ri cr . The surface sensible (latent) heat flux decreases (increases) as Ri cr increases. The influence of Ri cr on surface air temperature and specific humidity is not significant. The increasing Ri cr may affect the location of the Westerly Belt in the Southern Hemisphere. Further diagnosis reveals that changes in Ri cr affect stratiform and convective precipitations differently. Increasing Ri cr leads to an increase in the stratiform precipitation but a decrease in the convective precipitation. Significant changes of convective precipitation occur over the inter-tropical convergence zone, while changes of stratiform precipitation mostly appear over arid land such as North Africa and Middle East.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2010

FORMING PLANETESIMALS BY GRAVITATIONAL INSTABILITY. I. THE ROLE OF THE RICHARDSON NUMBER IN TRIGGERING THE KELVIN-HELMHOLTZ INSTABILITY

Gravitational instability (GI) of a dust-rich layer at the midplane of a gaseous circumstellar disk is one proposed mechanism to form planetesimals, the building blocks of rocky planets and gas giant cores. Self-gravity competes against the Kelvin-Helmholtz instability (KHI): gradients in dust content drive a vertical shear which risks overturning the dusty subdisk and forestalling GI. To understand the conditions under which the disk can resist the KHI, we perform three-dimensional simulations of stratified subdisks in the limit that dust particles are small and aerodynamically well coupled to gas, thereby screening out the streaming instability and isolating the KHI. Each subdisk is assumed to have a vertical density profile given by a spatially constant Richardson number Ri. We vary Ri and the midplane dust-to-gas ratio {mu}{sub 0} and find that the critical Richardson number dividing KH-unstable from KH-stable flows is not unique; rather, Ri{sub crit} grows nearly linearly with {mu}{sub 0} for {mu}{sub 0} = 0.3-10. Plausibly, a linear dependence arises for {mu}{sub 0} << 1 because in this regime the radial Kepler shear replaces vertical buoyancy as the dominant stabilizing influence. Why this dependence should persist at {mu}{sub 0} > 1 is a new puzzle. The bulk (height-integrated) metallicity is uniquely determined by Ri and {mu}{sub 0}. Only for disks of bulk solar metallicity is Ri{sub crit} {approx} 0.2, which is close to the classical value. Our empirical stability boundary is such that a dusty sublayer can gravitationally fragment and presumably spawn planetesimals if embedded within a solar metallicity gas disk {approx}4x more massive than the minimum-mass solar nebula; or a minimum-mass disk having {approx}3x solar metallicity; or some intermediate combination of these two possibilities. Gravitational instability seems possible without resorting to the streaming instability or to turbulent concentration of particles.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2014

Elementary stratified flows with stability at low Richardson number

We revisit the stability analysis for three classical configurations of multiple fluid layers proposed by Goldstein [“On the stability of superposed streams of fluids of different densities,” Proc. R. Soc. A. 132, 524 (1931)], Taylor [“Effect of variation in density on the stability of superposed streams of fluid,” Proc. R. Soc. A 132, 499 (1931)], and Holmboe [“On the behaviour of symmetric waves in stratified shear layers,” Geophys. Publ. 24, 67 (1962)] as simple prototypes to understand stability characteristics of stratified shear flows with sharp density transitions. When such flows are confined in a finite domain, it is shown that a large shear across the layers that is often considered a source of instability plays a stabilizing role. Presented are simple analytical criteria for stability of these low Richardson number flows.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2024

Computation of Richardson number and entrainment in a turbulent plume using DNS

This presentation will be presented by Pierre Carlotti (French foreign national) at the 1st European Fluid Dynamics Conference (EFDC1) in Aachen, Germany in mid-September. The work focuses on fundamental questions pertaining to entrainment processes in plumes. I am included as a co-author because Pierre used my previously published data to further develop theoretical estimates.

Carlotti, Pierre↗
DOE OSTI2018

Mixed convection heat transfer in a differentially heated cavity with two rotating cylinders

Mixed convection heat transfer in a differentially heated cavity with two rotating cylinders was studied numerically for various pertinent parameters such as Richardson number, Reynolds number, non-dimensional rotation speed of the cylinder, and the location of the cylinders. The results from these simulations were validated using an open-source spectral element code, Nek5000. The results of this study were presented in terms of streamlines, isotherms, local and average Nusselt number, and temperature profiles. The results illustrated that the average Nusselt number depends strongly on the rotation speed of the cylinder, Reynolds number, and Richardson number. However, the average Nusselt number was found to be independent of the rotation speed at high Richardson number (Ri = 10). In addition, the direction of the rotation speed of the cylinders has a profound effect on the average Nusselt. Finally, the study illustrated that the magnitude and direction of the rotation speed of the cylinders have a significant effect on the flow pattern and isotherms.

42 ENGINEERING↗
DOE OSTI2021

Nondimensional convection numbers modeling thermally stratified storage tanks: Richardson's number and hot-water tanks

Thermally stratified storage tank studies have spanned over 50 years to increase the thermal storage efficiency and accurate prediction of the outlet temperature particularly for solar applications. The studies have reviewed and modeled the jet and plume flow phenomena inside the tank due to the inlet mixing and stratification level. Kelvin–Helmholtz and Rayleigh–Taylor instabilities are the major drivers of the mixing in these tanks. Momentum jets deflecting off walls at the bottom of the tank also create significant mixing. Reviewing Richardson models shows that the categorization was based on the range of Reynolds numbers at the inlet. Unfortunately, the use of superficial velocity in calculating the Richardson number results in critical values in the literature ranging from below 0.25 to 100. The most used length scale associated with these flows is an inertial scale based on the tank height or diameter although the mixing can occur at a relatively smaller scale. The various inlet devices and a large span of flow rates experienced in thermally stratified storage tanks requisite the use of the Reynolds number in combination with a convection number for accurate one dimensional models that predict performance over the long-term. The evaluation of peak shifting of electric loads leveraging renewable sources for applications, including residential hot-water tanks, commercial water tanks, and large-scale chilled water storage tanks, require these models. Finally, this paper is focused on establishing the significance of the convection numbers in conjunction with the Reynolds number for modeling the thermal stratification in storage tanks.

14 SOLAR ENERGY↗
DOE OSTI2010

Fluxes across double-diffusive interfaces : a one-dimensional turbulence study.

The parameterization of the fluxes of heat and salt across double-diffusive interfaces is of interest in geophysics, astrophysics, and engineering. The present work is a parametric study of these fluxes using one-dimensional-turbulence (ODT) simulations. Its main distinction is that it considers a parameter space larger than previous studies. Specifically, this work considers the effect on the fluxes of the stability parameter R{sub {rho}}, Rayleigh number Ra, Prandtl number, Lewis number, and Richardson number. The ratio Ra/R{sub {rho}} is found to be a dominant parameter. Here Ra/R{sub {rho}} can be seen as a ratio of destabilizing and stabilizing effects. Trends predicted by the simulations are in good agreement with previous models and available measurements.

58 GEOSCIENCES↗
DOE OSTI2017

Dynamics of unstably stratified free shear flows: an experimental investigation of coupled Kelvin–Helmholtz and Rayleigh–Taylor instability

The dynamics of the coupled Kelvin–Helmholtz (KH) and Rayleigh–Taylor (RT) instability (referred to as KHRT instability or KHRTI) is studied using statistically steady experiments performed in a multi-layer gas tunnel. Experiments are performed at four density ratios ranging in Atwood number $A_{t}$ from 0.035 to 0.159, with varying amounts of shear and $\unicode[STIX]{x0394}U/U$ ranging from 0 to 0.48, where $\unicode[STIX]{x0394}U$ is the speed difference between the two flow streams being investigated and $U$ is the mean velocity of these two streams. Three types of diagnostics – back-lit visualization, hot-wire anemometry and particle image velocimetry (PIV) – are employed to obtain the mixing widths, velocity field and density field. The flow is found to be governed by KH dynamics at early times and RT dynamics at late times. This transition from KH-instability-like to RT-instability-like behaviour is quantified using the Richardson number. Transitional Richardson number magnitudes obtained for the present KHRT flows are found to be in the range 0.17–0.56 similar to the critical Richardson numbers for stably stratified free shear flows. Comparing the evolution of density and velocity mixing widths, the density mixing layer is found to be approximately two times as thick as the velocity mixing layer. Scaling of velocity fluctuations is attempted using combinations of KH and RT scales. It is found that the proposed KHRT velocity scale, obtained using the combined mixing-layer growth equation, is appropriate for intermediate stages of the flow when both KH and RT dynamics are comparable. Probability density functions (p.d.f.s) for different fluctuating quantities are presented. Multiple peaks in p.d.f.s are qualitatively explained from the development of coherent KH roll-ups and their subsequent transition into turbulent pockets. The evolution of energy spectra indicates that density fluctuations start to show an inertial subrange from earlier times compared to velocity fluctuations. The spectra exhibit a slightly steeper slope than the Kolmogorov–Obukhov five-thirds law.

Mechanics↗
DOE OSTI2025

Assessment of integral models for non-Boussinesq lazy plumes using numerical simulations

Integral modelling of turbulent buoyant plumes is crucial for rapid predictions of plume characteristics. While the governing equations are typically derived using self-similarity and a Boussinesq approximation, these assumptions may not hold for plumes originating from finite-area sources with large density ratios. Here, this work evaluates the accuracy of integral-scale models for non-Boussinesq lazy plumes using high-fidelity numerical simulations of turbulent helium plumes. We analyse the plume kinematics by computing vertical fluxes, plume radius and radial profiles, establishing some disparities between common practice and physical accuracy. We identify how the definition of the plume radius changes the perception of the plume structure when the flow is not self-similar and derive a relationship between the flux-based and threshold-based definitions without requiring self-similarity. We then examine the plume dynamics by evaluating the source terms from the governing plume equations. Our results support neglecting diffusive and viscous effects but emphasise the importance of the mean pressure gradient, even in the self-similar regime. Two coefficients need to be modelled: the well-known entrainment coefficient and the lesser-known momentum correction coefficient, which is a correction required for the momentum equation to account for self-similar and slender approximations. The momentum correction coefficient is found to be approximately constant and slightly greater than the assumed value of 1. The standard entrainment coefficient models perform well up to a local Richardson number three times the asymptotic value but overpredict entrainment for larger Richardson numbers. We propose a correction using the known finite limit of entrainment at infinite Richardson number.

Meehan, Michael Alexander [Sandia National Laborat↗
DOE OSTI2021

Scaling patch analysis of turbulent planar plume

Proper scaling in turbulent planar plumes is investigated in this study using a scaling patch approach. Based on the scaled boundary conditions, a proper velocity scale for the mean axial flow is the plume centerline velocity U ref = U ctr , and a proper temperature scale for the temperature excess is Θ ref = T ctr – T ∞ , where T ctr is the plume centerline temperature and T ∞ is the ambient fluid temperature. By seeking an admissible scaling, a key concept in the scaling patch approach, for the mean continuity, mean momentum, and mean energy equations, respectively, the following is found: (1) a proper scale for the mean transverse flow is V ref = ( d δ / d x ) U ctr , where d δ / d x is the growth rate of the plume width. (2) A proper scale for the Reynolds shear stress is R vu , ref = U ctr V ref = ( d δ / d x ) U ctr 2 , a mix of the scales for the mean axial and transverse flows. (3) A proper scale for the turbulent heat flux is R v θ , ref = V ref Θ ctr , a mix of the scales for the mean transverse flow and mean temperature excess. The mean transverse flow thus plays a critical role in the scaling of turbulent planar plumes. Approximate functions are developed for the scaled mean transverse flow, Reynolds shear stress, and turbulent temperature flux, and are found to agree favorably with experimental and numerical simulation data. The integral analysis of the mean momentum equation yields a Richardson number Ri, which remains invariant in the axial direction. The Richardson number is defined as Ri = def g β Θ ctr δ t / ( U ctr V ref ) ≈ 1 / 2 , where g is the gravitational acceleration, β is the thermal expansion coefficient, and δ t is the plume half-width based on the mean temperature profile. This Richardson number arises directly from the scaling patch analysis of the mean momentum equation, including both the streamwise and transverse velocity scales.

42 ENGINEERING↗
DOE OSTI2016

Closure Schemes for Stably Stratified Atmospheric Flows without Turbulence Cutoff

Two recently proposed turbulence closure schemes are compared against the conventional Mellor–Yamada (MY) model for stably stratified atmospheric flows. The Energy- and Flux-Budget (EFB) approach solves the budgets of turbulent momentum and heat fluxes and turbulent kinetic and potential energies. The Cospectral Budget (CSB) approach is formulated in wavenumber space and integrated across all turbulent scales to obtain flow variables in physical space. Unlike the MY model, which is subject to a “critical gradient Richardson number,” both EFB and CSB models allow turbulence to exist at any gradient Richardson number R i and predict a saturation of flux Richardson number ( R f → R fm ) at sufficiently large R i . The CSB approach further predicts the value of R fm and reveals a unique expression linking the Rotta and von Kármán constants. Hence, all constants in the CSB model are nontunable and stability independent. All models agree that the dimensionless sensible heat flux decays with increasing R i . However, the decay rate and subsequent cutoff in the MY model appear abrupt. The MY model further exhibits an abrupt cutoff in the turbulent stress normalized by vertical velocity variance, while the CSB and EFB models display increasing trends. The EFB model produces a rapid increase in the ratio of turbulent potential energy and vertical velocity variance as R fm is approached, suggesting a strong self-preservation mechanism. Vertical anisotropy in the turbulent kinetic energy is parameterized in different ways in MY and EFB, but this consideration is not required in CSB. Differences between EFB and CSB model predictions originate from how the vertical anisotropy is specified in the EFB model.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2016

TURBULENT TRANSPORT IN A STRONGLY STRATIFIED FORCED SHEAR LAYER WITH THERMAL DIFFUSION

This work presents numerical results on the transport of heat and chemical species by shear-induced turbulence in strongly stratified, thermally diffusive environments. The shear instabilities driven in this regime are sometimes called “secular” shear instabilities, and can take place when the Richardson number of the flow is large, provided the Péclet number is small. We have identified a set of simple criteria to determine whether these instabilities can take place or not. Generally speaking, we find that they may be relevant whenever the thermal diffusivity of the fluid is very large (typically larger than 10{sup 14} cm{sup 2} s{sup −1}), which is the case in the outer layers of high-mass stars (M ≥ 10 M{sub ⊙}), for instance. Using a simple model setup in which the shear is forced by a spatially sinusoidal, constant-amplitude body-force, we have identified several regimes ranging from effectively unstratified to very strongly stratified, each with its own set of dynamical properties. Unless the system is in one of the two extreme regimes (effectively unstratified or completely stable), however, we find that (1) only about 10% of the input power is used toward heat transport, while the remaining 90% is viscously dissipated; (2) that the effective compositional mixing coefficient is well-approximated by the model of Zahn, with D ≃ 0.02κ{sub T}/J where κ{sub T} is the thermal diffusivity and J is the Richardson number. These results need to be confirmed, however, with simulations in different model setups and at higher effective Reynolds number.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2017

Turbulent Transport by Diffusive Stratified Shear Flows: From Local to Global Models. I. Numerical Simulations of a Stratified Plane Couette Flow

Shear-induced turbulence could play a significant role in mixing momentum and chemical species in stellar radiation zones, as discussed by Zahn. In this paper we analyze the results of direct numerical simulations of stratified plane Couette flows, in the limit of rapid thermal diffusion, to measure the turbulent viscosity and the turbulent diffusivity of a passive tracer as a function of the local shear and the local stratification. We find that the stability criterion proposed by Zahn, namely that the product of the gradient Richardson number and the Prandtl number must be smaller than a critical values (JPr){sub c} for instability, adequately accounts for the transition to turbulence in the flow, with (JPr){sub c}≃0.007. This result recovers and confirms the prior findings of Prat et al. Zahn’s model for the turbulent diffusivity and viscosity, namely that the mixing coefficient should be proportional to the ratio of the thermal diffusivity to the gradient Richardson number, does not satisfactorily match our numerical data. It fails (as expected) in the limit of large stratification where the Richardson number exceeds the aforementioned threshold for instability, but it also fails in the limit of low stratification where the turbulent eddy scale becomes limited by the computational domain size. We propose a revised model for turbulent mixing by diffusive stratified shear instabilities that properly accounts for both limits, fits our data satisfactorily, and recovers Zahn’s model in the limit of large Reynolds numbers.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2016

Onset of transition from laminar to chaos in MHD mixed convection of a lid-driven trapezoidal cavity filled with Cu-water nanofluid

The present study investigates the thermal mixing scenarios of steady magneto-hydrodynamic (MHD) mixed convection in a two-dimensional lid-driven trapezoidal cavity filled with Cu-water nanofluid. The top wall of the cavity slides with a uniform velocity from left to right direction, while the other walls are fixed. The bottom wall is kept with a constant higher temperature than the top one. The governing mass, momentum and energy equations are expressed in non-dimensional forms and Galerkin finite element method has been employed to solve these equations. Special attention is paid on investigating the onset of transition from laminar to chaos at pure mixed convection case. Hence, the computations are carried out for a wide range of Reynolds numbers (Re = 0.1 − 400) and Grashof numbers (Gr = 10{sup −2} − 1.6 × 10{sup 5}) at unity Richardson number and fixed Hartmann number (Ha = 10). The variation of average Nusselt number of the bottom heated wall indicates the influence of governing parameters (Re and Gr) on heat transfer characteristics. The results are presented and explained through the visualisation of isotherms, streamlines and heatlines.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2026

Shear-free, inhomogeneous turbulence in a stably stratified fluid

High-resolution large eddy simulations are conducted of locally forced, shear-free turbulence in the presence of an initially sharp density interface. The simulations are reminiscent of oscillating grid turbulence experiments used to isolate the effect of turbulent diffusion and entrainment from background shear. By simulating such a flow we avoid common challenges of the experiments such as secondary-flow contamination due to sidewall effects and the inevitable interaction of the stratifying agent and forcing region. To address the latter concern, we add a heating term (potential energy sink) to the governing equations in the forcing layer, thereby preventing a heat flux through the source region. This modification sets up a continuous stratification in the mixed layer that is often assumed to be negligible in experiments. Despite this difference, we are able to make meaningful comparisons in terms of the overall entrainment rate, which varies as a power law with a turbulent Richardson number. Two exponents, −2 and −1, are measured depending on the definition of the Richardson number and entrainment rate used. The definition leading to −1 is consistent with most experiments, and we argue it is the superior choice if one is able to measure the relevant quantities. We also verify the self-similar scaling of turbulence velocity and length scales in the homogeneous fluid and propose ‘inner’ and ‘outer’ scalings for the stratified cases based on a local Froude number. The detailed scaling results are useful for turbulence model validation.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2021

Heat transfer and pseudo phase transition for low-Reynolds, mixed-convection channel flow in the supercritical thermodynamic regime

Fluids at supercritical thermodynamic conditions are inherently complex due to the large variations in thermodynamic and transport properties. Multiple recent numerical and experimental investigations indicate ongoing interest for these fluids, especially supercritical CO and supercritical water, for a variety of applications. The potential heat transfer benefits in this regime are directly influenced by the extreme variations in thermodynamic and transport properties, which occur at, and above, the critical point. Limited studies have been conducted for low-Reynolds/intermediate-Rayleigh numbers mixed-convection channel flow of supercritical water, which is the focus of this study. To investigate the thermally driven hydrodynamic instabilities in this regime, we use a high-order fully-implicit numerical method. As expected, in this channel configuration and flow regime, a competition arises between the forced and the natural convection. Buoyancy, driven by the thermal gradient at the wall, pushes the fluid upwards in the channel, while inertial forces drive the fluid from inlet to outlet. We observe significant differences in the heat transfer coefficient between the top and bottom walls of the channel flow, due to natural convection, and unstable plumes. We further quantify the buoyancy forces along the channel flow through evaluation of the Richardson number. Simulations show that with a higher negative Richardson number, there are more unstable structures along the channel, resulting in enhanced mixing. Furthermore, we demonstrate the existence of gas-like, liquid-like, and the possibility of pseudo-two-phase regimes in the supercritical fluid. The pseudo-two-phase regime occurs when the range of fluid temperatures is crossing the pseudo-critical line, also known as the Widom line. The density of the fluid varies significantly near the Widom line, and further influences the natural convection and heat transfer in the flow.

42 ENGINEERING↗
DOE OSTI2022

Comparison of planetary boundary layer height from ceilometer with ARM radiosonde data

Abstract. Ceilometer measurements of aerosol backscatter profiles have been widely used to provide continuous planetary boundary layer height (PBLHT) estimations. To investigate the robustness of ceilometer-estimated PBLHT under different atmospheric conditions, we compared ceilometer- and radiosonde-estimated PBLHTs using multiple years of U.S. Department of Energy (DOE) Atmospheric Radiation Measurement (ARM) ceilometer and balloon-borne sounding data at ARM fixed-location atmospheric observatories and from ARM mobile facilities deployed around the world for various field campaigns. These observatories cover from the tropics to the polar regions and over both ocean and land surfaces. Statistical comparisons of ceilometer-estimated PBLHTs from the Vaisala CL31 ceilometer data with radiosonde-estimated PBLHTs from the ARM PBLHT-SONDE Value-added Product (VAP) are performed under different atmospheric conditions including stable and unstable atmospheric boundary layer, low-level cloud-free conditions, and cloudy conditions at these ARM observatories. Under unstable conditions, good comparisons are found between ceilometer- and radiosonde-estimated PBLHTs at ARM low- and mid-latitude land observatories. However, it is still challenging to obtain reliable PBLHT estimations over ocean surfaces even using radiosonde data. Under stable conditions, ceilometer- and radiosonde-estimated PBLHTs have weak correlations. We compare different PBLHT estimations utilizing the Heffter, the Liu–Liang, and the bulk Richardson number methods applied to radiosonde data with ceilometer-estimated PBLHT. We find that ceilometer-estimated PBLHT compares better with the Liu–Liang method under unstable conditions and compares better with the bulk Richardson number method under stable conditions.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2017

Stability, intermittency and universal Thorpe length distribution in a laboratory turbulent stratified shear flow

Stratified shear flows occur in many geophysical contexts, from oceanic overflows and river estuaries to wind-driven thermocline layers. In this study, we explore a turbulent wall-bounded shear flow of lighter miscible fluid into a quiescent fluid of higher density with a range of Richardson numbers $0.05\lesssim Ri\lesssim 1$ . In order to find a stability parameter that allows close comparison with linear theory and with idealized experiments and numerics, we investigate different definitions of $Ri$ . We find that a gradient Richardson number defined on fluid interface sections where there is no overturning at or adjacent to the maximum density gradient position provides an excellent stability parameter, which captures the Miles–Howard linear stability criterion. For small $Ri$ the flow exhibits robust Kelvin–Helmholtz instability, whereas for larger $Ri$ interfacial overturning is more intermittent with less frequent Kelvin–Helmholtz events and emerging Holmboe wave instability consistent with a thicker velocity layer compared with the density layer. We compute the perturbed fraction of interface as a quantitative measure of the flow intermittency, which is approximately 1 for the smallest $Ri$ but decreases rapidly as $Ri$ increases, consistent with linear theory. For the perturbed regions, we use the Thorpe scale to characterize the overturning properties of these flows. The probability distribution of the non-zero Thorpe length yields a universal exponential form, suggesting that much of the overturning results from increasingly intermittent Kelvin–Helmholtz instability events. Finally, the distribution of turbulent kinetic energy, conditioned on the intermittency fraction, has a similar form, suggesting an explanation for the universal scaling collapse of the Thorpe length distribution.

58 GEOSCIENCES↗