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Results for “RICHARDSON NUMBER”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 19 records
All sourcesNASA NTRSDOE OSTI
NASA NTRS1992

Investigation of a co-flowing buoyant jet - Experiments on the effect of Reynolds number and Richardson number

The behavior of a vertical jet of helium issuing into a co-flow of air at a fixed exit velocity ratio of 2 was investigated experimentally over a wide range of governing parameters with emphasis on flow structure and the scaling properties of the natural frequency of the jet. The experiments were conducted in a variable-pressure facility, which made it possible to vary the Reynolds number and the Richardson number independently. At all the experimental conditions studied, the flow exhibits a strong self-excited periodicity. A buoyancy Strouhal number is defined and used to correlate frequency data from the approximately seventy different Reynolds and Richardson numbers studied. The buoyancy Strouhal number is found to be nearly independent of Reynolds number and Richardson number for Richardson numbers greater than one.

Subbarao, E. R.↗
NASA NTRS1989

The effects of Reynolds number and Richardson number on the structure of a vertical co-flowing buoyant jet

The behavior of a vertical jet of helium issuing into a coflow of air at a fixed exit velocity ratio of 2.0 has been studied for various Reynolds numbers and Richardson numbers. It is found that the transition to turbulence is very sudden and that the point of transition moves closer to the jet exit as either the Reynolds number or the Richardson number increases. Under most of the conditions considered, the flow exhibits a strong periodic longitudinal instability whose wavelength increases with Richardson number.

Subbarao, E. R.↗
NASA NTRS1985

Perturbations of the Richardson number field by gravity waves

An analytic solution is presented for a stratified fluid of arbitrary constant Richardson number. By computer aided analysis the perturbation fields, including that of the Richardson number can be calculated. The results of the linear analytic model were compared with nonlinear simulations, leading to the following conclusions: (1) the perturbations in the Richardson number field, when small, are produced primarily by the perturbations of the shear; (2) perturbations of in the Richardson number field, even when small, are not symmetric, the increase being significantly larger than the decrease (the linear analytic solution and the nonlinear simulations both confirm this result); (3) as the perturbations grow, this asymmetry increases, but more so in the nonlinear simulations than in the linear analysis; (4) for large perturbations of the shear flow, the static stability, as represented by N2, is the dominating mechanism, becoming zero or negative, and producing convective overturning; and (5) the convectional measure of linearity in lee wave theory, NH/U, is no longer the critical parameter (it is suggested that (H/u sub 0) (du sub 0/dz) takes on this role in a shearing flow).

Wurtele, M. G.↗
NASA NTRS1984

Numerical studies of baroclinic instability at small Richardson number

Baroclinic instability at small Richardson number consists of competition between symmetric (Solberg) modes, zonal (Eady) modes, and possibly other modes whose orientation is neither symmetric nor zonal. In FY-84, a study of the fully nonlinear development and energetics of the symmetric modes was completed. The nonlinear effects were quite strong and, in some senses, unexpected. Secondly, a study of the dependency of the energetics of the symmetric modes upon the physical parameters was completed.

Miller, T. L.↗
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↗
NASA NTRS1981

Case studies of clear air turbulence using the diagnostic Richardson Number Tendency formulation

The results of four case studies of clear air turbulence (CAT) using the diagnostic Richardson number tendency (DRT) formulation are highlighted. The performance of this technique in resolving regions of documented CAT encounters is encouraging. Its operational adaptability appears particularly attractive in that input data can be supplied by the currently operational rawinsonde system. Two CAT indices are calculated deterministically, sensing synoptic scale changes in static stability and vertical wind shear conductive for supporting mesoscale CAT layers. These two indices reveal volumes of the troposphere which act as source regions for patches of CAT. The first, the time to reach the critical Richardson number necessary for the initiation of turbulent conditions, was first used by Oard (1974). A second index is devised which is an adaptation of Roach's (1970) work relating synoptic scale and mesoscale energetical coupling and gives more information on the relative intensity of these source regions. The output from the DRT computer module highlights specific regions of the atmosphere which can be interpreted operationally in terms of a CAT encounter probability.

Keller, J. L.↗
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↗
NASA NTRS2020

A Second-Order Closure Turbulence Model: New Heat Flux Equations and No Critical Richardson Number

We formulate a new second-order closure turbulence model by employing a recent closure for the pressure-temperature correlation at the equation level. As a result, we obtain new heat flux equations that avoid the long-standing issue of a finite critical Richardson number. The new, structurally simpler model improves on the Mellor-Yamada 1982 and Galperin et al. 1988 models; key feature includes enhanced mixing under stable conditions facilitating agreement with observational, experimental and high-resolution numerical data sets. The model predicts a planetary boundary layer height deeper than predicted by models with low critical Richardson numbers, as demonstrated in single column model runs of the GISS ModelE general circulation model.

second-order closure turbulence model↗
NASA NTRS1983

Three-dimensional baroclinic instability of a Hadley cell for small Richardson number

For the case of a baroclinic flow whose Richardson number, Ri, is of order unity, a three-dimensional linear stability analysis is conducted on the basis of a model for a thin, horizontal, rotating fluid layer which is subjected to horizontal and vertical temperature gradients. The Hadley cell basic state and stability analysis are both based on the Navier-Stokes and energy equations, and perturbations possessing zonal, meridional, and vertical structures are considered. An attempt is made to extend the previous theoretical work on three-dimensional baroclinic instability for small Ri to a more realistic model involving the Prandtl and Ekman numbers, as well as to finite growth rates and a wider range of the zonal wavenumber. In general, it is found that the symmetric modes of maximum growth are not purely symmetric, but have a weak zonal structure.

Antar, B. N.↗
NASA NTRS1985

Three-dimensional baroclinic instability of a Hadley cell for small Richardson number

A three-dimensional, linear stability analysis of a baroclinic flow for Richardson number, Ri, of order unity is presented. The model considered is a thin horizontal, rotating fluid layer which is subjected to horizontal and vertical temperature gradients. The basic state is a Hadley cell which is a solution of the complete set of governing, nonlinear equations and contains both Ekman and thermal boundary layers adjacent to the rigid boundaries; it is given in a closed form. The stability analysis is also based on the complete set of equations; and perturbation possessing zonal, meridional, and vertical structures were considered. Numerical methods were developed for the stability problem which results in a stiff, eighth-order, ordinary differential eigenvalue problem. The previous work on three-dimensional baroclinic instability for small Ri was extended to a more realistic model involving the Prandtl number, sigma, and the Ekman number, E, and to finite growth rates and a wider range of the zonal wavenumber.

Antar, B. N.↗
NASA NTRS1981

Forecasting of Clear Air Turbulence using a Diagnostic Richardson Number Tendency formulation

The results of several case studies of Clear Air Turbulence (CAT) using the Diagnostic Richardson Number Tendency (DRT) formulation are highlighted. The performance of this technique in resolving regions of documented CAT encounters is encouraging. Its operational adaptability seems particularly attractive in that the input data can be supplied by the currently operational Rawinsonde system. A CAT index is calculated deterministically, sensing synoptic-scale changes in static stability and vertical wind shear conducive for supporting meso-scale CAT layers. This index reveals volumes of the troposphere which act as 'source regions' of Kelvin-Helmholtz instabilities. The results suggest that these regions are particularly efficient with respect to the synoptic/meso-scale energetical coupling necessary for supporting significantly turbulent layers. The output highlights specific regions of the atmosphere which can be interpreted operationally in terms of CAT-encounter probabilities.

Keller, J. L.↗
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↗
NASA NTRS1984

Laboratory studies of baroclinic instability at small Richardson number

As part of the support program for the Atmospheric General Circulation Experiment, laboratory studies of baroclinic and other convective instabilities were performed for a thin layer of fluid between thermally conducting horizontal discs. There were three types of modes identified. The first has a spiral-arm appearance, and exists for large enough horizontal thermal forcing, weak enough static stability, and large enough rotation. The source of this wave is shown to be the Eady mode of instability. The second mode is due to convective instability in the thermal boundary layers which exist due to the thermally conducting horizontal boundaries. Finally, for strong enough negative static stability, thermal convection of the Benard type appears. The most significant result is that the symmetric (Solberg) mode was not found, even though the infinite-plane theory predicts this mode under certain experimental conditions.

Miller, T. L.↗
NASA NTRS1991

Hourly observations of the jet stream - Wind shear, Richardson number and pilot reports of turbulence

Results are presented of observations of the jet stream made on the basis of over 400 hr of wind and temperature data taken during two prolonged jet stream passages above western and central Pennsylvania during mid-November 1986 and mid-January 1987. Wind profilers are found to be far better suited for the detailed examination of jet stream structure than are weather balloons. The combination of good vertical resolution with not previously obtained temporal resolution reveals structural details not seen before. Development of probability forecasts of turbulence based on wind profiler-derived shear values appears possible. A good correlation between pilot reports and turbulence and wind shear is found.

Syrett, William J.↗
NASA NTRS1995

Computation of three-dimensional mixed convective boundary layer flow

The paper presents the numerical solution of heat and mass transfer during cross-flow (orthogonal) mixed convection. In this class of flow, a buoyancy-driven transport in the vertical direction and a forced convective flow in the horizontal direction results in a three-dimensional boundary layer structure adjacent to the plate. The rates of heat and mass transfer are determined by a combined influence of the two transport processes. The equations for the conservation of mass, momentum, energy, and species concentration were solved along with appropriate boundary conditions to determine the distributions of velocity components, temperature, and concentration across the thickness of the boundary layer at different locations on the plate. Results were expressed in dimensionless form using Reynolds number, Richardson number for heat transfer, Richardson number for mass transfer, Prandtl number, and Schmidt number as parameters. It was found that the transport is dominated by buoyancy at smaller vertical locations and at larger distances away from the forced convection leading edge. Effects of forced convection appeared to be very strong at smaller horizontal distances from the leading edge. The cross stream forced convection enhanced the rate of heat and mass transfer by a very significant amount.

Gadepalli, Prashandt↗