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Showing papers on "Turbulence published in 1978"


Journal Article
01 Jun 1978
TL;DR: In this paper, the authors evaluated the applicability of the standard κ-ϵ equations and other turbulence models with respect to their applicability in swirling, recirculating flows.
Abstract: The standard κ-ϵ equations and other turbulence models are evaluated with respect to their applicability in swirling, recirculating flows. The turbulence models are formulated on the basis of two separate viewpoints. The first perspective assumes that an isotropic eddy viscosity and the modified Boussinesq hypothesis adequately describe the stress distributions, and that the source of predictive error is a consequence of the modeled terms in the κ-ϵ equations. Both stabilizing and destabilizing Richardson number corrections are incorporated to investigate this line of reasoning. A second viewpoint proposes that the eddy viscosity approach is inherently inadequate and that a redistribution of the stress magnitudes is necessary. Investigation of higher-order closure is pursued on the level of an algebraic stress closure. Various turbulence model predictions are compared with experimental data from a variety of isothermal, confined studies. Supportive swirl comparisons are also performed for a laminar flow case, as well as reacting flow cases. Parallel predictions or contributions from other sources are also consulted where appropriate. Predictive accuracy was found to be a partial function of inlet boundary conditions and numerical diffusion. Despite prediction sensitivity to inlet conditions and numerics, the data comparisons delineate the relative advantages and disadvantages of the various modifications. Possible research avenues in the area of computational modeling of strongly swirling, recirculating flows are reviewed and discussed.

5,396 citations


Proceedings ArticleDOI
01 Jan 1978
TL;DR: In this article, an algebraic turbulence model for two-and three-dimensional separated flows is specified that avoids the necessity for finding the edge of the boundary layer, and compared with experiment for an incident shock on a flat plate, separated flow over a compression corner, and transonic flow over an airfoil.
Abstract: An algebraic turbulence model for two- and three-dimensional separated flows is specified that avoids the necessity for finding the edge of the boundary layer. Properties of the model are determined and comparisons made with experiment for an incident shock on a flat plate, separated flow over a compression corner, and transonic flow over an airfoil. Separation and reattachment points from numerical Navier-Stokes solutions agree with experiment within one boundary-layer thickness. Use of law-of-the-wall boundary conditions does not alter the predictions significantly. Applications of the model to other cases are contained in companion papers.

3,701 citations


Journal ArticleDOI
TL;DR: In this article, a new three-dimensional cloud model was developed for investigating the dynamic character of convective storms, which solved the compressible equations of motion using a splitting procedure which provided numerical efficiency by treating the sound wave modes separately.
Abstract: A new three-dimensional cloud model has been developed for investigating the dynamic character of convective storms. This model solves the compressible equations of motion using a splitting procedure which provides numerical efficiency by treating the sound wave modes separately. For the subgrid turbulence processes, a time-dependent turbulence energy equation is solved which depends on local buoyancy, shear and dissipation. First-order closure is applied to nearly conservative variables with eddy coefficients based on the computed turbulence energy. Open lateral boundaries are incorporated in the model that respond to internal forcing and permit gravity waves to propagate out of the integration domain with little apparent reflection. Microphysical processes are included in the model using a Kessler-type parameterization. Simulations conducted for an unsheared environment reveal that the updraft temperatures follow a moist adiabatic lapse rate and that the convection is dissipated by water loadin...

1,453 citations


Journal ArticleDOI
TL;DR: In this paper, the interaction and coalescence of vortex rings in the transition region of a round jet were investigated for a range of Reynolds numbers by using flow-visualization and hotwire techniques.
Abstract: Late transitional and turbulent flows in the mixing-layer region of a round jet are investigated for a range of Reynolds numbers by using flow-visualization and hotwire techniques. Attention is focused on the vortices in the transition region and the large eddies in the turbulent region. The interaction and coalescence of vortex rings in the transition region are described. The transition region is characterized by a growth of three-dimensional flow due to a wave instability of the cores of the vortex rings. The merging of these distorted vortices produces large eddies which can remain coherent up to the end of the potential-core region of the jet. A conditional sampling technique is used to measure eddies moving near the jet centre-line. These eddies differ significantly from the ring vortices as they are three-dimensional and contain irregular small-scale turbulence. However, when averaged, their structure is similar in cross-section to that of a vortex ring. These sampled eddies contribute greatly to local velocity fluctuations and statistical correlations. The experiments indicate a need for careful consideration of the meanings of terms such as ‘vortex’, ‘eddy’ and ‘turbulent flow’. In particular care must be taken to discriminate between the orderly, easily visualized, vortices in the transition regions of free shear flows and the less clearly visualized, but strong, large eddies in the fully developed turbulent regions.

497 citations


Journal ArticleDOI
TL;DR: In this article, a high-order model is proposed for the study of the 24-hour evolution of clear planetary boundary layers, which includes the rate equations of correlations up to the third order, but it also takes into account interactions between radiative transfer and turbulence in order to achieve a physically reasonable description of the nocturnal structure of the boundary layer.
Abstract: A high-order model is proposed for the study of the 24 h evolution of clear planetary boundary layers. The model includes the rate equations of correlations up to the third order, as required for an accurate description of daytime convective phenomena, but it also takes into account interactions between radiative transfer and turbulence in order to achieve a physically reasonable description of the nocturnal structure of the boundary layer. This numerical model is tested against the Wangara boundary layer data of Day 33 and Night 33–34 (Clarke et al., 197l). The computed daytime mean structure of the boundary layer compares favorably with the Wangara data, while the daytime turbulent structure, expressed in the framework of the convective similarity theory, is in particularly good quantitative agreement with a number of experimental and numerical data concerning convection in the boundary layer, with particular concern to the production of turbulence at the top of the mixed layer. The computed no...

384 citations


Journal ArticleDOI
TL;DR: In this paper, a second-order turbulence model is used to study the stable boundary layer (SBL) over a horizontal surface, a constant surface cooling rate drives the SBL to a steady state within a few hours.
Abstract: A second-order turbulence model is used to study the stable boundary layer (SBL). Over a horizontal surface, a constant surface cooling rate drives the SBL to a steady state within a few hours. Parameterizations are developed for eddy diffusivities, the kinetic energy dissipation rate and the geostrophic drag law in this idealized case. Over a sloped surface, a constant cooling rate produces a quasi-steady-state SBL in which some flow properties continue to vary but h(|f|/u*L)½ becomes constant; however, this constant is a function of the wind direction relative to the slope and the baroclinity, as measured by the cooling rate times the slope. Calculated eddy diffusivity profiles in the baroclinic (sloping terrain) case compare well with recent data from Antarctica. If a surface energy budget is used rather than a constant cooling rate, the SBL does not reach a steady state even over a horizontal surface; the nondimensional height slowly decays. We conclude that equilibrium models of the SBL are ...

370 citations


Journal ArticleDOI
TL;DR: In this paper, boundary layer theory and spectral methods are used to predict turbulence near wind-tunnel walls and near flat plates placed parallel to the flow, where the turbulence is assumed to be weak, i.e. the streamwise co-ordinate, kinematic viscosity and mean velocity respectively.
Abstract: Grid turbulence convected by a free stream past a rigid surface moving at the same speed as the free stream is analysed by boundary-layer theory and spectral methods. The turbulence is assumed to be weak, i.e. are the streamwise co-ordinate, kinematic viscosity and mean velocity respectively. Here the turbulent velocity decays to zero at the surface. Spectra variances and cross-correlations are calculated and found to compare well with measurements of turbulence near moving walls by Uzkan & Reynolds (1967) and Thomas & Hancock (1977).The results of this theory are shown to have a number of applications including the prediction of turbulence near wind-tunnel walls and near flat plates placed parallel to the flow.

368 citations


Journal ArticleDOI
TL;DR: In this paper, the decay rate of passive temperature fluctuations produced by heating the grid is a function of the initial temperature fluctuation intensity, which is determined by the wave number of initial temperature fluctuations.
Abstract: Previous measurements of the decay rate of the fluctuation intensity of passive scalars in grid-generated turbulence show large variation. New results presented here show that the decay rate of passive temperature fluctuations produced by heating the grid is a function of the initial temperature fluctuation intensity. Although a full reason for this is wanting, spectra of the temperature fluctuations show that, by varying the heat applied to the grid, the wavenumber of the maximum in the temperature spectrum changes, indicating that the geometry of the thermal fluctuations is being altered in some way. In these experiments the one-dimensional temperature spectrum shows an anomalous slope. In order to eliminate the dependence of the decay rate of the temperature fluctuations on their intensity, we describe a new way of generating temperature fluctuations by means of placing a heated parallel array of fine wires (a mandoline) downstream from the unheated grid. Results of this experiment show that the decay rate of passive thermal fluctuations is uniquely determined by the wave-number of the initial temperature fluctuations. In this type of flow there appears to be no equilibrium value for the thermal fluctuation decay rate and hence for the mechanical/thermal time-scale ratio since the thermal fluctuation decay rate does not change within the tunnel length, which is the equivalent of nearly one turbulence decay time.

367 citations


Journal ArticleDOI
TL;DR: In this paper, the spectral distributions of the fluctuations in velocity are quantitatively related to the dimensions of the two unequal regions of flow recirculation, and it is shown that the intensity of fluctuating energy in these low Reynolds number flows can be larger than that in corresponding turbulent flows.
Abstract: Flow visualization and laser-Doppler anemometry have been used to provide a detailed description of the velocity characteristics of the asymmetric flows which form in symmetric, two-dimensional, plane, sudden-expansion geometries. The flow and geometry boundary conditions which give rise to asymmetric flow are indicated, and the reason for the phenomenon is shown to lie in disturbances generated at the edge of the expansion and amplified in the shear layers. The spectral distributions of the fluctuations in velocity are quantitatively related to the dimensions of the two unequal regions of flow recirculation. It is also shown that the intensity of fluctuating energy in these low Reynolds number flows can be larger than that in corresponding turbulent flows.

350 citations


Journal ArticleDOI
TL;DR: The existence of universal similarity of the fine-scale structure of turbulent velocity fields and the validity of the original Kolmogorov local similarity theory and the later reformulations were investigated in this paper.
Abstract: The existence of universal similarity of the fine-scale structure of turbulent velocity fields and the validity of the original Kolmogorov local similarity theory and the later reformulations were investigated. Recent studies of the fine-scale velocity field for many different flows, e.g. grid flows, wakes, jets and the atmospheric boundary layer, are shown to provide considerable evidence for the existence of Kolmogorov normalized spectral shapes which are universal in the sense that they describe the high wave-number spectral behaviour of all turbulent flow fields with a similar value of the turbulence Reynolds number Rλ. The normalized spectral shapes vary with Rλ in a manner consistent with the later reformulations. The Reynolds number dependence of the normalized spectra is demonstrated for the Rλ range from about 40 to 13 000. Expressions for the Kolmogorov normalized spectral functions are presented for three values of Rλ. Also revealed in this study is the importance of considering effects on spectra caused by deviations from Taylor's approximation in high intensity turbulent flows. Lumley's (1965) model is used to correct the high frequency portion of the measured one-dimensional spectra for these effects. An analytical solution to Lumley's expression is presented and applied to the data.

301 citations


Journal ArticleDOI
TL;DR: In this article, it was shown that the eddy viscosity for very stable conditions does not take the infinitesimally small value predicted from extrapolation of the so-called log-linear profile, and that the flux Richardson number has a limit in the range of 0.1-0.4, although the gradient Richardson number can become indefinitely large.
Abstract: Transfers of heat and momentum under strongly stable conditions in the atmospheric boundary layer have been studied through measurements of the turbulent fluctuations and vertical mean profiles of wind velocity and air temperature. As the local gradient Richardson number increases, intermittent turbulence appears, especially in temperature fluctuations. The ratio of the eddy conductivity to the eddy viscosity decreases with increasing Richardson number and tends to zero at high stabilities. The local value of the dimensionless shear function for wind velocity does not exceed a limit of about six. These results imply that the eddy viscosity for very stable conditions does not take the infinitesimally small value predicted from extrapolation of the so-called log-linear profile, and that the flux Richardson number has a limit in the range of 0.1–0.4, although the gradient Richardson number can become indefinitely large. It is also shown that the divergences of both the radiative and turbulent heat f...

Journal ArticleDOI
TL;DR: This review focusses on the wire-gauze screen, with brief consideration of other types of screen.
Abstract: Control of the velocity distribution of a fluid flow is a fundamental problem In engineering fluid mechanics. The possible consequences for the operation and efficiency of downstream components need no emphasis here. Ability to control the flow is also necessary in component testing where, for results to be meaningful, test conditions must reproduce the composite flow situation. A screen may be used in both these operational modes to remove or create time-mean velocity nonuniformities, change the flow direction, and reduce or increase the scale and intensity of turbulence in a controlled manner. A screen may be thought of as any distributed resistance that effects a change in flow direction and a reduction in pressure. Common examples of screens for aerodynamic applications are arrays of parallel rods, honeycombs, perforated plates, and wire-gauze screens. This review focusses on the wire-gauze screen, with brief consideration of other types of screen. A survey of the available literature on the topic of flow through screens divides roughly into three categories:

Journal ArticleDOI
TL;DR: In this article, a self contained review of recent progress of the statistical theory of fully developed turbulence is given, focusing on both analogies and differences with Hamiltonian statistical mechanics, in particular critical phenomena.
Abstract: This paper gives a self contained review of some recent progress of the statistical theory of fully developed turbulence. The emphasis is on both analogies and differences with Hamiltonian statistical mechanics, in particular critical phenomena. The method of spectral equations, which plays to a certain extent the role of a mean field theory, is discussed in detail. It is here viewed as a reformulation of the Kolmogorov 1941 theory leading to quantitative insight into the energetics of turbulence (power-law spectra, direct and inverse energy cascades, energy dissipation in the limit of zero viscosity, etc.). In addition, it sheds light on the proven and conjectured properties of the Navier-Stokes and Euler equations which are reviewed in terms more accessible than those of the mathematical literature. There are strong experimental indications (intermittency) that the Kolmogorov 1941 theory is only approximate. Some of the current efforts to handle higher than second order statistics by formal methods inspired from quantum field theory or critical phenomena are also discussed.

Journal ArticleDOI
TL;DR: In this article, an ensemble average is fitted to a conical growth law by using data at three streamwise stations to determine the virtual origin in x and t and the two-dimensional unsteady stream function is expressed as ψ=U^2_∞tg(ξ,η) in conical similarity co-ordinates.
Abstract: Laser-Doppler velocity measurements in water are reported for the flow in the plane of symmetry of a turbulent spot. The unsteady mean flow, defined as an ensemble average, is fitted to a conical growth law by using data at three streamwise stations to determine the virtual origin in x and t. The two-dimensional unsteady stream function is expressed as ψ=U^2_∞tg(ξ,η) in conical similarity co-ordinates ζ = x/U_∞t and η = y/U_∞t. In these co-ordinates, the equations for the unsteady particle displacements reduce to an autonomous system. This system is integrated graphically to obtain particle trajectories in invariant form. Strong entrainment is found to occur along the outer part of the rear interface and also in front of the spot near the wall. The outer part of the forward interface is passive. In terms of particle trajectories in conical co-ordinates, the main vortex in the spot appears as a stable focus with celerity 0·77U_∞. A second stable focus with celerity 0·64U_∞ also appears near the wall at the rear of the spot. Some results obtained by flow visualization with a dense, nearly opaque suspension of aluminium flakes are also reported. Photographs of the sublayer flow viewed through a glass wall show the expected longitudinal streaks. These are tentatively interpreted as longitudinal vortices caused by an instability of Taylor-Gortler type in the sublayer.

Journal ArticleDOI
TL;DR: In this article, a three-dimensional model for calculating the distribution of velocity, temperature, and pollutant concentration in open channel flows, and a depth-averaged two-dimensional version for situations with insignificant stratification and secondary currents are presented.
Abstract: The paper describes a three-dimensional model for calculating the distribution of velocity, temperature, and pollutant concentration in open channel flows, and a depth-averaged two-dimensional version for situations with insignificant stratification and secondary currents. Both models are restricted to parabolic flows where influences cannot be transmitted upstream. The turbulent stresses and heat/concentration fluxes appearing in these equations are determined from the so-called k-ϵ turbulence model that solves differential transport equations for the turbulence kinetic energy k and the rate of its dissipation ϵ. In the depth-averaged model, the bottom shear stress, surface heat flux and turbulence production due to bottom shear are accounted for by source/sink terms in the relevant equations. The 3D calculations compare favorably with available measurements. The 2D and 3D predictions agree well for high Froude numbers; for a Froude number of 5 they agree only for the rough bed, while for the smooth bed they start to deviate significantly at a Froude number of 10.

Journal ArticleDOI
TL;DR: In this article, the effects of the initial condition on the characteristic measures of an axisymmetric air free shear layer were investigated experimentally, and it was found that the spread rate, similarity parameter, and peak turbulent intensity in the self-preserving region are essentially independent of Rϑe, but dependent on whether the initial boundary layer is laminar or tripped (turbulent).
Abstract: Spurred by large discrepancies among previous data on the free shear layer, effects of the initial condition on the characteristic measures of an axisymmetric air free shear layer were investigated experimentally. The initial, boundary layer state (i.e., laminar or turbulent), momentum thickness Reynolds number Rϑe, and fluctuation intensity u″pe/Ue have been taken as three characteristic identifiers of the initial condition. The discrepancies among published data are reviewed, and data showing the effects of variations in Rϑe (at constant u″pe/Ue) for both initially laminar and tripped (turbulent) boundary layers are reported. It is found that the spread rate, similarity parameter, and peak turbulent intensity in the self‐preserving region are essentially independent of Rϑe, but dependent on whether the initial boundary layer is laminar or tripped (turbulent). Initially, tripped shear layers manifest two stages of linear growth. The virtual origin as well as the distance required for attainment of self‐preservation depend noticeably and systematically on Rϑe. The mean velocity and turbulence intensity profiles appear to reach self‐similarity together when the initial boundary layer is laminar, but not when the initial boundary layer is turbulent.

Proceedings ArticleDOI
01 Feb 1978
TL;DR: In this article, the authors developed correlations for the ignition delay and combustion energy release intervals in a homogeneous charge, spark-ignited engine with four fundamental quantities: turbulent integral scale, turbulent micro-scale, turbulent intensity, and laminar flame speed.
Abstract: Correlations for the ignition delay and combustion energy release intervals in a homogeneous charge, spark-ignited engine are developed. After incorporation within a simplified engine cycle simulation, predicted values of these two combustion parameters are compared to experimental engine data. The correlations are based on four fundamental quantities--the turbulent integral scale, the turbulent micro-scale, the turbulent intensity, and the laminar flame speed. The major assumptions include: (1) the turbulent integral scale is proportional to the instantaneous chamber height prior to flame initiation; (2) angular momentum is conserved in the individual turbulent eddies ahead of the flame front (i.e., a ''rapid distortion'' turbulence model); and (3) the turbulent intensity scales with the mean piston speed. Two empirical constants scale the correlations to a given engine. Predicted values for the ignition delay and burn intervals show good agreement with experimental results for wide variations in engine operating and design conditions (e.g., engine speed and load, spark timing, EGR, air-fuel ratio, and compression ratio). In addition, the shapes of the predicted mass fraction burned curves agree well with published data.

Journal ArticleDOI
TL;DR: In this article, the authors used a stereo-photogrammetric system coupled with a stroboscope to study the particle motion near the bottom of a turbulent open channel flow.
Abstract: This study continues the investigation of particle motions near the bottom in a turbulent open channel flow, reported by Sumer & Oguz (1978; hereafter referred to as part 1). Paths of suspended heavy particles were recorded in three dimensions and in time, employing a stereo-photogrammetric system coupled with a stroboscope. In the case of smooth bottom, the measured kinematical quantities concerning the particle motions were found to be in accord with the available information on the ‘bursting process’. Agreement between the particle motion and the bursting process provided further support for the mechanism of particle suspension near the bottom proposed in part 1. Similar experiments were carried out when the bottom was rough. Comparison between the smooth- and rough-bottom cases could be made on the same basis as the flow Reynolds number as well as the particle properties were kept almost unchanged in both the smooth and rough boundary experiments. The observations showed that particle motions close to the rough bottom are very similar in character to those in the smooth-bottom case. The findings of the present paper suggested that the suspension mechanism given for the smooth-boundary flow could be extended to the rough-boundary case.

Journal ArticleDOI
TL;DR: In this paper, the Eady problem instability is associated with energy transfer both up and down the vertical wavenumber spectrum although energy transfer from small to large three-dimensional wavenumbers may occur over a finite range of the spectrum.
Abstract: Uniform potential vorticity flows are examined. In the quasi-geostrophic system, conservation of total energy and conservation of available potential energy on plane rigid horizontal boundaries imply a restriction on energy exchanges as a result of scale interactions. It is shown that for the Eady problem instability is always associated with energy transfer both up and down the vertical wavenumber spectrum although energy transfer from small to large three-dimensional wavenumbers may occur over a finite range of the spectrum. An inertial theory of two-dimensional turbulence is also presented. The formal analysis, based on Leith's diffusion approximation, predicts two inertial subranges: −5/3 and −1 power dependences on the horizontal wavenumber for available potential energy on horizontal boundaries. In the former range, available potential energy on horizontal boundaries cascades at a constant rate toward higher wavenumbers; in the latter range, the depth-integrated total energy cascades at a c...

Journal ArticleDOI
TL;DR: In this article, a semi-empirical solution of a convective diffusion model is presented in the form of an asymptotic series to permit an estimate of the transfer rate for.
Abstract: A study has been made of mass transfer to a circular disk electrode located in the stagnation region of an impinging jet. A semiempirical solution of a convective diffusion model is presented in the form of an asymptotic series to permit an estimate of the transfer rate for . Experimental results reveal that the electrode possesses a property of "uniform accessibility" to the diffusing species if the electrode radius is less than 1 nozzle diameter for turbulent jet and nozzle diameter for laminar jet. Within this region, the mass transfer is relatively independent of radial positions, and the semiempirical correlations are presented for both laminar and turbulent flows over a range of nozzle heights from 0.2 to 6 nozzle diameters. The result indicates that the impinging jet electrode is a feasible tool for electroanalytical applications. This geometry can be easily adopted in process streams and closed systems at a pressure other than the ambient atmosphere.

Journal ArticleDOI
TL;DR: In this paper, temperature and velocity fields in a round heated jet were investigated in detail, both conventional measurements and conditional measurements (zone averages and point averages) were performed, and the probability density functions of the lengths of turbulent and non-turbulent durations were also measured.
Abstract: The temperature and velocity fields in a round heated jet were investigated in detail. Both conventional measurements and conditional measurements (zone averages and point averages) were performed. The probability density functions of the lengths of turbulent and non-turbulent durations were also measured. Filtered correlation measurements show that large-scale turbulent motions were responsible for the bulk of momentum and heat transport, and also that small scales were more efficient in transporting heat than in transporting momentum. In no case was heat transported further or more than momentum, however. These results are discussed in detail, particularly with regard to the entrainment. Conservation equations for turbulent-zone variables and the intermittency factor are derived and a model for some of the resulting higher-order correlations is suggested. An exact equation for the intermittency function is presented.

Journal ArticleDOI
TL;DR: In this article, the authors developed procedures for gas sparged contractors for both low and high viscosity liquids to predict overall kLa, and showed that intense liquid mixing and high interfacial area can be achieved in low-viscosity liquids by gas-sparging alone.
Abstract: Design procedures for gas sparged contractors for both low and high viscosity liquids were developed to predict overall kLa. Bubble size close to the orifice, for moderately high gas rates, was found to increase at a rate proportional to one third power of gas rate and one tenth power of liquid viscosity. Bubble breakup phenomenon was shown to be related to liquid turbulence in the vessel rather than gas turbulence in the orifice. Procedures were developed through a simple liquid circulation model to obtain a criterion for the onset of bubble breakup. Results indicate that intense liquid mixing and high interfacial area can be achieved in low viscosity liquids by gas sparging alone. In high viscosity fluids, bubble breakup was not observed. The liquid circulation model predicts laminar flow at these experimental conditions over the complete range of gas rates observed.

Journal ArticleDOI
29 Jan 1978
TL;DR: In this article, the equations describing conservation of mass, momentum and energy in a turbulent free surface flow are derived for a controle volume extending over the whole depth, where the equations are applied to the energy balance in a surf zone wave motion.
Abstract: The equations describing conservation of mass, momentum and energy in a turbulent free surface flow are derived for a controle volume extending over the whole depth. The effect of the turbulent surface oscillations are discussed but neglected in the following analysis, where the equations are applied to the energy balance in a surf zone wave motion. This leads to results for the wave height variation and the velocity of propagation. The results cannot be reconciled completely with measurements and the concluding discussion is aimed at revealing how the model can be improved.

Journal ArticleDOI
TL;DR: In this paper, a simple theory based on the invariants and on the selection rules governing triad interactions qualitatively explains the major features of forced equilibrium flow, which is very similar to that of Rhines (1977).
Abstract: In the case of equal layer depths and uniform vertical energy density, the quadratic integral invariants of two-layer rotating flow are close analogs of the corresponding invariants of two-dimensional turbulence. A simple theory based on the invariants and on the selection rules governing triad interactions qualitatively explains the major features of forced equilibrium flow. The general physical picture is very similar to that of Rhines (1977). In the geophysically interesting case. net baroclinic energy is produced at low wavenumbers and moves toward hisher wavenumbers in relatively nonlocal triad interactions which are unhampered by the constraint to conserve enstrophy. The energy converts to barotropic mode and moves back toward low wavenumbers in more local interactions which are similar to those in two-dimensional turbulence. Equilibrium wavenumber spectra are obtainable from a simple Markovian turbulence closure model in which the estimate of turbulent scramhling rate includes a contributi...

Journal ArticleDOI
TL;DR: In this article, thermal turbulence in thin shear flows is re-examined in order to evaluate the ratio of the time scale of the scalar-fluctuation field to that of the velocity wave field and it is found that the ratio is nearly uniform with a value close to 0.5.
Abstract: Various studies of thermal turbulence in thin shear flows are re‐examined in order to evaluate the ratio of the time scale of the scalar‐fluctuation field to that of the velocity‐fluctuation field. In all cases considered it is found that the ratio is nearly uniform with a value close to 0.5.

Journal ArticleDOI
TL;DR: In this article, a distortion parameter of liquid films, which is a ratio of an allowable difference in surface tension to the dynamic pressure of uniform film flow, is derived for each laminar and turbulent film flow.


Journal ArticleDOI
TL;DR: The difficulty lies in the intractability of the nonlinear hydrodynamic equations that express the conservation of mass, momentum and energy for a fluid continuum as discussed by the authors, which can be linearized and readily solved for a system near thermodynamic equilibrium.
Abstract: Fluid flows have been studied systematically for more than a century and their equations of motion are well known, yet the transition from laminar flow to turbulent flow remains an enigma. The difficulty lies in the intractability of the nonlinear hydrodynamic equations that express the conservation of mass, momentum and energy for a fluid continuum. Although these equations can be linearized and readily solved for a system near thermodynamic equilibrium, the solutions of the nonlinear equations—required to describe fluids far from equilibrium—are generally neither unique nor obtainable.

Journal ArticleDOI
TL;DR: In this paper, an experimental and computational investigation of the steady and unsteady transonic flowfields about a thick airfoil is described, and an operational computer code for solving the two-dimensional, compressible NavierStokes equations for flow over airfoils was modified to include solid-wall, slip-flow boundary conditions to properly assess the code and help guide the development of improved turbulence models.
Abstract: An experimental and computational investigation of the steady and unsteady transonic flowfields about a thick airfoil is described. An operational computer code for solving the two-dimensional, compressible NavierStokes equations for flow over airfoils was modified to include solid-wall, slip-flow boundary conditions to properly assess the code and help guide the development of improved turbulence models. Steady and unsteady fiowfieids about an 18% thick circular arc airfoil at Mach numbers of 0.720, 0.754, and 0.783 and a chord Reynolds number of 11 x 10 are predicted and compared with experiment. Results from comparisons with experimental pressure and skin-friction distributions show improved agreement when including test-section wall boundaries in the computations. Steady-flow results were in good quantitative agreement with experimental data for flow conditions which result in relatively small regions of separated flow. For flows with larger regions of separated flow, improvements in turbulence modeling are required before good agreement with experiment will be obtained. For the first time, computed results for unsteady turbulent flows with separation caused by a shock wave were obtained which qualitatively reproduce the time-dependent aspects of experiments. Features such as the intensity and reduced frequency of airfoil surface-pressure fluctuations, oscillatory regions of trailing-edge and shock-induced separation, and the Mach number range for unsteady flows were all qualitatively reproduced.

Journal Article
TL;DR: In this paper, the impulse response of boundary layers to step increases of curvature has been investigated in low-speed turbulent boundary layers on flat surfaces downstream of concave or convex bends with turning angles of 20 or 30 degrees.
Abstract: Measurements, including one-point double, triple or quadruple mean products of velocity fluctuations, have been made in low-speed turbulent, boundary layers on flat surfaces downstream of concave or convex bends with turning angles of 20 or 30 degrees, the length of the curved region being at most 6 times the boundary-layer thickness at entry. These short bends approximate to ‘impulses’ of curvature, and the object of the work was to investigate the impulse response of the boundary layer, essentially the decay of structural changes downstream of the bends. The work can be regarded as a sequel, with much more detailed measurements, to the study by So & Mellor (1972, 1973, 1975) who investigated the response to step increases of curvature: turbulent boundary layers being nonlinear systems, responses to several kinds of curvature history are needed to assemble an adequate description of the flow. The most striking feature of the ‘impulse’ response is that the decay of the high turbulent intensity found at exit from the concave bends is not monotonic; the Reynolds stresses in the outer layer collapse to well below the level at entry, and are still falling slowly at the end of the test rig although in principle they must recover eventually. On the convex (stabilized) side the flow recovers, monotonically in the main, from a low level of turbulent intensity at the exit. The pronounced second-order response on the concave side can be explained qualitatively by interaction between the shear stress and the mean shear and is not peculiar to curved flows, but in the present cases the response is complicated by large changes in the dimensionless structure parameters related to double or triple mean products of velocity fluctuations. Strong spanwise variations, due presumably to longitudinal vortices, further complicate the flow in the concave bends, and decay only very slowly downstream.