Showing papers on "Reynolds number published in 1991"

A dynamic subgrid‐scale model for compressible turbulence and scalar transport

Abstract: The dynamic subgrid-scale (SGS) model of Germano et al. (1991) is generalized for the large eddy simulation (LES) of compressible flows and transport of a scalar. The model was applied to the LES of decaying isotropic turbulence, and the results are in excellent agreement with experimental data and direct numerical simulations. The expression for the SGS turbulent Prandtl number was evaluated using direct numerical simulation (DNS) data in isotropic turbulence, homogeneous shear flow, and turbulent channel flow. The qualitative behavior of the model for turbulent Prandtl number and its dependence on molecular Prandtl number, direction of scalar gradient, and distance from the wall are in accordance with the total turbulent Prandtl number from the DNS data.

The spatial structure and statistical properties of homogeneous turbulence

Abstract: A direct numerical simulation at resolution 2403 is used to obtain a statistically stationary three-dimensional homogeneous and isotropic turbulent field at a Reynolds number around 1000 (Rλ ≈ 150). The energy spectrum displays an inertial subrange. The velocity derivative distribution, known to be strongly non-Gaussian, is found to be close to, but not, exponential. The nth-order moments of this distribution, as well as the velocity structure functions, do not scale with n as predicted by intermittency models. Visualization of the flow confirms the previous finding that the strongest vorticity is organized in very elongated thin tubes. The width of these tubes is of the order of a few dissipation scales, while their length can reach the integral scale of the flow.

A one-equation turbulence transport model for high Reynolds number wall-bounded flows

Abstract: A one-equation turbulence model that avoids the need for an algebraic length scale is derived from a simplified form of the standard k-epsilon model equations. After calibration based on well established properties of the flow over a flat plate, predictions of several other flows are compared with experiment. The preliminary results presented indicate that the model has predictive and numerical properties of sufficient interest to merit further investigation and refinement. The one-equation model is also analyzed numerically and robust solution methods are presented.

Low‐dimensional models for complex geometry flows: Application to grooved channels and circular cylinders

Abstract: Two‐dimensional unsteady flows in complex geometries that are characterized by simple (low‐dimensional) dynamical behavior are considered. Detailed spectral element simulations are performed, and the proper orthogonal decomposition or POD (also called method of empirical eigenfunctions) is applied to the resulting data for two examples: the flow in a periodically grooved channel and the wake of an isolated circular cylinder. Low‐dimensional dynamical models for these systems are obtained using the empirically derived global eigenfunctions in the spectrally discretized Navier–Stokes equations. The short‐ and long‐term accuracy of the models is studied through simulation, continuation, and bifurcation analysis. Their ability to mimic the full simulations for Reynolds numbers (Re) beyond the values used for eigenfunction extraction is evaluated. In the case of the grooved channel, where the primary horizontal wave number of the flow is imposed from the channel periodicity and so remains unchanged with Re, the models extrapolate reasonably well over a range of Re values. In the case of the cylinder wake, however, due to the significant spatial wave number changes of the flow with the Re, the models are only valid in a small neighborhood of the decompositional Reynolds number.

Theory of mean poloidal flow generation by turbulence

Abstract: The mechanism for generation of mean poloidal flow by turbulence is identified and elucidated. Two methods of calculating poloidal flow acceleration are given and shown to yield predictions which agree. These methods link flow generation to the quasilinear radial current or the Reynolds stress 〈VrVθ〉. It is shown that poloidal acceleration will occur if the turbulence supports radially propagating waves and if radial gradients in the turbulent Reynolds stress and wave energy density flux are present. In practice, these conditions are met in the tokamak edge region when waves propagate through the outermost closed flux surface or when convection cells with large radial correlation length are situated in steep gradient regions. The possible impact of these results on the theory of the L→H transition is discussed.

Inertial migration of a small sphere in linear shear flows

Abstract: The motion of a small, rigid sphere in a linear shear flow is considered. Saffman's analysis is extended to other asymptotic cases in which the particle Reynolds number based on its slip velocity is comparable with or larger than the square root of the particle Reynolds number based on the velocity gradient. In all cases, both particle Reynolds numbers are assumed to be small compared to unity. It is shown that, as the Reynolds number based on particle slip velocity becomes larger than the square root of the Reynolds number based on particle shear rate, the magnitude of the inertial migration velocity rapidly decreases to very small values. The latter behaviour suggests that contributions that are higher order in the particle radius may become important in some situations of interest.

Rotary oscillation control of a cylinder wake

Abstract: Exploratory experiments have been performed on circular cylinders executing forced rotary oscillations in a steady uniform flow. Flow visualization and wake profile measurements at moderate Reynolds numbers have shown that a considerable amount of control can be exerted over the structure of the wake by such means. In particular, a large increase, or decrease, in the resulting displacement thickness, estimated cylinder drag, and associated mixing with the free stream can be achieved, depending on the frequency and amplitude of oscillation.

On the Nature of Turbulence in a Stratified Fluid. Part I: The Energetics of Mixing

Abstract: The definition of the flux Richardson number Rf is generalized to be the ratio of the turbulent buoyancy flux b to the net turbulent mechanical energy m available from all sources. For mechanically energized turbulence where turbulence kinetic energy is used to sustain an upward buoyancy flux (b > 0), it is shown the magnitude of Rf is quantitatively determined by the location of the event in the FrT,–ReT where FrT and –ReT are the local instantaneous overturn Froude number and Reynolds number. In this parameter space the value of Rf varies between 0 and 0.20 for a fluid with Prandtl number greater than one, and between 0 and 0.15 for a fluid with a Prandtl number less than one. For turbulence sustained by a negative buoyancy flux (b < 0), such as penetrative convection in a cooling surface layer, it is shown that the flux Richardson number Rf is a fraction of depth below the surface Rf−1 varies between 0.55 at the surface and –∞ towards the base of the surface layer where the buoyancy flux vanis...

Reynolds number effects in Lagrangian stochastic models of turbulent dispersion

Abstract: A second‐order autoregressive equation is used to model the acceleration of fluid particles in turbulence in order to study the effect of Reynolds number on Lagrangian turbulence statistics. It is shown that this approach provides a good representation of dissipation subrange structure of Lagrangian velocity and acceleration statistics. The parameters of the model, two time scales representing the energy‐containing and dissipation scales, are determined by matching the model velocity autocorrelation function to Kolmogorov similarity forms in the inertial subrange and the dissipation subrange. The model is tested against the Lagrangian statistics obtained by Yeung and Pope [J. Fluid Mech. 207, 531 (1989)] from direct numerical simulations of turbulence. Agreement between the model predictions and simulation data for second‐order Lagrangian statistics such as the velocity structure function, the acceleration correlation function, and the dispersion of fluid particles is excellent, indicating that the main departures from Kolmogorov’s theory of local isotropy shown by the simulation data are due to low Reynolds number. For Reynolds numbers typical of laboratory experiments and direct numerical simulations of turbulence the root‐mean‐square dispersion of marked particles is changed from the Langevin equation (i.e., infinite Reynolds number) prediction by up to about 50% at large times. Most of this change can be accounted for by the change in the Lagrangian integral time scale. It is also shown that Reynolds number effects in laboratory dispersion or Lagrangian turbulence measurements can cause significant errors (typically of order 50%) when the value of the Kolmogorov Lagrangian structure function constant C0 is estimated by fitting the predictions of the Langevin equation to these data. A value C0 = 7 is obtained by fitting the new model to the direct simulation data.

On Local Isotropy of Passive Scalars in Turbulent Shear Flows

Abstract: An assessment of local isotropy and universality in high-Reynolds-number turbulent flows is presented. The emphasis is on the behaviour of passive scalar fields advected by turbulence, but a brief review of the relevant facts is given for the turbulent motion itself. Experiments suggest that local isotropy is not a natural concept for scalars in shear flows, except, perhaps, at such extreme Reynolds numbers that are of no practical relevance on Earth. Yet some type of scaling exists even at moderate Reynolds numbers. The relation between these two observations is a theme of this paper.

Experimental study of turbulent swirling flow in a straight pipe.

Abstract: Swirling flow through a pipe is a highly complex turbulent flow and is still challenging to predict. An experimental investigation is performed to obtain systematic data about the flow and to understand its physics. A free-vortex-type swirling flow is introduced in a long straight circular pipe. The swirling component decays downstream as a result of wall friction. The velocity distributions are continuously changing as they approach fully developed parallel flow. The swirl intensity Ω, defined as a non-dimensional angular momentum flux, decays exponentially. The decay coefficients, however, are not constant as conventionally assumed, but depend on the swirl intensity. The wall shear stresses are measured by a direct method and, except in a short inlet region, are a function only of the swirl intensity and the Reynolds number. The velocity distributions and all Reynolds stress components are measured at various axial positions in the pipe. The structure of the tangential velocity profile is classified into three regions: core, annular and wall regions. The core region is characterized by a forced vortex motion and the flow is dependent upon the upstream conditions. In the annular region, the skewness of the velocity vector is noticeable and highly anisotropic so that the turbulent viscosity model does not work well here. The tangential velocity is expressed as a sum of free and forced vortex motion. In the wall region the skewness of the flow becomes weak, and the wall law modified by the Monin–Oboukhov formula is applicable. Data on the microscale and the spectrum are also presented and show quite different turbulence structures in the core and the outer regions.

On the dynamics of near-wall turbulence

Abstract: A model of the dynamic physical processes that occur in the near-wall region of a turbulent flow at high Reynolds numbers is described The hairpin vortex is postulated to be the basic flow structure of the turbulent boundary layer It is argued that the central features of the near-wall flow can be explained in terms of how asymmetric hairpin vortices interact with the background shear flow, with each other, and with the surface layer near the wall The physical process that leads to the regeneration of new hairpin vortices near the surface is described, as well as the processes of evolution of such vortices to larger-scale motions farther from the surface The model is supported by recent important developments in the theory of unsteady surface-layer separation and a number of `kernel' experiments which serve to elucidate the basic fluid mechanics phenomena believed to be relevant to the turbulent boundary layer Explanations for the kinematical behaviour observed in direct numerical simulations of low Reynolds number boundary-layer and channel flows are given An important aspect of the model is that it has been formulated to be consistent with accepted rational mechanics concepts that are known to provide a proper mathematical description of high Reynolds number flow

The effect of weak inertia on flow through a porous medium

Abstract: Using the theory of homogenization we examine the correction to Darcy's law due to weak convective inertia of the pore fluid. General formulae are derived for all constitutive coefficients that can be calculated by numerical solution of certain canonical cell problems. For isotropic and homogeneous media the correction term is found to be cubic in the seepage velocity, hence remains small even for Reynolds numbers which are not very small. This implies that inertia, if it is weak, is of greater importance locally than globally. Existing empirical knowledge is qualitatively consistent with our conclusion since the linear law of Darcy is often accurate for moderate flow rates.

An investigation of transition to turbulence in bounded oscillatory Stokes flows Part 1. Experiments

Abstract: Experimental results on flow-field statistics are presented for turbulent oscillatory flow in a circular pipe for the range of Reynolds numbers Reδ = U0δ/ν (U0 = amplitude of cross-sectional mean velocity, δ = (2ν/ω)½) = Stokes layer thickness) from 550 to 2000 and Stokes parameters Λ = R/δ (R = radius of the pipe) from 5 to 10. Axial and radial velocity components were measured simultaneously using a two-colour laser-Doppler anemometer, providing information on ensemble-averaged velocity profiles as well as various turbulence statistics for different phases during the cycle. In all flows studied, turbulence appeared explosively towards the end of the acceleration phase of the cycle and was sustained throughout the deceleration phase. During the turbulent portion of the cycle, production of turbulence was restricted to the wall region of the pipe and was the result of turbulent bursts. The statistics of the resulting turbulent flow showed a great deal of similarity to results for steady turbulent pipe flows; in particular the three-layer description of the flow consisting of a viscous sublayer, a logarithmic layer (with von Karman constant = 0.4) and an outer wake could be identified at each phase if the corresponding ensemble-averaged wall-friction velocities were used for normalization. Consideration of similarity laws for these flows reveals that the existence of a logarithmic layer is a dimensional necessity whenever at least two of the scales R, u*/ω and ν/u* are widely separated; with the exact structure of the flow being dependent upon the parameters u*/Rω and u2*/ων. During the initial part of the acceleration phase, production of turbulence as well as turbulent Reynolds stresses were reduced to very low levels and the velocity profiles were in agreement with laminar theory. Nevertheless, the fluctuations retained a small but finite energy. In Part 2 of this paper, the major features observed in these experiments are used as a guideline, in conjunction with direct numerical simulations of the ‘perturbed’ Navier–Stokes equations for oscillatory flow in a channel, to identify the nature of the instability that is most likely to be responsible for transition in this class of flows.

Turbulent Free Shear Layer Mixing and Combustion

Abstract: : Some experimental data on turbulent free-shear-layer growth, mixing, and chemical reactions are reviewed. The dependence of these phenomena on such fluid and flow parameters as Reynolds number, Schmidt number, and Mach number are discussed, with the aid of some direct consequences deducible from the large-scale organization of the flow as well as from some recent models. The mixing of two or more fluids that are entrained into a turbulent region is an important process from both a scientific and an applications vantage point. Species can be transported by turbulence to produce a more uniform distribution than some initial mean profile. This process is sometimes also referred to as mixing, without regard to whether the transported species are mixed on a molecular scale or not. If the issue of mixing arises in the context of chemical reactions and combustion, however, we recognize that only fluid mixed on a molecular scale can contribute to chemical product formation and associated heat release. The discussion in this paper will be limited to molecular mixing.

Direct simulation of turbulent spots in plane couette flow

Abstract: The development of turbulent spots in plane Couette flow was studied by means of direct numerical simulation. The Reynolds number was varied between 300 and 1500 (based on half the velocity difference between the two surfaces and half the gap width) in order to determine the lowest possible Reynolds number for which localised turbulent regions can persist, i.e. a critical Reynolds number, and to determine basic characteristics of the spot in plane Couette flow. It was found that spots can be sustained for Reynolds number above approximately 375 and that the shape is elliptical with a streamwise elongation that is more accentuated for high Reynolds numbers. At large times though there appears to be a slow approach towards a circular spot shape. Various other features of this spot suggest that it may be classified as an interesting intermediate case between the Pouseuille and boundary-layer spots. In the absence of experiments for this case the present results represent a true prediction of the physical situation.

On strongly nonlinear vortex/wave interactions in boundary-layer transition

Abstract: The interactions between longitudinal vortices and accompanying waves considered are strongly nonlinear, in the sense that the mean-flow profile throughout the boundary layer is completely altered from its original undisturbed state. Nonlinear interactions between vortex flow and Tollmien-Schlichting waves are addressed first, and some analytical and computational properties are described. These include the possibility in the spatial-development case of a finite-distance break-up, inducing a singularity in the displacement thickness. Second, vortex/Rayleigh wave nonlinear interactions are considered for the compressible boundary-layer, along with certain special cases of interest and some possible solution properties. Both types, vortex/Tollmien-Schlichting and vortex/Rayleigh, are short-scale/long-scale interactions and they have potential applications to many flows at high Reynolds numbers. The strongly nonlinear nature is believed to make them very relevant to fully fledged transition to turbulence.

Surface Curvature Effect on Slot-Air-Jet Impingement Cooling Flow and Heat Transfer Process

Abstract: Experiments are performed to study 'surface curvature effects on the impingement cooling flow and the heat transfer processes over a concave and a convex surface. A single air jet issuing from different size slots continuously impinges normally on the concave side or the convexside of a heated semicylindrical surface. An electrical resistance wire is used to generate smoke, which allows us to visualize the impinging flow structure. The local heat transfer Nusselt number along the surfaces is measured. For impingement on a convex surface, three-dimensional counterrotating vortices on the stagnation point are initiated, which result in the enhancement of the heat transfer process. For impingement on a concave surface, the heat transfer Nusselt number increases with increasing surface curvature, which suggests the initiation of Taylor-Gortler vortices along the surface. In the experiment, the Reynolds number ranges from 6000 to 350,000, the slot-to-plate spacing from 2 to 16, and the diameter-to-slot-width ratio D/b from 8 to 45.7. Correlations of both the stagnation point and the average Nusselt number over the curved surface, which account for the surface curvature effect, are presented. 1 Introduction Impingement cooling has been widely used to cool a heat transfer component exposed to a high temperature or a high heat flux environment. The impingement cooling jet has the advantage that it is readily moved to the location of interest and removes a large amount of heat. It has been widely used in such industrial systems as high-temperature gas turbines, paper drying, glass manufacturing, and high-density electronic equipment. The impinging jet used in these systems is air. Over the past 30 years, impingement cooling heat transfer has been extensively studied. Good review articles are available (Martin, 1977; Becko, 1976). The impinging flow structure (Donaldson and Snedeker, 1971a, 1971b), the local heat transfer, and the correlations of average Nusselt number in terms of relevant parameters have been well studied (Gardon and Cobonpue, 1963; Gardon and Akfirat, 1966; Korger and Krizek, 1965; Zumbrunnen et al., 1989). However, the impingement cooling studied in the past was on a flat plate. The situation of impingement cooling over a curved surface may frequently be encountered. However, the studies of impingement cooling on a curved surface are rela­tively few. Chupp et al. (1969) studied the impingement cooling heat transfer for an array of round jets impinging on a concave surface. The geometric configuration studied is very similar to the case for cooling of the leading edge of a gas turbine airfoil. They measure the local Nusselt number and correlate the av­erage Nusselt number in terms of the Reynolds number, the nozzle-to-plate spacing, and some nondimensional parameters of geometry. However, the local heat transfer obtained is ac­tually an average over a relatively large space. A similar ge­ometry is also studied by Metzger et al. (1969,1972) and Hrycak (1978, 1981). Tabakoff and Clevenger (1972) study three dif­ferent configurations of impinging jets on a concave surface: the single slot jet, the one-dimensional row of round jets, and the two-dimensional array of jets. Both the local and the av­erage Nusselt number are determined. However, the local heat transfer Nusselt number obtained is again an average over a relatively large space. A few correlations of average Nusselt numbers for slot jet impingement cooling over a concave or a

Unsteady wave structure near separation in a Mach 5 compression rampinteraction

Abstract: Fluctuating wall-pressure measurements have been made under the unsteady separation shock and the separated shear layer in a Mach 5 compression ramp-induced turbulent interaction. The freestream unit Reynolds number was 49.6x10 6 m -1 and the turbulent boundary layer developed on the tunnel floor under approximately adiabatic wall-temperature conditions. Conditional sampling and «variable-window» ensemble-averaging techniques have been used to determine ensemble-averaged pressure distributions for different separation shock-wave positions.

Hyperconcentrated Flow and Sediment Transport at Steep Slopes

Abstract: In order to simulate a fine-material slurry of a debris flow, a clay suspension of various concentrations was recirculated in a steep flume. The effect of an increasing fluid density and viscosity on the flow behavior and the bed-load transport capacity of the flow was examined. Viscous effects were found to become important below a limiting particle Reynolds number of about 10. Above this limiting value, density effects cause an increase in the bed-load transport rates as compared to similar conditions with clear water as transporting fluid. The experimental data in this range can be described with conventional (Newtonian) formulas and is analyzed together with other bed-load transport data. Two different calculation schemes are proposed for the steep slope range (\IS\N >≈\N 10%) where the bed-load concentration is significant with respect to the total flow depth. Below the critical particle Reynolds number of 10, the bed-load transport rates decreased strongly.

Large eddy simulation of turbulence‐driven secondary flow in a square duct

Abstract: The fully developed turbulent flow in a straight duct of square cross section has been simulated using the large eddy simulation (LES) technique. A mixed spectral‐finite difference method has been used in conjunction with the Smagorinsky eddy‐viscosity model for the subgrid scales. The simulation was performed for a Reynolds number of 360 based on friction velocity (5810 based on bulk velocity) and duct width. The simulation correctly predicted the existence of secondary flows and their effects on the mean flow and turbulence statistics. The results are in good qualitative agreement with the experimental data available at much higher Reynolds numbers. It is observed that both the Reynolds normal and shear stresses equally contribute to the production of mean streamwise vorticity.

Onset of three-dimensionality, equilibria, and early transition in flow over a backward-facing step

Abstract: A numerical study of three-dimensional equilibria and transition to turbulence in flow over a backward-facing step is performed using direct numerical solution of the incompressible Navier-Stokes equations. The numerical method is a high-order-accurate mixed spectral/spectral-element method with efficient viscous outflow boundary conditions. The appearance of three-dimensionality in nominally two-dimensional geometries is investigated at representative Reynolds numbers ranging from the onset of three-dimensional bifurcation to later transitional stages. Strongly three-dimensional regions are identified through standard correlation coefficients and new three-dimensionality indices, as well as through instantaneous and time-average streamline patterns and vorticity contours. Our results indicate that onset of three-dimensionality occurs at the boundaries between the primary and secondary recirculating zones with the main channel flow, the latter being the most stable flow component. There is. therefore, strong secondary instability in the shear layers, mainly due to the one emanating from the step corner.The flow further downstream is excited through the action of the upstream shear layers acquiring a wavy form closely resembling Tollmien–Schlichting waves both spatially and temporally with a characteristic frequency f1; upstream, at the shear layer another incommensurate frequency, f2, is present. The two-frequency flow locks-in to a single frequency if external excitations are imposed at the inflow at a frequency close to f1 or f2; the smaller amplitude excitations, however, may cause a strong quasi-periodic response. Such excitations may significantly increase or decrease (by more than 20%) the length of the primary separation zone XR at lock-in or quasi-periodic states. The equilibrium states resulting from the secondary instability at supercritical Reynolds numbers produce a flow modulated in the spanwise direction, with corresponding variations in the reattachment location XR. While three-dimensionality explains partially the discrepancy between numerical predictions and experimental results on XR at higher Reynolds number Re, the main source of discrepancy is attributed to the inflow conditions, and in particular to external disturbances superimposed on the mean flow, the latter being the main reason also for the somewhat earlier transition found in laboratory experiments.

Nonlinear Random Waves and Turbulence in Nondispersive Media: Waves, Rays, Particles

Abstract: Part 1 One-dimensional waves in nonlinear nondispersive media: the basic equations and statistical problems of the theory of random waves in nondispersive media physical examples of nonlinear waves. Part 2 One-dimensional wave dynamics: exact solution of Burgers equation, Reynolds number Burgers equation solution at large Reynolds numbers evolution of the basic disturbance types Burghers equation, hydrodynamics of noninteracting particles and parabolic equation quasioptics. Part 3 Lagrangian and Eulerian statistics of random fields: connection of the statistical properties of random fields connection of statistical properties of random functions with behaviour of their realizations Lagrangian and Eulerian statistics of random fields. Part 4 Random waves of hydrodynamic type: probability properties of random Riemann waves Riemann wave spectrum density fluctuations of noninteracting particle gas probability properties of density fluctuations fluctuations of the optical wave parameters beyond a random phase screen concentrations of a passive impurity in a flow with random velocity field motion of noninteracting particles under the action of external forces. Part 5 Statistical properties of discontinuous waves: discontinuity influence on the nonlinear wave statistics - initial stage qualitative theory of one-dimensional turbulence at the stage of developed discontinuities self-preservation of random waves in nonlinear dissipative media asymptotic analysis of nonlinear random waves at large Reynolds numbers turbulence at finite Reynolds numbers - final stage of decay statistical properties of the waves in a medium with arbitrary nonlinearity. Part 6 Three-dimensional potential turbulence - the large-scale structure of the Universe: cellular structure formation in three-dimensional potential turbulence asymptotic features of potantial turbulence density fluctuations in model gas. Appendices: Properties of delta-functions and their statistical averages nonlinear gravitational instability of random density waves in the expanding universe, A.L.Melott and S.F.Shandarin singularities and bifurcations of potential flows, V.I.Arnold et al.

A characteristics model of transient friction in pipes

Abstract: A quasi two-dimensional model of transient flows in pipes of circular cross-section is developed, using the one dimensional method of characteristics in concentric cylindrical annuli. Lateral velocity components are permitted between adjacent cylinders. The model can nominally incorporate any desired relationship between shear stresses and local velocities. In this paper, it is applied to laminar flows and to a five-region model of turbulent flows. The accuracy of Zielke's (1969) one-dimensional expression for transient wall-shear stresses in laminar flows is verified, and it is shown that his expression is also a reasonable approximation for smooth-wall, turbulent flows, at least at low Reynolds numbers. Quasi-steady relationships are shown to be highly inaccurate in transient laminar or turbulent flows.

On the Nature of Turbulence in a Stratified Fluid. Part II: Application to Lakes

Abstract: A strong debate has continued for a number of years over the magnitude of the ratio of the buoyancy flux b to the rate of production of turbulent kinetic energy from the mean velocity sheer. This ratio has traditionally been called the flux Richardson number Rf. In part I of Ivey and Imberger this definition was generalized by broadening the denominator to include all sources and sinks of mechanical turbulent kinetic energy, the net being defined as m. It was shown that for mechanically energized turbulence (m > 0, b > 0) the magnitude of Rf was completely determined by the magnitude of the overturn Froude FrT and the Reynolds ReT numbers By contrast, for the penetrative convection case (b < 0) Rf was shown to be dependent only on the distance from the source of buoyancy. In the present contribution, scaling arguments are presented for the magnitudes of FrT and ReT. It is shown that these may vary widely and depend, in the first instance, on the physics of the underlying processes energizing the ...

Asymmetric Vortices on a Slender Body of Revolution

Abstract: The symmetric and asymmetric leeward-side flow fields on an inclined ogive-cylinder have been investigated using a number of experimental techniques. Naturally occurring and perturbed flow fields were studied at a moderate Reynolds number and at many incidence angles. By close examination of the steady side force behavior at different roll orientations of the tip, it has been established that micro-variations in the tip geometry of the model have a large influence on the downstream development of the flow field. Under certain conditions, a bistable flow field was observed.