bluuebunny/crossref_metadata_2025_split huggingface dataset:
Direct numerical simulation of stratified homogeneous turbulent shear flows
Authors: Gerz T. , Schumann U. , Elghobashi S. E. 
Published: April 2006

The exact time-dependent three-dimensional Navier-Stokes and temperature equations are integrated numerically to simulate stably stratified homogeneous turbulent shear flows at moderate Reynolds numbers whose horizontal mean velocity and mean temperature have uniform vertical gradients. The method uses shear-periodic boundary conditions and a combination of finite-difference and pseudospectral approximations. The gradient Richardson number Ri is varied between 0 and 1. The simulations start from isotropic Gaussian fields for velocity and temperature both having the same variances.The simulations represent approximately the conditions of the experiment by Komori et al. (1983) who studied stably stratified flows in a water channel (molecular Prandtl number Pr = 5). In these flows internal gravity waves build up, superposed by hot cells leading to a persistent counter-gradient heat-flux (CGHF) in the vertical direction, i.e. heat is transported from lower-temperature to higher-temperature regions. Further, simulations with Pr = 0.7 for air have been carried out in order to investigate the influence of the molecular Prandtl number. In these cases, no persistent CGHF occurred. This confirms our general conclusion that the counter-gradient heat flux develops for strongly stable flows (Ri ≈ 0.5–1.0) at sufficiently large Prandtl numbers (Pr = 5). The flux is carried by hot ascending, as well as cold descending turbulent cells which form at places where the highest positive and negative temperature fluctuations initially existed. Buoyancy forces suppress vertical motions so that the cells degenerate to two-dimensional fossil turbulence. The counter-gradient heat flux acts to enforce a quasi-static equilibrium between potential and kinetic energy.Previously derived turbulence closure models for the pressure-strain and pressure-temperature gradients in the equations for the Reynolds stress and turbulent heat flux are tested for moderate-Reynolds-number flows with strongly stable stratification (Ri = 1). These models overestimate the turbulent interactions and underestimate the buoyancy contributions. The dissipative timescale ratio for stably stratified turbulence is a strong function of the Richardson number and is inversely proportional to the molecular Prandtl number of the fluid.
A natural low-frequency oscillation of the flow over an airfoil near stalling conditions
Authors: Zaman K. B. M. Q. , Mckinzie D. J. , Rumsey C. L. 
Published: April 2006

An unusually low-frequency oscillation in the flow over an airfoil is studied experimentally as well as computationally. Wind-tunnel measurements are carried out with two-dimensional airfoil models in the chord Reynolds number (Rc) range of 0.15 × 105−3.0 × 105. During deep stall, at α [gsim ] 18°, the usual ‘bluff-body shedding’ occurs at a Strouhal number, Sts ≈ 0.2. But at the onset of static stall around α = 15°, a low-frequency periodic oscillation is observed, the corresponding Sts being an order of magnitude lower. The phenomenon apparently takes place only with a transitional state of the separating boundary layer. Thus, on the one hand, it is not readily observed with a smooth airfoil in a clean wind tunnel, while on the other, it is easily removed by appropriate ‘acoustic tripping’. Details of the flow field for a typical case are compared with a case of bluff-body shedding. The flow field is different in many ways from the latter case and does not involve a Kármán Vortex street. The origin of the flow fluctuations traces to the upper surface of the airfoil and is associated with a periodic switching between stalled and unstalled states. The mechanism of the frequency selection remains unresolved, but any connection to blower instabilities, acoustic standing waves or structural resonances has been ruled out.A similar result has been encountered computationally using a two-dimensional Navier–Stokes code. While with the assumption of laminar flow, wake oscillation akin to the bluff-body shedding has been observed previously, the Sts is found to drop to about 0.03 when a ‘turbulent’ boundary layer is assumed. Details of the flow field and unsteady forces, computed for the same conditions as in the experiment, compare reasonably well with the experimental data.The phenomenon produces intense flow fluctuations imparting much larger unsteady forces to the airfoil than that experienced in bluff-body shedding, and may represent the primary aerodynamics of stall flutter of blades and wings.
The effect of geometry on the gravitational instability of a buoyant region of viscous fluid
Authors: Lister John R. , Kerr Ross C. 
Published: April 2006

The low-Reynolds-number stability of a region of buoyant fluid surrounded by denser fluid is analysed in two situations. In the first study, the buoyant fluid lies in a thin layer sandwiched between two denser and much deeper layers. The growth rate and wavelength of the most unstable sinusoidal perturbation are calculated and the effects of the viscosity ratios and density differences between the fluids are investigated. It is found that if the buoyant fluid is much less viscous than the overlying fluid then, in quite general circumstances, both the most unstable wavelength and the corresponding growth rate are inversely proportional to the cube root of the viscosity of the buoyant fluid. A physical explanation of this result is given by scaling analysis of the total dissipation. In the second study, the buoyant fluid takes the form of a cylinder rising through a uniform environment. The eigenmodes of small perturbation about this state of motion are found for each axial wavenumber in terms of Fourier series of separable solutions to the Stokes equations. In contrast to the first study, it is found that the most unstable wavelength and growth rate are asymptotically independent of the viscosity of the buoyant fluid when this viscosity is small.The difference between the results of the two studies is of importance, particularly for geophysical applications in which viscosity ratios are very large. Previous models of linear regions of volcanism at mid-ocean ridges and at island arcs have assumed that results obtained in simple two-layered systems can be generalized to other geometries. The conclusions of these models are discussed in the light of the stability results for a cylindrical (and hence linea.
The Dean equations extended to a helical pipe flow
Authors: Germano M. 
Published: April 2006

In this paper the Dean (1928) equations are extended to the case of a helical pipe flow, and it is shown that they depend not only on the Dean number K but also on a new parameter λ/[Rscr ] where λ is the ratio of the torsion τ to the curvature κ of the pipe axis and [Rscr ] the Reynolds number referred in the usual way to the pipe radius a and to the equivalent maximum speed in a straight pipe under the same axial pressure gradient. The fact that the torsion has no first-order effect on the flow is confirmed, but it is shown that this is peculiar to a circular cross-section. In the case of an elliptical cross-section there is a first-order effect of the torsion on the secondary flow, and in the limit λ/[Rscr ] → ∞ (twisted pipes, provided only with torsion), the first-order ‘displacement’ effect of the walls on the secondary flow, analysed in detail by Choi (1988), is recovered.Different systems of coordinates and different orders of approximations have recently been adopted in the study of the flow in a helical pipe. Thus comparisons between the equations and the results presented in different reports are in some cases difficult and uneasy. In this paper the extended Dean equations for a helical pipe flow recently derived by Kao (1987) are converted to a simpler form by introducing an appropriate modified stream function, and their equivalence with the present set of equations is recovered. Finally, the first-order equivalence of this set of equations with the equations obtained by Murata et al. (1981) is discussed.
Structure of turbulence at high shear rate
Authors: Lee Moon Joo , Kim John , Moin Parviz 
Published: April 2006

The structure of homogeneous turbulence subject to high shear rate has been investigated by using three-dimensional, time-dependent numerical simulations of the Navier–Stokes equations. The instantaneous velocity fields reveal that a high shear rate produces structures in homogeneous turbulence similar to the ‘streaks’ that are present in the sublayer of wall-bounded turbulent shear flows. Statistical quantities such as the Reynolds stresses are compared with those in the sublayer of a turbulent channel flow at a comparable shear rate made dimensionless by turbulent kinetic energy and its dissipation rate. This study indicates that high shear rate alone is sufficient for generation of the streaky structures, and that the presence of a solid boundary is not necessary.Evolution of the statistical correlations is examined to determine the effect of high shear rate on the development of anisotropy in turbulence. It is shown that the streamwise fluctuating motions are enhanced so profoundly that a highly anisotropic turbulence state with a ‘one-component’ velocity field and ‘two-component’ vorticity field develops asymptotically as total shear increases. Because of high shear rate, rapid distortion theory predicts remarkably well the anisotropic behaviour of the structural quantities.
Material-element deformation in isotropic turbulence
Authors: Girimaji S. S. , Pope S. B. 
Published: April 2006

The evolution of infinitesimal material line and surface elements in homogeneous isotropic turbulence is studied using velocity-gradient data generated by direct numerical simulations (DNS). The mean growth rates of length ratio (l) and area ratio (A) of material elements are much smaller than previously estimated by Batchelor (1952) owing to the effects of vorticity and of non-persistent straining. The probability density functions (p.d.f.'s) of l/〈l〉 and A/〈A〉 do not attain stationarity as hypothesized by Batchelor (1952). It is shown analytically that the random variable l/〈l〉 cannot be stationary if the variance and integral timescale of the strain rate along a material line are non-zero and DNS data confirm that this is indeed the case. The application of the central limit theorem to the material element evolution equations suggests that the standardized variables $\hat{l}(\equiv (\ln l - \langle \ln l\rangle)/({\rm var} l)^{\frac{1}{2}})$ and Â(≡(ln A − 〈ln A〉)/(var A)½) should attain stationary distributions that are Gaussian for all Reynolds numbers. The p.d.f.s of $\hat{l}$ and Â calculated from DNS data appear to attain stationary shapes that are independent of Reynolds number. The stationary values of the flatness factor and super-skewness of both $\hat{l}$ and Â are in close agreement with those of a Gaussian distribution. Moreover, the mean and variance of ln l (and ln A) grow linearly in time (normalized by the Kolmogorov timescale, τη), at rates that are nearly independent of Reynolds number. The statistics of material volume-element deformation are also studied and are found to be nearly independent of Reynolds number. An initially spherical infinitesimal volume of fluid deforms into an ellipsoid. It is found that the largest and the smallest of the principal axes grow and shrink respectively, exponentially in time at comparable rates. Consequently, to conserve volume, the intermediate principal axis remains approximately constant.The performance of the stochastic model of Girimaji & Pope (1990) for the velocity gradients is also studied. The model estimates of the growth rates of 〈ln l〉 and 〈ln A〉 are close to the DNS values. The growth rate of the variances are estimated by the model to within 17%. The stationary distributions of $\hat{l}$ and Â obtained from the model agree very well with those calculated from DNS data. The model also performs well in calculating the statistics of material volume-element deformation.
On the evolution of the turbulent spot in a laminar boundary layer with a favourable pressure gradient
Authors: Katz Y. , Seifert A. , Wygnanski I. 
Published: April 2006

The evolution of a turbulent spot in an accelerating laminar boundary-layer flow was investigated. The type of boundary layer chosen for this experiment resembles in every respect the flow in the vicinity of a stagnation point theoretically described by Falkner and Skan. The rate of growth of the spot was significantly inhibited by the favourable pressure gradient in all three directions. It became much shorter and narrower in comparison with a similar spot generated in a Blasius boundary layer at comparable distances from its origin and comparable Reynolds numbers. The celerities of its boundaries did not scale with the local free-stream velocity as they do in the absence of a pressure gradient. Dimensional analysis was used to identify and correlate the independent variables determining the size, the convection speed, and the relative rate of growth of this spotThe familiar arrowhead shape of the spot gave way to a rounded triangular shape with the trailing interface being straight and perpendicular to the direction of streaming. The familiar Tollmien-Schlichting wave packet was not observed in this pressure gradient because the surrounding boundary layer was very stable at theReconsidered. Since the arrowhead shape of the spot is associated with the breakdown of the waves within the packet it cannot occur below the criticalRe.The relative size of the ‘calmed region’ following the spot also diminished; however, one could only speculate as to the origin of this region.
Unsteady flow in trailing vortices
Authors: Green S. I. , Acosta A. J. 
Published: April 2006

The instantaneous velocity distribution in trailing vortices generated by lifting hydrofoils has been measured in the Low Turbulence Water Tunnel at the California Institute of Technology. Two different rectangular planform hydrofoils with small aspect ratios were tested. Double-pulsed holography of injected microbubbles, which act much as Lagrangian flow tracers, was used to determine instantaneous axial and tangential velocities. Measurements were made at various free-stream velocities, angles of attack, and downstream distances. The vortex core mean axial velocity is consistently greater than the free-stream velocity near the hydrofoil trailing edge, and decreases with downstream distance. The mean axial velocity is strongly Reynolds-number dependent.Axial flow in the trailing vortex is highly unsteady for all the flow conditions studied; peak-to-peak fluctuations on the centreline as large as the free-stream velocity have been observed. The amplitude of these fluctuations falls rapidly with increasing distance from the centreline. For an angle of attack of 10° the fluctuations consist of both ‘fast’ and ‘slow’ components, whereas for α = 5° only ‘fast’ fluctuations have been observed. Peak decelerations of the centreline fluid occur with amplitude comparable to the maximum centripetal acceleration around the centreline. Certain unusual structures of the vortex core - regions in which the flow direction quickly diverges from the free-stream direction, and then equally quickly recovers - have been labelled ‘vortex kinks.’
Frequency downshift in narrowbanded surface waves under the influence of wind
Authors: Hara Tetsu , Mei Chiang C. 
Published: April 2006

It is well known that the spectral peak of wind-induced gravity waves on the sea surface tends to shift to lower frequencies as the fetch increases. In past theories the nonlinear dynamics subsequent to Benjamin–Feir instability has been found to initiate the downshift in narrow-banded waves in the absence of wind. However, these weakly nonlinear theories all predict the downshift to be only the first phase of an almost cyclic process. Limited by the length of a wave tank, existing experiments are usually made with relatively steep waves which often break. Although there is a theory on how breaking adds dissipation to stop the reversal of the initial trend of downshift, the details of breaking must be crudely characterized by semi-empirical hypotheses.Since the direct role of wind itself must be relevant to the entire development of wind-wave spectrum, we examine here the effect of wind on the nonlinear evolution of unstable sidebands in narrow-banded waves. We assume that the waves do not break and consider the case where the nonlinear effects that initiate the downshift, energy input by wind and damping by internal dissipation all occur on the same timescale. This means that not only must the waves be mild but the wind stress intensity must also lie within a certain narrow range. With these limitations we couple the air flow above the waves with Dysthe's extension of the cubic Schrödinger equation, and examine the initial as well as the long-time evolution of a mechanically generated wavetrain. For a variety of wind intensities, downshift is indeed found to be enhanced and rendered long lasting.
The rate of collisions due to Brownian or gravitational motion of small drops
Authors: Zhang Xiaoguang , Davis Robert H. 
Published: April 2006

A dilute dispersion containing drops of one fluid dispersed in a second, immiscible fluid is considered. The drops are sufficiently small that inertia is negligible and that they remain spherical. Two drops of different size are in relative motion due to either Brownian diffusion or gravitational sedimentation. When the drops become close, they interact with each other owing to hydrodynamic disturbances and van der Waals attractions, and, under favourable conditions, they will collide with each other and coalesce. The rate at which two drops collide is predicted by solving the diffusion equation for Brownian coalescence, and by using a trajectory analysis to follow the relative motion of pairs of drops for gravity-induced coalescence.The emphasis of our analysis is on the effects of drop interactions on their collision rate, and these are described by the collision efficiency. Since the hydrodynamic resistance to the drop relative motion reduces with a decreasing ratio of the viscosities of the drop fluid and the surrounding fluid, the collision efficiency increases with decreasing viscosity ratio. A qualitative difference in the collision behaviour of viscous drops from that of rigid spheres is demonstrated; finite collision rates for drops are predicted even in the absence of attractive forces, provided that drop deformation is negligible, whereas rigid particles with smooth surfaces will not come into contact in a fluid continuum unless an attractive force is present which is able to overcome the lubrication forces resisting the relative motion. Hydrodynamic interactions between two spherical drops are accounted for exactly by determining the two-sphere relative mobility functions from previous solutions for two drops moving along and normal to their line of centres. These solutions are based on the method of reflections for widely separated drops, lubrication theory for drops in near-contact, and bispherical coordinates for general separations. The hydrodynamic interactions have a greater effect on reducing the rate of gravity collisions than the rate of Brownian collisions.
Reflection and transmission from porous structures under oblique wave attack
Authors: Dalrymple Robert A. , Losada Miguel A. , Martin P. A. 
Published: April 2006

The linear theory for water waves impinging obliquely on a vertically sided porous structure is examined. For normal wave incidence, the reflection and transmission from a porous breakwater has been studied many times using eigenfunction expansions in the water region in front of the structure, within the porous medium, and behind the structure in the down-wave water region. For oblique wave incidence, the reflection and transmission coefficients are significantly altered and they are calculated here.Using a plane-wave assumption, which involves neglecting the evanescent eigenmodes that exist near the structure boundaries (to satisfy matching conditions), the problem can be reduced from a matrix problem to one which is analytic. The plane-wave approximation provides an adequate solution for the case where the damping within the structure is not too great.An important parameter in this problem is Γ2= ω2h(s- if)/g, where ω is the wave angular frequency,hthe constant water depth,gthe acceleration due to gravity, andsandfare parameters describing the porous medium. As the friction in the porous medium,f, becomes non-zero, the eigenfunctions differ from those in the fluid regions, largely owing to the change in the modal wavenumbers, which depend on Γ2.For an infinite number of values of ΓF2, there are no eigenfunction expansions in the porous medium, owing to the coalescence of two of the wavenumbers. These cases are shown to result in a non-separable mathematical problem and the appropriate wave modes are determined. As the two wavenumbers approach the critical value of Γ2, it is shown that the wave modes can swap their identity.
Boundary-driven mixing
Authors: Woods Andrew W. 
Published: April 2006

There are two separate mechanisms which can generate a boundary flow in a non-rotating, stratified fluid. The Phillips–Wunsch boundary flow arises in a stratified, quiescent fluid along a sloping boundary. Isopycnals are deflected from the horizontal in order to satisfy the zero normal mass flux condition at the boundary; this produces a horizontal density gradient which drives a boundary flow. The second mechanism arises when there is an independently generated turbulent boundary layer at the wall such that the eddy diffusion coefficients decay away from the wall; if the vertical density gradient is non-uniform the greater eddy diffusion coefficients near the wall result in a greater accumulation or diminution of density near the wall. This produces a horizontal density gradient which drives a boundary flow, even at a vertical wall. The turbulent Phillips Wunsch flow, in which there is a vigorous recirculation in the boundary layer, develops if the wall is sloping. This recirculation produces an additional dispersive mass flux along the wall, which also generates a net volume flux along the wall if the density gradient is non-uniform.We investigate the effect of these boundary flows upon the mixing of the fluid in the interior of a closed vessel. The mixing in the interior fluid resulting from the laminar Phillips–Wunsch-driven boundary flow is governed by
\[
\rho_t = \frac{\kappa_{\rm m}}{A}(\rho z A)_z.
\]
The turbulence-driven boundary flow mixes the interior fluid according to
\[
\rho_\frac{1}{A}\left(\kappa_{\rm e}\rho z\int\delta\,{\rm d}s\right)z.
\]
Here ρ is the density, κm and κe are the far-field (molecular) and effective boundary (eddy) diffusivities, including the dispersion, A is the cross-sectional area of the basin and ∫ δ ds is the cross-sectional area of the boundary layer. The interior fluid is only mixed significantly faster than the rate of molecular diffusion if there is a turbulent boundary layer at the sidewalls of the containing vessel which either (i) varies in intensity with depth in the vessel or (ii) is mixing a non-uniform density gradient. These mixing phenomena are consistent with published experimental data and we consider the effect of such mixing in the ocean.