bluuebunny/crossref_metadata_2025_split huggingface dataset:
A numerical study of the evolution and structure of homogeneous stably stratified sheared turbulence
Authors: Holt Steven E. , Koseff Jeffrey R. , Ferziger Joel H. 
Published: April 2006

The structure and evolution of homogeneous stably stratified sheared turbulence have been investigated through direct numerical simulation. In these simulations the primary dimensionless parameter is the Richardson number which measures the relative importance of stratification and mean shear.For Richardson numbers less than the transition value the Reynolds stress and vertical density flux are down-gradient. Some of the vertical kinetic energy gained indirectly through production is expended in creating potential energy. Included in this shear-dominated regime is the stationary Richardson number at which the turbulent kinetic energy is constant in time although the spectra are evolving. At low dimensionless shear rate the stationary Richardson number increases with increasing Reynolds number.At the transition Richardson number the maximum anisotropy and energy partition are achieved. For larger Richardson numbers potential energy is released into vertical kinetic energy and the vertical density flux becomes counter-gradient. The associated production reversal enhances the decay rate of the turbulent kinetic energy.The effects of other dimensionless parameters have been investigated. After initial transients the developed flow is rather insensitive to the presence of significant initial potential energy. An increase in the Schmidt number increases the effect of stable stratification, e.g. the counter-gradient vertical density flux occurs earlier.In the shear dominated case the down-gradient fluxes are produced by the pumping of fluid through coherent hairpin-shaped vorticity. In the buoyancy dominated flow the counter-gradient fluid parcels induce helical vorticity structures as they move toward a position of neutral buoyancy.
An experimental study of vortex shedding behind linearly tapered cylinders at low Reynolds number
Authors: Piccirillo Paul S. , Van Atta C. W. 
Published: April 2006

Experiments were performed to study vortex shedding behind a linearly tapered cylinder. Four cylinders were used, with taper ratios varying from 50:1 to 100:1. The cylinders were each run at four different velocities, adjusted to cover the range of laminar vortex shedding for a non-tapered cylinder. The flow was confirmed to consist of discrete shedding cells, each with a constant frequency. For a centrespan Reynolds number greater than 100, the dimensionless mean cell length was found to be a constant. Individual cell size was found to be roughly self-similar. New shedding cells were created on the ends of the cylinders, or in regions adjacent to areas not shedding. Successful scalings were found for both the cell shedding frequencies and their differences, the modulation frequencies. The modulation frequencies were found to be constant along the cylinder span. The shedding frequency Strouhal number versus Reynolds number curve was found to have a slightly steeper slope than the Strouhal number curve for a non-tapered cylinder. Vortex shedding was found to begin at a local Reynolds number of about 60, regardless of any other factors. End effects were found to be of little importance.The vortex splits, which form the links between shedding cells, were found to be similar in some respects to those found by earlier investigators. Amplitude results suggested that the splits at different spanwise locations are temporally sequenced by an overall flow mechanism, a supposition confirmed by flow visualization. Wavelet analysis results showed that while the behaviour of the shedding frequencies in time was relatively unaffected by changing taper ratio, the behaviour of the modulation frequency in time was greatly affected. Comparisons with other experiments point out the universality of vortex splitting phenomena.
The long-wave limit in the asymptotic theory of hypersonic boundary-layer stability
Authors: Grubin S. E. , Trigub V. N. 
Published: April 2006

This paper discusses the long-wave limit of the asymptotic theory of hypersonic boundary-layer stability for a gas with the Prandtl number ½ < σ < 1 and with the viscosity–temperature law being a power function. The investigation is confined to the local-parallel approximation.In the long-wave limit the vorticity mode starts to interact with the acoustic disturbances in the boundary-layer region. The general solution of the linear problem in the boundary-layer inner region is analysed numerically and analytically. This solution is matched with the long-wave vorticity-mode solution near the transition layer. As a result, the inviscid instability problem for a hypersonic boundary layer is formulated. The analytical solution of this problem is found and analysed. The different limits of the solution are considered and the universal forms of the dependence are obtained. A similarity parameter is found which is a function of the Prandtl number and the power in the viscosity–temperature law. A significant change of the solution behaviour is noticed when this parameter passes a critical value. The asymptotic structure of the amplification rate, as a function of the wavenumber, is described and discussed.
On the instability of hypersonic flow past a flat plate
Authors: Blackaby Nicholas D. , Cowley Stephen J. , Hall Philip 
Published: April 2006

The instability of hypersonic boundary-layer flow over a flat plate is considered. The viscosity of the fluid is taken to be governed by Sutherland's formula, which gives a more accurate representation of the temperature dependence of fluid viscosity at hypersonic speeds than Chapman's approximate linear law. A Prandtl number of unity is assumed. Attention is focused on inviscid instability modes of viscous hypersonic boundary layers. One such mode, the ‘vorticity’ mode, is thought to be the fastest growing disturbance at high Mach numbers, M [Gt ] 1; in particular it is believed to have an asymptotically larger growth rate than any viscous instability. As a starting point we investigate the instability of the hypersonic boundary layer which exists far downstream from the leading edge of the plate. In this regime the shock that is attached to the leading edge of the plate plays no role, so that the basic boundary layer is non-interactive. It is shown that the vorticity mode of instability operates on a different lengthscale from that obtained if a Chapman viscosity law is assumed. In particular, we find that the growth rate predicted by a linear viscosity law overestimates the size of the growth rate by O((log M)½). Next, the development of the vorticity mode as the wavenumber decreases is described. It is shown, inter alia, that when the wavenumber is reduced to O(M-3/2) from the O(1) initial, ‘vorticity-mode’ scaling, ‘acoustic’ modes emerge.Finally, the inviscid instability of the boundary layer near the leading-edge interaction zone is discussed. Particular attention is focused on the strong-interaction zone which occurs sufficiently close to the leading edge. We find that the vorticity mode in this regime is again unstable. The fastest growing mode is centred in the adjustment layer at the edge of the boundary layer where the temperature changes from its large, O(M2). value in the viscous boundary layer, to its O(1) free-stream value. The existence of the shock indirectly, but significantly, influences the instability problem by modifying the basic flow structure in this layer.
Instability waves on the air–sea interface
Authors: Wheless G. H. , Csanady G. T. 
Published: April 2006

We used a compound matrix method to integrate the Orr–Sommerfeld equation in an investigation of short instability waves (λ < 6 cm) on the coupled shear flow at the air–sea interface under suddenly imposed wind (a gust model). The method is robust and fast, so that the effects of external variables on growth rate could easily be explored. As expected from past theoretical studies, the growth rate proved sensitive to air and water viscosity, and to the curvature of the air velocity profile very close to the interface. Surface tension had less influence, growth rate increasing somewhat with decreasing surface tension. Maximum growth rate and minimum wave speed nearly coincided for some combinations of fluid properties, but not for others.The most important new finding is that, contrary to some past order of magnitude estimates made on theoretical grounds, the eigenfunctions at these short wavelengths are confined to a distance of the order of the viscous wave boundary-layer thickness from the interface. Correspondingly, the perturbation vorticity is high, the streamwise surface velocity perturbation in typical cases being five times the orbital velocity of free waves on an undisturbed water surface. The instability waves should therefore be thought of as fundamentally different flow structures from free waves: given their high vorticity, they are akin to incipient turbulent eddies. They may also be expected to break at a much lower steepness than free waves.
The sweeping decorrelation hypothesis and energy–inertial scale interaction in high Reynolds number flows
Authors: Praskovsky Alexander A. , Gledzer Evgeny B. , Karyakin Mikhail Yu. , Zhou And Ye 
Published: April 2006

The random sweeping decorrelation hypothesis was analysed theoretically and experimentally in terms of the higher-order velocity structure functions $D_{u_i}^{(m)}(r) = \left< [u_i^m(x + r) - u_i^m(x)]^2\right>$. Measurements in two high Reynolds number laboratory shear flows were used: in the return channel (Rλ ≈ 3.2 × 103) and in the mixing layer (Rλ ≈ 2.0 × 103) of a large wind tunnel. Two velocity components (in the direction of the mean flow, u1, and in the direction of the mean shear, u2) were processed for m = 1−4. The effect of using Taylor's hypothesis was estimated by a specially developed method, and found to be insignificant. It was found that all the higher-order structure functions scale, in the inertial subrange, as r2/3. Such a scaling has been argued as supporting evidence for the sweeping hypothesis. However, our experiments also established a strong correlation between energy- and inertial-range excitation. This finding leads to the conclusion that the sweeping decorrelation hypothesis cannot be exactly valid.The hypothesis of statistical independence of large- and small-scale excitation was directly checked with conditionally averaged moments of the velocity difference $\left< [u_i(x + r) - u_i(x)]^l\right>_{u_i^*}, l = 2-4$, at a fixed value of the large-scale parameter u*i. Clear dependence of the conditionally averaged moments on the level of averaging was found. In spite of a strong correlation between the energy-containing and the inertial-scale excitation, universality of the intrinsic structure of the inertial subrange was shown.
Scaling laws for fully developed turbulent shear flows. Part 1. Basic hypotheses and analysis
Authors: Barenblatt G. I. 
Published: April 2006

The present work consists of two parts. Here in Part 1, a scaling law (incomplete similarity with respect to local Reynolds number based on distance from the wall) is proposed for the mean velocity distribution in developed turbulent shear flow. The proposed scaling law involves a special dependence of the power exponent and multiplicative factor on the flow Reynolds number. It emerges that the universal logarithmic law is closely related to the envelope of a family of power-type curves, each corresponding to a fixed Reynolds number. A skin-friction law, corresponding to the proposed scaling law for the mean velocity distribution, is derived.In Part 2 (Barenblatt & Prostokishin 1993), both the scaling law for the velocity distribution and the corresponding friction law are compared with experimental data.
Scaling laws for fully developed turbulent shear flows. Part 2. Processing of experimental data
Authors: Barenblatt G. I. , Prostokishin V. M. 
Published: April 2006

In Part 1 of this work (Barenblatt 1993) a non-universal scaling law (depending on the Reynolds number) for the mean velocity distribution in fully developed turbulent shear flow was proposed, together with the corresponding skin friction law. The universal logarithmic law was also discussed and it was shown that it can be understood, in fact, as an asymptotic branch of the envelope of the curves corresponding to the scaling law.Here in Part 2 the comparisons with experimental data are presented in detail. The whole set of classic Nikuradze (1932) data, concerning both velocity distribution and skin friction, was chosen for comparison. The instructive coincidence of predictions with experimental data suggests the conclusion that the influence of molecular viscosity within the main body of fully developed turbulent shear flows remains essential, even at very large Reynolds numbers. Meanwhile, some incompleteness of the experimental data presented in the work of Nikuradze (1932) is noticed, namely the lack of data in the range of parameters where the difference between scaling law and universal logarithmic law predictions should be the largest.
Convection in a rotating cylinder. Part 1 Linear theory for moderate Prandtl numbers
Authors: Goldstein H. F. , Knobloch E. , Mercader I. , Net M. 
Published: April 2006

The onset of convection in a uniformly rotating vertical cylinder of height h and radius d heated from below is studied. For non-zero azimuthal wavenumber the instability is a Hopf bifurcation regardless of the Prandtl number of the fluid, and leads to precessing spiral patterns. The patterns typically precess counter to the rotation direction. Two types of modes are distinguished: the fast modes with relatively high precession velocity whose amplitude peaks near the sidewall, and the slow modes whose amplitude peaks near the centre. For aspect ratios τ ≡ d/h of order one or less the fast modes always set in first as the Rayleigh number increases; for larger aspect ratios the slow modes are preferred provided that the rotation rate is sufficiently slow. The precession velocity of the slow modes vanishes as τ → ∞. Thus it is these modes which provide the connection between the results for a finite-aspect-ratio System and the unbounded layer in which the instability is a steady-state one, except in low Prandtl number fluids.The linear stability problem is solved for several different sets of boundary conditions, and the results compared with recent experiments. Results are presented for Prandtl numbers σ in the range 6.7 ≤ σ ≤ 7.0 as a function of both the rotation rate and the aspect ratio. The results for rigid walls, thermally conducting top and bottom and an insulating sidewall agree well with the measured critical Rayleigh numbers and precession frequencies for water in a τ = 1 cylinder. A conducting sidewall raises the critical Rayleigh number, while free-slip boundary conditions lower it. The difference between the critical Rayleigh numbers with no-slip and free-slip boundaries becomes small for dimensionless rotation rates Ωh2/v ≥ 200, where v is the kinematic viscosity.
Surface motion induced by the interaction of pulsed laser radiation with highly absorbing dielectric fluids
Authors: Naugol'nykh Konstantin A. , Puchenkov Oleg V. , Zosimov Victor V. , Pashin Alexander E. 
Published: April 2006

The disturbances on the free surface of dielectric fluids resulting from intense laser heating of their boundary layer are studied theoretically and experimentally. The heating is accompanied by pronounced evaporation from the surface and thereby leads to a recoil pressure momentum applied to the surface. For small values of total momentum transferred to the fluid, the low-amplitude initially hollow-like displacement of the surface in the impact zone decays to produce linear gravity–capillary waves (GCW) spreading out on the surface. This regime is treated analytically and the results obtained are compared with experiments involving weakly viscous (water, ethanol) and highly viscous (glycerol) liquids. An experimental arrangement for remote generation and subsequent detection of probe GCW-packets is given. The evolution of broadband GCW-disturbances on clean and surfactant-contaminated water surfaces are described. Results of GCW-attenuation spectrum measurements on clean water surfaces and on film-covered surfaces are presented.High total recoil momentum values give rise to substantially nonlinear surface motion: after a short transient stage the surface takes the shape of a hemisphere expanding into the liquid, and later the liquid above the hemisphere closes up to form a cavity and slow down the expansion. For this regime the dynamics of the hemisphere expansion are determined and satisfactory agreement with experimental data obtained with the shadowgraph technique is established. Consistency of theory and experiment allowed the determination of the total recoil pressure momentum and its surface distribution.In the intermediate case of moderate values of recoil momentum, the nonlinear evolution of broadband GCW-packets on clean and surfactant-contaminated water surfaces is investigated experimentally.
Interactions between a solid surface and a viscous compressible flow field
Authors: Wu Jie-Zhi , Wu Jain-Ming 
Published: April 2006

This paper presents a general theory and physical interpretation of the interaction between a solid body and a Newtonian fluid flow in terms of the vorticity ω and the compression/expansion variable Π instead of primitive variables, i.e. velocity and pressure. Previous results are included as special simplified cases of the theory. The first part of this paper shows that the action of a solid wall on a fluid can be exclusively attributed to the creation of a vorticity-compressing ω–Π field directly from the wall, a process represented by respective boundary fluxes. The general formulae for these fluxes, applicable to any Newtonian flow over an arbitrarily curved surface, are derived from the force balance on the wall. This part of the study reconfirms and extends Lighthil's (1963) assertion on vorticity-creation physics, clarifies some currently controversial issues, and provides a sound basis for the formulation of initial boundary conditions for the ω-Π variables.The second part of this paper shows that the reaction of a Newtonian flow to a solid body can also be exclusively attributed to that of the ω-Π field created. In particular, the integrated force and moment formulae can be expressed solely in terms of the boundary vorticity flux. This implies an inherent unity of the action and reaction between a solid body and a ω-Π field.In both action and reaction phases the ω-Π coupling on the wall plays an essential role. Thus, once a solid wall is introduced into a flow, any theory that treats ω and Π separately will be physically incomplete.
On internal waves generated by travelling wind
Authors: Kundu Pijush K. 
Published: April 2006

Oceanic internal waves forced by a latitude-independent wind field travelling eastward at speed U is investigated, extending the hydrostatic f-plane model of Kundu & Thomson (1985). The ocean has a well-mixed surface layer overlying a stratified interior with a depth-dependent buoyancy frequency N(z), and f can vary with latitude. Solutions are found by decomposition into vertical normal modes. Problems discussed are (i) the response to a slowly moving line front, and (ii) the response in a variable f ocean.For the slowly moving line front assuming a depth-independent N, the trailing waves are found to have large frequencies, and the vertical acceleration ∂w/∂t is important (that is the dynamics are non-hydrostatic) if the frequency ω is larger than a few times (Nf)½. The wake contains waves associated with all vertical modes, in contrast to hydrostatic dynamics in which slowly moving line fronts do not generate trailing waves of low-order modes. It is argued that slowly moving wind fields can provide an explanation for the frequently observed broad peak in the spectrum of vertical motion at a frequency somewhat smaller than N, and of the vertical coherence of the associated waves in the upper ocean.To study lower-frequency internal waves, the hydrostatic constant-f model of Kundu & Thomson is extended to variable f. Various sections through such a flow clearly illustrate the development of a meridional wavelength λy = 2π/βt as predicted by D'Asaro (1989), in addition to the zonal wavelength λx due to translation of the wind. The two effects combine to cause a greater horizontal inhomogeneity, so that energy from the surface layer descends quickly, travelling equatorward and downward. Since waves at any point arrive from different latitudes, spectra no longer consist of discrete peaks but are more continuous and broader than those in the constant-f model. The waves are more intermittent because of the larger spectral width, and vertically less correlated in the thermocline because of a larger bandwidth of vertical modes. The vertical correlation in the deep ocean, however, is still high because the response is dominated by one or two low-order modes after 30 days of integration. As U decreases, the larger bandwidth of frequency increases the intermittency, and the larger bandwidth of vertical wavenumber decreases the vertical correlation. A superposition of travelling wind events intensifies the high-frequency end of the spectrum; a month-long travelling series of realistic strength can generate waves with amplitudes of order 4 cm/s in the deep ocean.It is suggested that propagating winds and linear dynamics are responsible for the generation of a large fraction of internal waves in the ocean at all depths. The main effect of nonlinearity and mean flow may be to shape the internal wave spectra to a ω-2 form.
The difference between monopole vortices in planetary flows and laboratory experiments
Authors: Nycander J. 
Published: April 2006

This work is an attempt to explain observations of vortices in experiments with shallow water in rotating paraboloidal vessels. The most long-lived vortices are invariably anticyclones, while cyclones quickly disperse, and they are larger than the Rossby radius. These experiments are designed to simulate geophysical flows, where large, long-lived, anticyclonic vortices are common.The general condition for vortices to be steady is that they propagate faster than linear Rossby waves, so that the vortex energy is not dispersed by coupling to linear waves. The propagation velocity is determined by a general integral relation that gives the velocity of the centre of mass. In geophysical flows, to lowest order in the Rossby number, the difference between the centre-of-mass velocity and the maximum phase velocity of the Rossby waves is proportional to the relative perturbation of the fluid depth. Since for anticyclones the difference is positive they may be steady, whereas cyclones cannot be.In the laboratory experiments this velocity difference is absent because of the latitudinal dependence of the effective gravity caused by the centrifugal force. However, to the next order in the Rossby number, there is another nonlinear contribution, so that anticyclones (but not cyclones) still propagate faster than the linear Rossby waves, and may thus be steady. The velocity difference is smaller than for geophysical flows, and vanishes in the limit of small Rossby number. The existence conditions also show that we can expect the experimental vortices to be smaller (as measured by the Rossby radius) than the planetary vortices. The theory does not apply to vortices that are much smaller than the Rossby radius.