摘要:

The time evolution of a vortex sheet is calculated by using a simple generalization of Rosenhead’s point vortex approximation. The results confirm that the vortex sheet develops a singularity in curvature at a finite time. Numerical evidence of the rolling up of the vortex sheet is presented.

ISSN:0899-8213    

DOI:10.1063/1.858740

出版商:AIP    

年代:1993

数据来源: AIP

摘要:

Decaying isotropic turbulence with initial Taylor microscale Reynolds number (R&lgr;≤258) is studiedviadirect numerical simulations (DNS), with spectral resolution ≤2563. DNS results are compared with two‐point closure, in the form of the direct interaction approximation (DIA) and the test field model (TFM). The goals of this study are to understand the time‐dependence of enstrophy and spectra as they evolve from random initial conditions, and to assess and interpret differences between DNS and closure. Two time scales are identified in the DNS. The first is that for the development of normalized enstrophy production (velocity derivative skewness) and is independent ofR&lgr;. The second is that for the saturation of the enstrophy which follows after a longer period of near exponential growth and is stronglyR&lgr;dependent. For &ngr;≠0, the DIA represents the time development of both integral quantities, such as enstrophy and spectra, with surprising accuracy in spite of its lack of invariance to random large‐scale sweeping. The TFM has significant energy range errors, which we attribute to its Markovianization assumption.

ISSN:0899-8213    

DOI:10.1063/1.858741

出版商:AIP    

年代:1993

数据来源: AIP

摘要:

The far wake of a sphere towed horizontally in a linearly stratified fluid with Froude numbersF∈ (0.25,12.7) and Reynolds numbers Re ∈ [150,30 000] is investigated. Regardless of the initial Froude number, the wake becomes quasi two dimensional at times large compared with the Brunt–Va¨isa¨la¨ period. ForF≤4.5, the horizontal motions are coherent over the whole depth of the wake. The wake takes the form of a regular von Ka´rma´n street forF≤1.5 but is irregular at largerF. ForF≥4.5 the far wake consists of, vertically incoherent, horizontal motions in several layers. The transition occurs smoothly by a vertical decorrelation of the horizontal motion in the depth of the far which starts atF=4.5. The most novel result is that the horizontal velocity and vertical vorticity diffuse vertically in a time much shorter than predicted by a viscous diffusion law. The ratio of the observed diffusion time to the viscous diffusion time is expected to depend on Reynolds number as is indicated by a simple model.

ISSN:0899-8213    

DOI:10.1063/1.858742

出版商:AIP    

年代:1993

数据来源: AIP

摘要:

The influence of the properties of the size distribution of seeding particles on the results of laser Doppler anemometry (LDA) velocity measurements in the vicinity of a large velocity gradient downstream of an aerodynamic shock is studied numerically. Accounting for the differing velocity lag of particles of different sizes the average velocity and the pertaining rms values are determined in the relaxation region within which the particles adjust towards the changed flow velocity downstream of the shock. It is shown how the average velocity and the rms value depend on the mean particle size and the density of the particle material. It is demonstrated in a numerical simulation how the LDA system’s ‘‘amplitude limit,’’ which can offer a means of excluding the contribution of large particles towards the experimental results, affects the average velocity and the rms value to be measured in the relaxation region. Experimental LDA data of velocity measurements across an oblique shock are presented. A good qualitative agreement of the numerical and the experimental results is found.

ISSN:0899-8213    

DOI:10.1063/1.858743

出版商:AIP    

年代:1993

数据来源: AIP

摘要:

A weakly nonlinear analysis of the Go¨rtler vortex problem is performed. It is demonstrated that the system of streamwise vortices enhances the heat transfer rate at the wall. The inherently nonlinear physical mechanism responsible for this enhancement is discussed both mathematically, as well as heuristically; the latter using kinematic arguments. Remarks are made on the relation of the weakly nonlinear results to their fully nonlinear counterparts, as well as on the inadequacy of linear analyses.

ISSN:0899-8213    

DOI:10.1063/1.858744

出版商:AIP    

年代:1993

数据来源: AIP

摘要:

Consider an airfoil which is impulsively started from rest to a constant speed relative to an otherwise quiescent fluid at an angle of attack. The paper attempts to propose a precise definition for the ‘‘starting vortex’’ in viscous flow and investigate how an airfoil gains its lift through the starting vortex. It is found adequate to view the vortex itself as a source of the lift through the vorticity contained within it. Actually, the total lift on the airfoil is contributed by all the regions of nonvanishing vorticity in the flow. For an impulsive flow, the initial lift is due to the vortex sheet distributed along the airfoil; the lift is then rapidly dominated by the starting vortex near the trailing edge. In the next stage, the regions of vorticity next to the airfoil on both sides gradually become the major contributor to the lift. Relative importance of the starting vortex is assessed based on the angle of attack and the Reynolds number.

ISSN:0899-8213    

DOI:10.1063/1.858745

出版商:AIP    

年代:1993

数据来源: AIP

摘要:

Lundgren’s [Phys. Fluids25, 2193 (1982)] model for turbulent fine structure comprises coherent vortices which wind up vorticity variations into spiral structures; simultaneously the vortices are stretched axially by a background strain field. The model predicts ak−5/3energy spectrum and is remarkably robust to the form of the coherent vortices and the form of the vorticity variations. To understand this the present article introduces a simple cascade argument which illuminates how the dynamical processes of vortex stretching and reduction of scale conspire to give this Kolmogorov spectrum. Some generalizations are considered.

ISSN:0899-8213    

DOI:10.1063/1.858746

出版商:AIP    

年代:1993

数据来源: AIP

摘要:

A dynamical analysis is made of the Lagrangian and Eulerian two‐time velocity correlationsQLandQEfor small time difference in turbulence at very high Reynolds number. The short‐time analysis yields a refinement of the so‐called random sweeping model approximation for the Eulerian correlationQE. An estimate of the Lagrangian frequency spectrum of the Lagrangian correlationQLin the inertial subrange is derived on the basis of a deductive Lagrangian renormalized approximation (LRA), which is consistent with the short‐time analysis. Estimates of some nondimensional constants associated with the Eulerian and Lagrangian time microscales are also obtained by making use of the energy spectrum predicted by the LRA.

ISSN:0899-8213    

DOI:10.1063/1.858747

出版商:AIP    

年代:1993

数据来源: AIP

摘要:

The Lagrangian velocity autocorrelation and the time correlations for individual wave‐number bands are computed by direct numerical simulation (DNS) using the passive vector method (PVM), and the accuracy of the method is studied. It is found that the PVM is accurate whenKmax/kd≥2 whereKmaxis the maximum wave number carried in the simulation andkdis the Kolmogorov wave number. The Eulerian and Lagrangian time correlations for various wave‐number bands are compared. At moderate to high wave number the Eulerian time correlation decays faster than the Lagrangian, and the effect of sweep on the former is observed. The time scale of the Eulerian correlation is found to be (kU0)−1while that of the Lagrangian is [∫0k p2E(p)dp]−1/2. The Lagrangian velocity autocorrelation in a frozen turbulent field is computed using the DIA, ALHDIA, and LRA theories and is compared with DNS measurements. The Markovianized Lagrangian renormalized approximation (MLRA) is compared with the DNS, and good agreement is found for one‐time quantities in decaying turbulence at low Reynolds numbers and for the Lagrangian velocity autocorrelation in stationary turbulence at moderate Reynolds number. The effect of non‐Gaussianity on the Lagrangian correlation predicted by the theories is also discussed.

ISSN:0899-8213    

DOI:10.1063/1.858748

出版商:AIP    

年代:1993

数据来源: AIP

摘要:

An experimental investigation of a steady‐state negatively buoyant jet has been performed using a hot water jet projected vertically downwards from a 7.5 mm radius inlet pipe into a cold ambient. The Richardson number was 0.1 based on inlet pipe radius and the Reynolds number was 5000. Mean and fluctuating velocities and temperatures, triple velocity correlations and velocity–temperature correlations were measured for the jet in a constant temperature ambient. Correlations between orthogonal velocity components were also measured. Velocity measurements were performed using laser Doppler anemometry (LDA), and errors associated with beam movement (due to refractive index fluctuations) were experimentally quantified. Temperatures were measured with fast response thermocouples. The two techniques were used in conjunction to provide velocity–temperature correlations. The intermittency factors around the edge of the flow were measured optically, employing refractive index as a tracer. The normal stresses were found to be high in the shear region at the jet‐flow/reverse‐flow interface and in the region of large‐scale fluid reversal. The contribution from the intermittency at the boundary of the flow was evident in the velocity and temperature fluctuations. The triple velocity products were interpreted as fluxes of the Reynolds stresses and in general exhibited net fluxes away from the regions of high stress intensity. Balances of the terms in the axial momentum and turbulent kinetic energy equations showed that the main contribution from buoyancy was in the mean motion, with very little direct input to the turbulence field.

ISSN:0899-8213    

DOI:10.1063/1.858749

出版商:AIP    

年代:1993

数据来源: AIP