Phys. Fluids (1994-Present) - Physics of Fluids

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Suppression of vortex-shedding noise via derivative-free shape optimization

Alison L. Marsden, Meng Wang, J. E. Dennis, and Parviz Moin

Phys. Fluids 16, L83 (2004); http://dx.doi.org/10.1063/1.1786551 (4 pages) | Cited 8 times

Online Publication Date: 8 September 2004

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In this Letter we describe the application of a derivative-free optimization technique, the surrogate management framework (SMF), for designing the shape of an airfoil trailing edge which minimizes the noise of vortex shedding. Constraints on lift and drag are enforced within SMF using a filter. Several optimal shapes have been identified for the case of laminar vortex shedding with reasonable computational cost using several shape parameters, and results show a significant reduction in acoustic power. Physical mechanisms for noise reduction are discussed.

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47.32.C-	Vortex dynamics
47.11.-j	Computational methods in fluid dynamics
47.27.Sd	Turbulence generated noise
47.15.ki	Inviscid flows with vorticity
43.28.Ra	Generation of sound by fluid flow, aerodynamic sound and turbulence
47.40.-x	Compressible flows; shock waves
43.50.Nm	Aerodynamic and jet noise

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Transient growth and minimal defects: Two possible initial paths of transition to turbulence in plane shear flows

Damien Biau and Alessandro Bottaro

Phys. Fluids 16, 3515 (2004); http://dx.doi.org/10.1063/1.1775194 (15 pages) | Cited 14 times

Online Publication Date: 10 August 2004

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Two possible initial paths of transition to turbulence in simple wall-bounded shear flows are examined by looking at the development in space of infinitesimal disturbances. The first is the—by-now-classical—transient growth scenario which may have an important role in the bypass transition of flows for which traditional eigenmode analysis predicts asymptotic stability. It is studied by means of a simplified parabolic model justified by the underlying physics of the problem; results for optimal disturbances and maximum transient growth are found in excellent agreement with computations based on the full Orr–Sommerfeld/Squire equations. The second path starts with the exponential amplification, in nominally subcritical conditions, of modal disturbances superposed to base flows mildly distorted compared to their idealized counterparts. Such mean flow distortions might arise from the presence of unwanted external forcing related, for example, to the experimental environment. A technique is described that is capable of providing the worst case distortion of fixed norm for any ideal base flow, i.e., that base flow modification capable of maximizing the amplification rate of a given instability mode. Both initial paths considered here provide feasible initial conditions for the transition process, and it is likely that in most practical situations algebraic and exponential growth mechanisms are concurrently at play in destabilizing plane shear flows.

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47.27.E-	Turbulence simulation and modeling
47.27.Cn	Transition to turbulence
47.27.nb	Boundary layer turbulence
47.60.-i	Flow phenomena in quasi-one-dimensional systems
47.11.-j	Computational methods in fluid dynamics
47.20.Ft	Instability of shear flows (e.g., Kelvin-Helmholtz)
47.15.Fe	Stability of laminar flows

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Free stream turbulence induced disturbances in boundary layers with wall suction

Shuya Yoshioka, Jens H. M. Fransson, and P. Henrik Alfredsson

Phys. Fluids 16, 3530 (2004); http://dx.doi.org/10.1063/1.1775222 (10 pages) | Cited 10 times

Online Publication Date: 10 August 2004

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An experimental investigation of free stream turbulence (FST) induced disturbances in asymptotic suction boundary layers (ASBL) has been performed. In the present study four different suction rates are used and the highest is 0.40% of the free stream velocity, together with three different FST levels (Tu = 1.6, 2.0, and 2.3%). A turbulence generating grid of the active type is used and offers the possibility to vary the Tu-level while the scales of the turbulence remain almost constant. It is known that FST induces elongated disturbances consisting of high and low velocity regions, usually denoted streaky structures, into the boundary layer. The experiments show that wall suction suppresses the disturbance growth and may significantly delay or inhibit the break-down to turbulence. Two-point correlation measurements in the spanwise direction show that the averaged streak spacing decreases with increasing FST-level, whereas the spanwise scale in the ASBL is more or less constant if scaled with the free stream velocity and viscosity. This is in contrast to what is observed in a Blasius boundary layer where streaks develop and adapt their spanwise scale close to the boundary layer thickness.

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47.27.nb	Boundary layer turbulence
66.20.-d	Viscosity of liquids; diffusive momentum transport

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On the equilibrium states predicted by second moment models in rotating, stably stratified homogeneous shear flow

Minsuk Ji and Paul A. Durbin

Phys. Fluids 16, 3540 (2004); http://dx.doi.org/10.1063/1.1775806 (17 pages) | Cited 4 times

Online Publication Date: 10 August 2004

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The structural equilibrium behavior of the general linear second-moment closure model in a stably stratified, spanwise rotating homogeneous shear flow is considered with the aid of bifurcation analysis. A closed form equilibrium solution for the anisotropy tensor a_ij, dispersion tensor K_ij, dimensionless scalar variance math

²/k(S/S_θ)², and the ratio of mean to turbulent time scale ε/Sk is found. The variable of particular interest to bifurcation analysis, ε/Sk is shown as a function of the parameters characterizing the body forces: Ω/S (the ratio of the rotation rate to the mean shear rate) for rotation and Ri_g (the gradient Richardson number) for buoyancy; it determines the bifurcation surface in the ε/Sk−Ω/S−Ri_g space. It is shown, with the use of the closed form solution, that the Isotropization of Production model does not have a real and stable equilibrium solution when rotational and buoyant forces of certain magnitudes are simultaneously imposed on the flow. When this occurs, time integration of the turbulence model results in a diverging solution. A new set of scalar model coefficients that is consistent with experimental data, predicts turbulence decay past the critical gradient Richardson number Rigcr = 0.25, and ensures the existence of stable, real solutions for all combinations of rotation and buoyancy is proposed.

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47.32.-y	Vortex dynamics; rotating fluids
47.55.Hd	Stratified flows
47.27.nb	Boundary layer turbulence
47.20.Ky	Nonlinearity, bifurcation, and symmetry breaking
47.11.-j	Computational methods in fluid dynamics
47.27.E-	Turbulence simulation and modeling
47.20.Ft	Instability of shear flows (e.g., Kelvin-Helmholtz)

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Effect of a temperature difference between the cylinders on the Taylor–Couette bifurcation in a gas

Masato Handa and Toshiyuki Doi

Phys. Fluids 16, 3557 (2004); http://dx.doi.org/10.1063/1.1776511 (9 pages)

Online Publication Date: 10 August 2004

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A gas in a time-independent state between rotating coaxial circular cylinders with different temperatures is considered. The effect of the temperature difference on the Taylor–Couette bifurcation in the continuum limit is studied on the basis of the fluid-dynamic-type equations and their boundary conditions derived from the Boltzmann system. The behavior of the bifurcation point for a wide range of temperature differences is presented, and the mechanism of the shift of the bifurcation point owing to a small temperature difference is clarified analytically. The effect of the temperature difference on the bifurcation cannot be explained correctly by the guess by the analogy with the Bénard problem.

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47.60.-i	Flow phenomena in quasi-one-dimensional systems
47.20.Ky	Nonlinearity, bifurcation, and symmetry breaking
47.10.-g	General theory in fluid dynamics
47.15.-x	Laminar flows
47.40.-x	Compressible flows; shock waves
47.45.-n	Rarefied gas dynamics
47.32.-y	Vortex dynamics; rotating fluids

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On the dynamics of self-sustained one-dimensional detonations: A numerical study in the shock-attached frame

Aslan R. Kasimov and D. Scott Stewart

Phys. Fluids 16, 3566 (2004); http://dx.doi.org/10.1063/1.1776531 (13 pages) | Cited 12 times

Online Publication Date: 10 August 2004

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In this work we investigate the dynamics of self-sustained detonation waves that have an embedded information boundary such that the dynamics is influenced only by a finite region adjacent to the lead shock. We introduce the boundary of such a domain, which is shown to be the separatrix of the forward characteristic lines, as a generalization of the concept of a sonic locus to unsteady detonations. The concept plays a fundamental role both in steady detonations and in theories of much more frequently observed unsteady detonations. The definition has a precise mathematical form from which its relationship to known theories of detonation stability and nonlinear dynamics can be clearly identified. With a new numerical algorithm for integration of reactive Euler equations in a shock-attached frame, that we have also developed, we demonstrate the main properties of the unsteady sonic locus, such as its role as an information boundary. In addition, we introduce the so-called “nonreflecting” boundary condition at the far end of the computational domain in order to minimize the influence of the spurious reflected waves.

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47.40.Nm	Shock wave interactions and shock effects
47.70.Fw	Chemically reactive flows
47.11.-j	Computational methods in fluid dynamics
62.60.+v	Acoustical properties of liquids

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Hybrid continuum-atomistic simulation of singular corner flow

Xiaobo Nie, Shiyi Chen, and Mark O. Robbins

Phys. Fluids 16, 3579 (2004); http://dx.doi.org/10.1063/1.1779531 (13 pages) | Cited 21 times

Online Publication Date: 10 August 2004

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A hybrid numerical method is used to study cavity flow driven by a moving wall. Continuum equations with no-slip boundary conditions predict singular stresses at the corners between moving and static walls. Molecular dynamics simulations are used to resolve these singular regions, and the flow field in the remainder of the cavity is obtained from the Navier-Stokes (NS) equations. This hybrid solution agrees well with fully atomistic simulations on small systems, and allows calculations to be accelerated by orders of magnitude in larger systems. Fully continuum and hybrid solutions for the stress and velocity also agree over most of the cavity. Both yield a shear stress that scales as the inverse of the distance from the corner over almost two orders of magnitude. However, in the hybrid solution, this divergence is cut off within a distance S from the corners. In the limit of low wall velocities U, S is a few molecular diameters and corresponds to the length over which slip occurs. By comparing the hybrid solution to NS solutions, we show that the slip cannot be quantitatively described by the Navier slip condition. At higher U, non-Newtonian behavior near the corner causes S to rise linearly with U.

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47.11.-j	Computational methods in fluid dynamics
47.27.N-	Wall-bounded shear flow turbulence
47.10.-g	General theory in fluid dynamics
47.60.-i	Flow phenomena in quasi-one-dimensional systems
47.50.-d	Non-Newtonian fluid flows
47.45.Gx	Slip flows and accommodation

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Linear stability of radial displacements in porous media: Influence of velocity-induced dispersion and concentration-dependent diffusion

A. Riaz, C. Pankiewitz, and E. Meiburg

Phys. Fluids 16, 3592 (2004); http://dx.doi.org/10.1063/1.1775431 (7 pages) | Cited 13 times

Online Publication Date: 13 August 2004

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A parametric study is conducted in order to investigate the influence of (a) velocity dependent dispersion, and (b) concentration-dependent diffusion on the stability of miscible porous media displacements in the radial geometry. Numerical solutions for the base concentration profile demonstrate that velocity induced dispersion dominates for short times and large Péclet numbers. For large times, the growth rates approach those obtained when only molecular diffusion is taken into account. Concentration-dependent diffusion coefficients are seen to modify the mobility profiles of the base flow, and to shift the eigenfunctions into more or less viscous environments. This results in a destabilization for nearly all Péclet values and mobility ratios.

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47.56.+r	Flows through porous media
47.20.Gv	Viscous and viscoelastic instabilities
47.11.-j	Computational methods in fluid dynamics

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Experimental study of velocity filtered joint density function for large eddy simulation

Danhong Wang, Chenning Tong, and Stephen B. Pope

Phys. Fluids 16, 3599 (2004); http://dx.doi.org/10.1063/1.1776194 (15 pages) | Cited 15 times

Online Publication Date: 13 August 2004

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The velocity filtered joint density function (VFJDF) used in large eddy simulation and the structure of the subgrid-scale (SGS) velocity are studied experimentally. Measurements are made in the fully developed region of an axisymmetric turbulent jet (with jet Reynolds number U_jD_j/ν = 40 000) using an array consisting of three X-wire probes. Filtering in the cross-stream and streamwise directions is realized by using the array and by invoking Taylor’s hypothesis, respectively. On the jet centerline the means of the VFJDF conditional on the SGS turbulent kinetic energy are found to be close to joint normal when the SGS energy is small compared to its mean but has a uniform portion when the SGS energy is large. The latter distribution has not been observed previously and suggests that the SGS velocity contains approximately linear structures and is under local rapid distortion. The results at off-centerline positions are also consistent with the existence of linear structures. Further analyses show that the SGS velocity field with large SGS energy is in nonequilibrium (SGS production exceeds dissipation) and that the degree of nonequilibrium largely determines the shape of the VFJDF. The conditional energy dissipation has moderate dependence on the SGS velocity as expected due to their scale separation. However, the off-diagonal component of the conditional dissipation tensor is non-negligible when the SGS energy is large, at least for the Reynolds number studied. The present study suggests that the different structures and the local rapid distortion observed are important for SGS modeling. The results also suggest that the eddy-viscosity-type models for the SGS stress generally cannot give qualitatively correct predictions for SGS turbulence under local rapid distortion.

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47.27.wg	Turbulent jets
66.20.-d	Viscosity of liquids; diffusive momentum transport

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The flow in a cylindrical container with a rotating end wall at small but finite Reynolds number

Benson K. Muite

Phys. Fluids 16, 3614 (2004); http://dx.doi.org/10.1063/1.1779567 (13 pages) | Cited 2 times

Online Publication Date: 20 August 2004

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Similarity solutions of the first kind are intermediate asymptotic solutions for the Stokes flow field and for the first-order inertial correction to the Stokes flow field in small aspect ratio geometries with both no-slip and free-slip boundary conditions opposite the rotating end wall. These results differ from the semi-infinite cylindrical container, where similarity solutions of the second kind are intermediate asymptotic representations of the Stokes and first-order flow fields. Lanczos factors are used to show that for Reynolds numbers less than 1, the boundary discontinuity has a limited influence on the flow field with a no-slip boundary condition opposite the rotating end wall but the boundary discontinuity is important in determining the flow field with a free-slip boundary condition opposite the rotating end wall.

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47.60.-i	Flow phenomena in quasi-one-dimensional systems
47.11.-j	Computational methods in fluid dynamics
47.32.-y	Vortex dynamics; rotating fluids

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Experimental and theoretical investigation of the nonmodal growth of steady streaks in a flat plate boundary layer

Jens H. M. Fransson, Luca Brandt, Alessandro Talamelli, and Carlo Cossu

Phys. Fluids 16, 3627 (2004); http://dx.doi.org/10.1063/1.1773493 (12 pages) | Cited 33 times

Online Publication Date: 27 August 2004

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An experimental and theoretical investigation aimed at describing the nonmodal growth of steady and spanwise periodic streamwise streaks in a flat plate boundary layer is presented. Stable laminar streaks are experimentally generated by means of a spanwise periodic array of small cylindrical roughness elements fixed on the plate. The streamwise evolution of the streaks is measured and it is proved that, except in a small region near the roughness elements, they obey the boundary layer scalings. The maximum achievable amplitude is mainly determined by the relative height of the roughness elements. Results are compared with numerical simulations of optimal and suboptimal boundary layer streaks. The theory is able to elucidate some of the discrepancies recently noticed between experimentally realizable nonmodal growth and optimal perturbation theory. The key factor is found to be the wall normal location and the extension of the laminar standing streamwise vortices inducing the streaks. The differences among previous experimental works can be explained by different dominating streak generation mechanisms which can be linked to the geometry and to the ratio between the roughness height and the boundary layer scale.

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47.15.Cb	Laminar boundary layers
47.32.C-	Vortex dynamics

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Stability analysis of the flow in a cubical cavity heated from below

D. Puigjaner, J. Herrero, Francesc Giralt, and C. Simó

Phys. Fluids 16, 3639 (2004); http://dx.doi.org/10.1063/1.1778031 (17 pages) | Cited 11 times

Online Publication Date: 27 August 2004

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A numerical study of bifurcations and stability of the steady convective flow of air in a cubical enclosure heated from below was carried out using a Galerkin spectral method. The set of basis functions was chosen so that all boundary conditions and the continuity equation were implicitly satisfied. A parameter continuation method was applied to determine the steady solutions and bifurcations of the nonlinear governing equations as a function of Rayleigh number (Ra) for values of Ra up to 1.5×10⁵. The eigenvalue problem associated with the stability analysis of the steady solutions along the different branches of solutions was solved using the Arnoldi method. The convergence of the method was consistent with the number of modes used and the results were also verified by a numerical solution of the unsteady equations of motion using a finite-difference solver. Present results show that different stable convective flow patterns can coexist for different ranges of the Rayleigh number.

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47.20.Ky	Nonlinearity, bifurcation, and symmetry breaking
47.27.T-	Turbulent transport processes
47.60.-i	Flow phenomena in quasi-one-dimensional systems
47.11.-j	Computational methods in fluid dynamics

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Stability and transport properties of multiple-patch quasiequilibria

R. M. Schoemaker, H. J. H. Clercx, and G. J. F. van Heijst

Phys. Fluids 16, 3656 (2004); http://dx.doi.org/10.1063/1.1785111 (14 pages) | Cited 1 time

Online Publication Date: 1 September 2004

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A novel subclass of exact solutions to the Euler equations in two dimensions has been put forward recently [D. Crowdy, “A class of exact multipolar vortices,” Phys. Fluids 11, 2556 (1999)]. The solutions show vortical equilibria which can be described by only two parameters. The first one designates the multipolar aspect of these equilibria, i.e., the number of point vortices involved, while the other parameter signatures the shape of the finite area of uniform vorticity in which the point vortices are embedded. The main aspect of these equilibria is that the vortical configuration is static, meaning that the velocity induced at the patch edge, outside the vortical area, and also at the locations of the point vortices is zero. We show with numerical experiments that quite remarkably the linearly stable equilibria of Crowdy seem to mix very efficiently in contrast to the unstable vortex solutions. In the second part of this paper we report on the dynamics, stability, and mixing properties of similar vortex systems where the point vortices are regularized to vortex patches (with uniform vorticity). Several of these multiple-patch vortices turn out to be remarkably stable, although the regularization itself should be considered as a (symmetric) perturbation of Crowdy’s multipolar solutions.

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47.11.-j	Computational methods in fluid dynamics
47.32.C-	Vortex dynamics
47.20.-k	Flow instabilities
47.60.-i	Flow phenomena in quasi-one-dimensional systems

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An eddy-viscosity subgrid-scale model for turbulent shear flow: Algebraic theory and applications

A. W. Vreman

Phys. Fluids 16, 3670 (2004); http://dx.doi.org/10.1063/1.1785131 (12 pages) | Cited 44 times

Online Publication Date: 1 September 2004

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An eddy-viscosity model is proposed and applied in large-eddy simulation of turbulent shear flows with quite satisfactory results. The model is essentially not more complicated than the Smagorinsky model, but is constructed in such a way that its dissipation is relatively small in transitional and near-wall regions. The model is expressed in first-order derivatives, does not involve explicit filtering, averaging, or clipping procedures, and is rotationally invariant for isotropic filter widths. Because of these highly desirable properties the model seems to be well suited for engineering applications. In order to provide a foundation of the model, an algebraic framework for general three-dimensional flows is introduced. Within this framework several types of flows are proven to have zero energy transfer to subgrid scales. The eddy viscosity is zero in the same cases; the theoretical subgrid dissipation and the eddy viscosity have the same algebraic structure. In addition, the model is based on a fundamental realizability inequality for the theoretical subgrid dissipation. Results are shown for a transitional and turbulent mixing layer at high Reynolds number and a turbulent channel flow. In both cases the present model is found to be more accurate than the Smagorinsky model and as good as the standard dynamic model. Unlike the Smagorinsky model, the present model is able to adequately handle not only turbulent but also transitional flow.

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47.27.E-	Turbulence simulation and modeling
47.27.nb	Boundary layer turbulence
47.10.-g	General theory in fluid dynamics
47.60.-i	Flow phenomena in quasi-one-dimensional systems
47.15.Fe	Stability of laminar flows
47.27.Cn	Transition to turbulence

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A simplified Fourier method for computing the internal wavefield generated by an oscillating source in a horizontally moving, depth-dependent background

Dave Broutman and James W. Rottman

Phys. Fluids 16, 3682 (2004); http://dx.doi.org/10.1063/1.1785140 (8 pages) | Cited 4 times

Online Publication Date: 1 September 2004

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A method is developed to describe the linear internal wavefield generated by an oscillating source in horizontally moving, depth-dependent background. Ray theory is used to approximate the vertical eigenfunctions. A spatial solution is then obtained by inverse Fourier transform. This is a practical approach with a more convenient range of validity than the method of spatial ray tracing. The solutions for a stationary source and for a vertically oscillating source in a vertically sheared background current are given for illustration.

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47.35.-i	Hydrodynamic waves
47.10.-g	General theory in fluid dynamics
47.55.Hd	Stratified flows

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Stability of convection induced by selective absorption of radiation in a fluid overlying a porous layer

Min-Hsing Chang

Phys. Fluids 16, 3690 (2004); http://dx.doi.org/10.1063/1.1789551 (9 pages) | Cited 4 times

Online Publication Date: 1 September 2004

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A linear stability analysis for the onset of convection induced by selective absorption of radiation in a two-layer system is presented. The system comprises a layer of fluid which lies above a porous layer saturated with the same fluid. The model for selective absorption of radiation is based on a similar one introduced by Krishnamurti [Dyn. Atmos. Oceans, 27, 367 (1997)] for a viscous fluid. Both the upper and lower surfaces are assumed to be fixed and it is found that the heating direction between both plates has a strong effect on the onset of convection. If the system is heated from below, the instability seems to have a bimodal nature in which convection may be dominated by fluid layer or by porous layer. While if heating from above, only one instability mode may exist in which convection is dominated by porous layer. Results for the stability characteristics with respect to the variations of depth ratio (the ratio of the depth of fluid layer to that of porous layer), strength of radiative heating, and Lewis number are also demonstrated in detail.

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47.27.T-

Turbulent transport processes

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Upstream entrainment in numerical simulations of spatially evolving round jets

Pradeep C. Babu and Krishnan Mahesh

Phys. Fluids 16, 3699 (2004); http://dx.doi.org/10.1063/1.1780548 (7 pages) | Cited 15 times

Online Publication Date: 1 September 2004

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Direct numerical simulation is used to study the effect of entrainment near the inflow nozzle on spatially evolving round jets. Inflow entrainment is obtained by providing a buffer region upstream of the inflow nozzle. Simulations are performed at Reynolds numbers of 300 (laminar) and 2400 (turbulent), respectively. Simulations without the inflow buffer are contrasted to those with the buffer region. The potential core is seen to close earlier in the presence of inflow entrainment. As a result, near-field turbulent intensities and pressure fluctuations on the jet centerline are noticeably affected. It is suggested that inflow entrainment results in an effective co-flow, whose effect on the volumetric flow rate near the inflow nozzle is appreciable for both laminar and turbulent jets. When plotted in similarity variables, the far-field solutions with and without inflow entrainment agree well with each other, and experiment. The results suggest the importance of allowing for inflow entrainment in simulations of turbulent jets, particularly for studies where near-field behavior is important.

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47.55.Hd	Stratified flows
47.11.-j	Computational methods in fluid dynamics
47.27.wg	Turbulent jets
47.27.E-	Turbulence simulation and modeling
47.15.-x	Laminar flows
47.60.-i	Flow phenomena in quasi-one-dimensional systems
47.27.-i	Turbulent flows

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Oscillatory convection in a two-dimensional porous box with asymmetric lateral boundary conditions

D. Andrew S. Rees and Peder A. Tyvand

Phys. Fluids 16, 3706 (2004); http://dx.doi.org/10.1063/1.1781160 (9 pages) | Cited 4 times

Online Publication Date: 1 September 2004

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The onset of convection in a two-dimensional porous cavity is investigated where the cavity is subject to asymmetric boundary conditions at the lateral walls: one vertical wall is thermally conducting and impermeable, while the other is thermally insulating and open. At the open boundary the saturating fluid flows freely in and out from a hydrostatic reservoir in contact with the porous medium. The top and bottom of the box are impermeable and perfectly conducting. It is shown that the mode for onset of convection is oscillatory in time. This corresponds to a disturbance traveling as a wave through the box from the impermeable wall to the open wall. The preferred eigensolution, its oscillation frequency, and critical Rayleigh number are calculated numerically for different aspect ratios of the porous box, and these values are confirmed by means of suitable asymptotic analyses.

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47.27.T-	Turbulent transport processes
47.60.-i	Flow phenomena in quasi-one-dimensional systems
47.56.+r	Flows through porous media
47.35.-i	Hydrodynamic waves
47.11.-j	Computational methods in fluid dynamics
47.55.dp	Cavitation and boiling

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Control of drop rebound with solid target motion

Heon Ju Lee and Ho-Young Kim

Phys. Fluids 16, 3715 (2004); http://dx.doi.org/10.1063/1.1787842 (5 pages) | Cited 1 time

Online Publication Date: 8 September 2004

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Drops with a high surface tension and a low viscosity, such as water and molten metal drops, exhibit a vigorous recoiling and a long-lasting oscillation upon impacting with nonwetting solid surfaces. Here we report a scheme of controlling drop rebound using target movement, without resorting to chemical modification of either drop liquid or solid surface. Our experimental study reveals that drop rebound is promoted when the target moves upward at the moment of impact. On the other hand, an effective suppression of drop rebound is achieved by moving the target downward upon drop impact. It is shown that these modifications in drop rebound behavior are not due to the drop impact speed change. Furthermore, a properly timed reversal of the target’s moving direction is shown to control drop rebound more effectively than the monotonous target motions.

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47.55.D-	Drops and bubbles
68.03.Cd	Surface tension and related phenomena
66.20.-d	Viscosity of liquids; diffusive momentum transport
47.35.-i	Hydrodynamic waves

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Ageostrophic, anticyclonic instability of a geostrophic, barotropic boundary current

James C. McWilliams, M. Jeroen Molemaker, and Irad Yavneh

Phys. Fluids 16, 3720 (2004); http://dx.doi.org/10.1063/1.1785132 (6 pages) | Cited 7 times

Online Publication Date: 9 September 2004

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After having previously demonstrated the occurrence of ageostrophic, anticyclonic instability (AAI) for several other steady flows, in this paper we further test the hypothesis that rotating, stably stratified, shear flows are generally subject to AAI at finite Rossby (Ro) and Froude (Fr) numbers by calculating the inviscid, incompressible normal modes of a geostrophic, barotropic boundary current that vanishes toward the interior of the domain. We focus on a background current profile with no inflection point and nonvanishing absolute vorticity to exclude other known instability types. The hypothesis is again confirmed. The instability occurs for finite Ro only in an anticyclonic background flow. Its modal growth rate steeply decreases (approximately inverse exponentially, ∼ e^−c/Ro) as Ro→0. The downstream phase velocity of the unstable mode lies within the speed range for the background current, so the eigenmode has a near-critical layer within the zone of strong background shear. Its unstable eigenmode has an aspect ratio of downstream and vertical wave numbers, l/m, on the order of the ratio of the Coriolis and Brünt-Väisällä frequencies (as is typical for rotating, stratified flows). The maximum growth rate is independent of Fr for small Fr (the usual geophysical regime), and it decreases with large Fr, disappearing when there is no stratification. The eigenmode has a weakly decaying, oscillatory, interior far-field structure similar to an inertia-gravity wave. This supports the interpretation that the modal instability arises through the coalescence (i.e., resonance) of two stable normal-mode branches, one associated with the background shear flow and the other an inertia-gravity or Kelvin wave mode.

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47.20.Cq	Inviscid instability
47.10.-g	General theory in fluid dynamics
47.55.Hd	Stratified flows
47.32.C-	Vortex dynamics
47.20.Ft	Instability of shear flows (e.g., Kelvin-Helmholtz)

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Analysis of convective hydrodynamic instabilities in a symmetric wavy channel

S. Blancher, R. Creff, and P. Le Quéré

Phys. Fluids 16, 3726 (2004); http://dx.doi.org/10.1063/1.1779511 (12 pages) | Cited 4 times

Online Publication Date: 10 September 2004

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The dynamic development of a laminar flow in a two-dimensional symmetric wavy channel is studied numerically by numerical integration of the unsteady Navier–Stokes equations. It is shown that beyond a critical Reynolds number the flow is convectively unstable and exhibits an exponential spatial growth of the velocity fluctuations. The amplification factor for these “natural instabilities” increases with Reynolds number. It is characteristic of the geometry but independent of the number of the periods chosen for the simulation and other numerical parameters. The amplitude of velocity fluctuations saturates at a distance from the entry that decreases with increasing Reynolds number. The structure of the developing unsteady flow is compared with the most unstable modes of the fully developed laminar steady flow obtained by linear stability analysis. Although visual inspection would tend to favor the assumption of a single mode disturbance, it is found that the disturbances are wave packets centered around a dominant wavenumber which does not correspond to the geometrical periodicity. Spatial amplification factors computed with the theoretical group velocities determined from linear stability of the fully developed flow are in very good agreement with the numerically measured values, both for the sinuous and varicous modes.

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47.10.-g	General theory in fluid dynamics
47.60.-i	Flow phenomena in quasi-one-dimensional systems
47.15.Fe	Stability of laminar flows
47.20.-k	Flow instabilities
47.27.T-	Turbulent transport processes

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Transient Marangoni convection in hanging evaporating drops

R. Savino and S. Fico

Phys. Fluids 16, 3738 (2004); http://dx.doi.org/10.1063/1.1772380 (17 pages) | Cited 12 times

Online Publication Date: 10 September 2004

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A combined experimental and numerical analysis has been carried out to study Marangoni effects during the evaporation of droplets. The experiments are performed with pendant drops of silicone oils (with different viscosities) and hydrocarbons. The temperature of the disk sustaining the drop is rapidly increased or decreased in order to study transient heating or cooling processes. The velocity field in the droplet is evaluated monitoring the motion of tracers in the meridian plane, using a laser sheet illumination system and a video camera. Surface temperature distributions of the drops are detected by infrared thermocamera. The numerical model is based on axisymmetric Navier–Stokes equations, taking into account the presence of Marangoni shear stresses and evaporative cooling at the liquid-air interface. Marangoni flows cause a larger, more uniform surface temperature, increasing heat transfer from disk to droplet, as well as evaporation rate. When Marangoni effects are negligible, larger surface temperature differences occur along the drop surface and heat transfer is relatively small. The role of Marangoni and buoyancy flows in silicone oils with different viscosities and hydrocarbons is discussed and correlations are presented between experimental and numerical results.

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47.55.D-	Drops and bubbles
47.27.T-	Turbulent transport processes
66.20.-d	Viscosity of liquids; diffusive momentum transport
47.10.-g	General theory in fluid dynamics
68.03.Fg	Evaporation and condensation of liquids
68.03.Cd	Surface tension and related phenomena
47.60.-i	Flow phenomena in quasi-one-dimensional systems

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Nonparallel linear stability analysis of unconfined vortices

M. A. Herrada and A. Barrero

Phys. Fluids 16, 3755 (2004); http://dx.doi.org/10.1063/1.1779228 (10 pages)

Online Publication Date: 10 September 2004

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Parabolized stability equations [F. P. Bertolotti, Th. Herbert, and P. R. Spalart, J. Fluid. Mech. 242, 441 (1992)] have been used to study the stability of a family of swirling jets at high Reynolds numbers whose velocity and pressure fields decay far from the axis as r^m−2 and r^2(m−2), respectively [M. Pérez-Saborid, M. A. Herrada, A. Gómez-Barea, and A. Barrero, J. Fluid. Mech. 471, 51 (2002)]; r is the radial distance and m is a real number in the interval 0<m<2. Results show that the nonparallel effects of the basic flow play an important role in the development of both axisymmetric and nonaxisymmetric unstable perturbations upstream of the vortex breakdown station. A complementary local nonparallel analysis shows the convective nature of these instabilities. Therefore, a criterion based on the transition from convective to absolute instabilities cannot be applied to predict the vortex breakdown of this kind of swirling jets. On the contrary, the failure of the quasicylindrical approximation used to compute the downstream evolution of the basic flow gives a clear breakdown criterion based on the catastrophic transition between slender and nonslender flows.

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47.32.C-	Vortex dynamics
47.20.Ky	Nonlinearity, bifurcation, and symmetry breaking
47.27.wg	Turbulent jets
47.11.-j	Computational methods in fluid dynamics
47.27.T-	Turbulent transport processes

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Standing shocks in a rotating channel

Tivon E. Jacobson and Esteban G. Tabak

Phys. Fluids 16, 3765 (2004); http://dx.doi.org/10.1063/1.1780172 (14 pages)

Online Publication Date: 10 September 2004

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This paper discusses the stationary shallow water shocks occurring in a reentrant rotating channel with wind stress and topography. Asymptotic predictions for the shock location, strength, and associated energy dissipation are developed by taking the topographic perturbation to be small. It is shown that under appropriate conditions, a mean flow develops under the action of the wind stress, with a transverse profile determined by the need to support stationary shocks. The scaling arguments for the asymptotics are developed by demanding integrated energy and momentum balance, with the result that the free surface perturbation is of the order of the square root of the topographic perturbation. Shock formation requires that linear waves be nondispersive, which sets a solvability condition on the mean flow and which leads to a class of generalized Kelvin waves. Two-dimensional shock-resolving numerical simulations validate the asymptotic expressions and demonstrate the presence of stationary separated flow shocks in some cases.

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47.11.-j	Computational methods in fluid dynamics
47.35.-i	Hydrodynamic waves
47.40.Nm	Shock wave interactions and shock effects
47.60.-i	Flow phenomena in quasi-one-dimensional systems
47.32.Ff	Separated flows

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Velocity slip and temperature jump coefficients for gaseous mixtures. III. Diffusion slip coefficient

Felix Sharipov and Denize Kalempa

Phys. Fluids 16, 3779 (2004); http://dx.doi.org/10.1063/1.1781159 (7 pages) | Cited 12 times

Online Publication Date: 10 September 2004

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The diffusion slip coefficient is calculated for binary gaseous mixtures on the basis of the McCormack kinetic model of the Boltzmann equation, which is solved by the discrete velocity method. The calculations are carried out for the three mixtures of noble gases: neon–argon, helium–argon, and helium–xenon. Two models of the intermolecular interaction potential were considered. It was shown that this coefficient strongly depends on the potential. It was concluded that the use of the rigid spheres model does not provide physical results. An example of application of the diffusion slip coefficient is given.

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