Volume 16, Issue 10, October 2004
 LETTERS


Suppression of vortexshedding noise via derivativefree shape optimization
View Description Hide DescriptionIn this Letter we describe the application of a derivativefree 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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 ARTICLES


Transient growth and minimal defects: Two possible initial paths of transition to turbulence in plane shear flows
View Description Hide DescriptionTwo possible initial paths of transition to turbulence in simple wallbounded shear flows are examined by looking at the development in space of infinitesimal disturbances. The first is the—bynowclassical—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.

Free stream turbulence induced disturbances in boundary layers with wall suction
View Description Hide DescriptionAn 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 (, 2.0, and 2.3%). A turbulence generating grid of the active type is used and offers the possibility to vary the 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 breakdown to turbulence. Twopoint correlation measurements in the spanwise direction show that the averaged streak spacing decreases with increasing FSTlevel, 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.

On the equilibrium states predicted by second moment models in rotating, stably stratified homogeneous shear flow
View Description Hide DescriptionThe structural equilibrium behavior of the general linear secondmoment 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 anisotropytensor, dispersion tensor, dimensionless scalar variance , and the ratio of mean to turbulent time scale is found. The variable of particular interest to bifurcation analysis, is shown as a function of the parameters characterizing the body forces: (the ratio of the rotation rate to the mean shear rate) for rotation and (the gradient Richardson number) for buoyancy; it determines the bifurcation surface in the 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 turbulencemodel 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 , and ensures the existence of stable, real solutions for all combinations of rotation and buoyancy is proposed.

Effect of a temperature difference between the cylinders on the Taylor–Couette bifurcation in a gas
View Description Hide DescriptionA gas in a timeindependent 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 fluiddynamictype 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.

On the dynamics of selfsustained onedimensional detonations: A numerical study in the shockattached frame
View Description Hide DescriptionIn this work we investigate the dynamics of selfsustained 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 shockattached 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 socalled “nonreflecting” boundary condition at the far end of the computational domain in order to minimize the influence of the spurious reflected waves.

Hybrid continuumatomistic simulation of singular corner flow
View Description Hide DescriptionA hybrid numerical method is used to study cavity flow driven by a moving wall. Continuum equations with noslip 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 NavierStokes (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 from the corners. In the limit of low wall velocities , 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 , nonNewtonian behavior near the corner causes to rise linearly with .

Linear stability of radial displacements in porous media: Influence of velocityinduced dispersion and concentrationdependent diffusion
View Description Hide DescriptionA parametric study is conducted in order to investigate the influence of (a) velocity dependent dispersion, and (b) concentrationdependent diffusion on the stability of miscibleporous 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. Concentrationdependent 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.

Experimental study of velocity filtered joint density function for large eddy simulation
View Description Hide DescriptionThe velocity filtered joint density function (VFJDF) used in large eddy simulation and the structure of the subgridscale (SGS) velocity are studied experimentally. Measurements are made in the fully developed region of an axisymmetric turbulent jet (with jet Reynolds number) using an array consisting of three Xwire probes. Filtering in the crossstream 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 offcenterline 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 offdiagonal component of the conditional dissipation tensor is nonnegligible 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 eddyviscositytype models for the SGS stress generally cannot give qualitatively correct predictions for SGS turbulence under local rapid distortion.

The flow in a cylindrical container with a rotating end wall at small but finite Reynolds number
View Description Hide DescriptionSimilarity solutions of the first kind are intermediate asymptotic solutions for the Stokes flow field and for the firstorder inertial correction to the Stokes flow field in small aspect ratio geometries with both noslip and freeslip boundary conditions opposite the rotating end wall. These results differ from the semiinfinite cylindrical container, where similarity solutions of the second kind are intermediate asymptotic representations of the Stokes and firstorder 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 noslip boundary condition opposite the rotating end wall but the boundary discontinuity is important in determining the flow field with a freeslip boundary condition opposite the rotating end wall.

Experimental and theoretical investigation of the nonmodal growth of steady streaks in a flat plate boundary layer
View Description Hide DescriptionAn 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.

Stability analysis of the flow in a cubical cavity heated from below
View Description Hide DescriptionA 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 for values of up to . 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 finitedifference solver. Present results show that different stable convective flow patterns can coexist for different ranges of the Rayleigh number.

Stability and transport properties of multiplepatch quasiequilibria
View Description Hide DescriptionA 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 vortexsolutions. 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 multiplepatch vortices turn out to be remarkably stable, although the regularization itself should be considered as a (symmetric) perturbation of Crowdy’s multipolar solutions.

An eddyviscosity subgridscale model for turbulent shear flow: Algebraic theory and applications
View Description Hide DescriptionAn eddyviscosity model is proposed and applied in largeeddy 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 nearwall regions. The model is expressed in firstorder 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 threedimensional flows is introduced. Within this framework several types of flows are proven to have zero energy transfer to subgrid scales. The eddyviscosity is zero in the same cases; the theoretical subgrid dissipation and the eddyviscosity 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.

A simplified Fourier method for computing the internal wavefield generated by an oscillating source in a horizontally moving, depthdependent background
View Description Hide DescriptionA method is developed to describe the linear internal wavefield generated by an oscillating source in horizontally moving, depthdependent 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.

Stability of convection induced by selective absorption of radiation in a fluid overlying a porous layer
View Description Hide DescriptionA linear stability analysis for the onset of convection induced by selective absorption of radiation in a twolayer 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.

Upstream entrainment in numerical simulations of spatially evolving round jets
View Description Hide DescriptionDirect 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, nearfield turbulent intensities and pressure fluctuations on the jet centerline are noticeably affected. It is suggested that inflow entrainment results in an effective coflow, 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 farfield 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 nearfield behavior is important.

Oscillatory convection in a twodimensional porous box with asymmetric lateral boundary conditions
View Description Hide DescriptionThe onset of convection in a twodimensional 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.

Control of drop rebound with solid target motion
View Description Hide DescriptionDrops with a high surface tension and a low viscosity, such as water and molten metaldrops, exhibit a vigorous recoiling and a longlasting 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 dropliquid 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.

Ageostrophic, anticyclonic instability of a geostrophic, barotropic boundary current
View Description Hide DescriptionAfter 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, ) as . The downstream phase velocity of the unstable mode lies within the speed range for the background current, so the eigenmode has a nearcritical layer within the zone of strong background shear. Its unstable eigenmode has an aspect ratio of downstream and vertical wave numbers, , on the order of the ratio of the Coriolis and BrüntVäisällä 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 farfield structure similar to an inertiagravity wave. This supports the interpretation that the modal instability arises through the coalescence (i.e., resonance) of two stable normalmode branches, one associated with the background shear flow and the other an inertiagravity or Kelvin wave mode.
