Showing papers in "Physics of Fluids in 1991"
TL;DR: In this article, a new eddy viscosity model is presented which alleviates many of the drawbacks of the existing subgrid-scale stress models, such as the inability to represent correctly with a single universal constant different turbulent fields in rotating or sheared flows, near solid walls, or in transitional regimes.
Abstract: One major drawback of the eddy viscosity subgrid‐scale stress models used in large‐eddy simulations is their inability to represent correctly with a single universal constant different turbulent fields in rotating or sheared flows, near solid walls, or in transitional regimes. In the present work a new eddy viscosity model is presented which alleviates many of these drawbacks. The model coefficient is computed dynamically as the calculation progresses rather than input a priori. The model is based on an algebraic identity between the subgrid‐scale stresses at two different filtered levels and the resolved turbulent stresses. The subgrid‐scale stresses obtained using the proposed model vanish in laminar flow and at a solid boundary, and have the correct asymptotic behavior in the near‐wall region of a turbulent boundary layer. The results of large‐eddy simulations of transitional and turbulent channel flow that use the proposed model are in good agreement with the direct simulation data.
6,747 citations
TL;DR: Germano et al. as discussed by the authors generalized the dynamic subgrid-scale (SGS) model for the large eddy simulation (LES) of compressible flows and transport of a scalar.
Abstract: The dynamic subgrid-scale (SGS) model of Germano et al. (1991) is generalized for the large eddy simulation (LES) of compressible flows and transport of a scalar. The model was applied to the LES of decaying isotropic turbulence, and the results are in excellent agreement with experimental data and direct numerical simulations. The expression for the SGS turbulent Prandtl number was evaluated using direct numerical simulation (DNS) data in isotropic turbulence, homogeneous shear flow, and turbulent channel flow. The qualitative behavior of the model for turbulent Prandtl number and its dependence on molecular Prandtl number, direction of scalar gradient, and distance from the wall are in accordance with the total turbulent Prandtl number from the DNS data.
1,588 citations
TL;DR: In this paper, a direct numerical simulation of isotropic turbulence was used to investigate the effect of turbulence on the concentration fields of heavy particles, and it was shown that the particles collect preferentially in regions of low vorticity and high strain rate.
Abstract: Direct numerical simulation of isotropic turbulence was used to investigate the effect of turbulence on the concentration fields of heavy particles. The hydrodynamic field was computed using 643 points and a statistically stationary flow was obtained by forcing the low‐wave‐number components of the velocity field. The particles used in the simulations were time advanced according to Stokes drag law and were also assumed to be much more dense than the fluid. Properties of the particle cloud were obtained by following the trajectories of 1 000 000 particles through the simulated flow fields. Three values of the ratio of the particle time constant to large‐scale turbulence time scale were used in the simulations: 0.075, 0.15, and 0.52. The simulations show that the particles collect preferentially in regions of low vorticity and high strain rate. This preferential collection was most pronounced for the intermediate particle time constant (0.15) and it was also found that the instantaneous number density was as much as 25 times the mean value for these simulations. The fact that dense particles collect in regions of low vorticity and high strain in turn implies that turbulence may actually inhibit rather than enhance mixing of particles.
853 citations
TL;DR: In this paper, low-dimensional dynamical models for two-dimensional unsteady flows in complex geometries that are characterized by simple (low-dimensional) dynamical behavior are considered.
Abstract: Two‐dimensional unsteady flows in complex geometries that are characterized by simple (low‐dimensional) dynamical behavior are considered. Detailed spectral element simulations are performed, and the proper orthogonal decomposition or POD (also called method of empirical eigenfunctions) is applied to the resulting data for two examples: the flow in a periodically grooved channel and the wake of an isolated circular cylinder. Low‐dimensional dynamical models for these systems are obtained using the empirically derived global eigenfunctions in the spectrally discretized Navier–Stokes equations. The short‐ and long‐term accuracy of the models is studied through simulation, continuation, and bifurcation analysis. Their ability to mimic the full simulations for Reynolds numbers (Re) beyond the values used for eigenfunction extraction is evaluated. In the case of the grooved channel, where the primary horizontal wave number of the flow is imposed from the channel periodicity and so remains unchanged with Re, the models extrapolate reasonably well over a range of Re values. In the case of the cylinder wake, however, due to the significant spatial wave number changes of the flow with the Re, the models are only valid in a small neighborhood of the decompositional Reynolds number.
547 citations
TL;DR: In this article, the effects of the inertia of a particle on its flow-tracking accuracy and particle dispersion were studied using direct numerical simulations of 2D compressible free shear layers in convective Mach number (Mc) range of 0.2 to 0.6.
Abstract: The effects of the inertia of a particle on its flow-tracking accuracy and particle dispersion are studied using direct numerical simulations of 2D compressible free shear layers in convective Mach number (Mc) range of 0.2 to 0.6. The results show that particle response is well characterized by tau, the ratio of particle response time to the flow time scales (Stokes' number). The slip between particle and fluid imposes a fundamental limit on the accuracy of optical measurements such as LDV and PIV. The error is found to grow like tau up to tau = 1 and taper off at higher tau. For tau = 0.2 the error is about 2 percent. In the flow visualizations based on Mie scattering, particles with tau more than 0.05 are found to grossly misrepresent the flow features. These errors are quantified by calculating the dispersion of particles relative to the fluid. Overall, the effect of compressibility does not seem to be significant on the motion of particles in the range of Mc considered here.
452 citations
TL;DR: In this paper, it was shown through experimental data from flapping foils and data from fish observation that thrust develops through the formation of a reverse von Karman street whose preferred Strouhal number is between 0.25 and 0.35.
Abstract: Foils oscillating transversely to an oncoming uniform flow produce, under certain conditions, thrust. It is shown through experimental data from flapping foils and data from fish observation that thrust develops through the formation of a reverse von Karman street whose preferred Strouhal number is between 0.25 and 0.35, and that optimal foil efficiency is achieved within this Strouhal range.
452 citations
TL;DR: In this article, the backscatter and forward scatter contributions to the SGS dissipation were comparable, and each was often much larger than the other, in the presence of a Fourier cutoff filter.
Abstract: Most subgrid‐scale (SGS) models for large‐eddy simulations (LES) are absolutely dissipative (that is, they remove energy from the large scales at each point in the physical space). The actual SGS stresses, however, may transfer energy to the large scales (backscatter) at a given location. Recent work on the LES of transitional flows [Piomelli et al., Phys. Fluids A 2, 257 (1990)] has shown that failure to account for this phenomenon can cause inaccurate prediction of the growth of the perturbations. Direct numerical simulations of transitional and turbulent channel flow and compressible isotropic turbulence are used to study the backscatter phenomenon. In all flows considered roughly 50% of the grid points were experiencing backscatter when a Fourier cutoff filter was used. The backscatter fraction was less with a Gaussian filter, and intermediate with a box filter in physical space. Moreover, the backscatter and forward scatter contributions to the SGS dissipation were comparable, and each was often much...
452 citations
TL;DR: In this paper, the scaling laws for the low, mid and high frequency regions of the spectrum were established for the wall pressure field in a low-noise flow facility, and the existence of two distinct wave number groups: a high wave number group that scales on the similarity variable k1ξ=ωξ/Uc(ξ,ω) associated with turbulent sources in the log region of the boundary layer, in which eddies decay in proportion to their size.
Abstract: Experimental measurements of the frequency spectra and frequency cross‐spectra of the wall pressure fluctuations beneath a turbulent boundary layer were made in a low‐noise flow facility. The data, taken over a range of flow speeds, clearly display a dimensionless frequency (ωδ/uτ=50) at which the spectra achieve a maximum and a low‐frequency range with an approximately ω2 rolloff. The scaling laws for the low‐, mid‐, and high‐frequency regions of the spectrum are established. The cross‐spectral data, obtained over a range of streamwise separations (0.21≤ξ/δ≤16.4), allow for the computations of the decay Γ(ξ,ω) and convection velocity Uc(ξ,ω) of the wall pressure field. These data show the existence of two distinct wave number groups: a high wave number group that scales on the similarity variable k1ξ=ωξ/Uc(ξ,ω) associated with turbulent sources in the log region of the boundary layer, in which eddies decay in proportion to their size, and a low wave number group that defines the cutoff for the large‐scal...
361 citations
TL;DR: In this paper, a second-order autoregressive equation is used to model the acceleration of fluid particles in turbulence in order to study the effect of Reynolds number on Lagrangian turbulence statistics.
Abstract: A second‐order autoregressive equation is used to model the acceleration of fluid particles in turbulence in order to study the effect of Reynolds number on Lagrangian turbulence statistics. It is shown that this approach provides a good representation of dissipation subrange structure of Lagrangian velocity and acceleration statistics. The parameters of the model, two time scales representing the energy‐containing and dissipation scales, are determined by matching the model velocity autocorrelation function to Kolmogorov similarity forms in the inertial subrange and the dissipation subrange. The model is tested against the Lagrangian statistics obtained by Yeung and Pope [J. Fluid Mech. 207, 531 (1989)] from direct numerical simulations of turbulence. Agreement between the model predictions and simulation data for second‐order Lagrangian statistics such as the velocity structure function, the acceleration correlation function, and the dispersion of fluid particles is excellent, indicating that the main departures from Kolmogorov’s theory of local isotropy shown by the simulation data are due to low Reynolds number. For Reynolds numbers typical of laboratory experiments and direct numerical simulations of turbulence the root‐mean‐square dispersion of marked particles is changed from the Langevin equation (i.e., infinite Reynolds number) prediction by up to about 50% at large times. Most of this change can be accounted for by the change in the Lagrangian integral time scale. It is also shown that Reynolds number effects in laboratory dispersion or Lagrangian turbulence measurements can cause significant errors (typically of order 50%) when the value of the Kolmogorov Lagrangian structure function constant C0 is estimated by fitting the predictions of the Langevin equation to these data. A value C0 = 7 is obtained by fitting the new model to the direct simulation data.
347 citations
TL;DR: In this paper, a three-dimensional simulation of the mixing of miscible fluids by Rayleigh-Taylor instability is described for density ratios, ρ 1/ρ2, in the range 1.5 to 20.
Abstract: Three‐dimensional simulation of the mixing of miscible fluids by Rayleigh–Taylor instability is described for density ratios, ρ1/ρ2, in the range 1.5 to 20. Significant dissipation of density fluctuations and kinetic energy occurs via the cascade to high wave numbers. Comparison is made with experimental measurements of the overall growth of the mixing zone and of the magnitude of density fluctuations. The differences between 2‐D and 3‐D simulation are discussed.
321 citations
TL;DR: In this article, the variable soft sphere (VSS) model was introduced for both the viscosity and diffusion cross sections (coefficients) to be consistent with those of the inverse power law (IPL) or Lennard Jones (LJ) potential.
Abstract: The variable soft sphere (VSS) molecular model is introduced for both the viscosity and diffusion cross sections (coefficients) to be consistent with those of the inverse‐power‐law (IPL) or Lennard‐Jones (LJ) potential. The VSS model has almost the same analytical and computational simplicity (computation time) as the variable hard sphere (VHS) model in the Monte Carlo simulation of rarefied gas flows. The null‐collision Monte Carlo method is used to make comparative calculations for the molecular diffusion in a heat‐bath gas and the normal shock wave structure in a simple gas. For the most severe test of the VSS model for the IPL potential, the softest practical model corresponding to the Maxwell molecule is chosen. The agreement in the molecular diffusion and shock wave structure between the VSS model and the IPL or LJ potential is remarkably good.
TL;DR: In this article, a Langevin equation of motion with a random driving force not limited to white noise is derived and a suitable form of kinetic equation is then sought that reproduces this equation of state and predicts Gaussian spatial diffusion in the longterm limit with the correct form for the diffusion coefficient in homogeneous stationary turbulence.
Abstract: The work described is part of a long‐term study in pursuit of a kinetic equation for particles suspended in a turbulent flow. This equation represents the transport of the average particle phase space density and can be used to derive the continuum equations and constitutive relations for a two‐fluid model of a dispersed particle flow and to establish the correct form of boundary conditions. A key role in this study is played by the equation of state of the dispersed particles, which is derived here for a Langevin equation of motion with a random driving force not limited to white noise. A suitable form of kinetic equation is then sought that reproduces this equation of state and predicts Gaussian spatial diffusion in the long‐term limit with the correct form for the diffusion coefficient in homogeneous stationary turbulence. It is shown that both these requirements are automatically satisfied by constructing forms for the phase space diffusion coefficient that preserve invariance to a random Galilean transformation. The most general form is shown to be an expansion in successively higher‐order cumulants of the aerodynamic driving force. When this force is a Gaussian process all terms apart from the first term contract to zero, i.e., the phase space diffusion current is of the form −[μ⋅(∂/∂v) +λ⋅(∂/∂x)]〈W〉 , where 〈W〉 is the average phase space density of particles with velocity v and position x at time t and μ and λ are phase space diffusion tensors whose components are memory integrals involving the correlation of the aerodynamic force along a particle trajectory. With both this form and the more general form of phase space diffusion current, the kinetic equation contracts to the classical Fokker–Planck equation in the white noise limit. Finally with the Gaussian form for the diffusion current, the form of the average phase space density is examined for the important case of a point source diffusing in an unbounded homogeneous stationary flow.
TL;DR: In this article, three-dimensional flows of an incompressible fluid and an inviscid subsonic compressible gas are considered and how the WKB method can be used for investigating their stability.
Abstract: Three‐dimensional flows of an inviscid incompressible fluid and an inviscid subsonic compressible gas are considered and it is demonstrated how the WKB method can be used for investigating their stability. The evolution of rapidly oscillating initial data is considered and it is shown that in both cases the corresponding flows are unstable if the transport equations associated with the wave which is advected by the flow have unbounded solutions. Analyzing the corresponding transport equations, a number of classical stability conditions are rederived and some new ones are obtained. In particular, it is demonstrated that steady flows of an incompressible fluid and an inviscid subsonic compressible gas are unstable if they have points of stagnation.
TL;DR: In this paper, the existence of eddy shocklets in three-dimensional compressible turbulence is investigated, and they are verified to have all the characteristics of a typical shock wave, such as proper jumps in pressure and density along with a local entropy peak inside the high compression zone.
Abstract: The existence of eddy shocklets in three‐dimensional compressible turbulence is controversial. To investigate the occurrence of eddy shocklets, numerical simulations of temporally decaying isotropic turbulence are conducted. Dilatation statistics from simulations with different initial fluctuation Mach numbers, Mt, show that dilatation is more intermittent and more negatively skewed for higher Mt. By studying instantaneous flow fields, shocklets are found and verified to have all the characteristics of a typical shock wave, such as proper jumps in pressure and density along with a local entropy peak inside the high‐compression zone. Although overall compressible dissipation contributes to less than one‐tenth of the total dissipation, compressible dissipation around shocklets is about an order of magnitude larger than typical values of incompressible dissipation. In the zones of eddy shocklets, pressure is highly correlated with dilatation to convert kinetic energy into internal energy. These mechanisms ne...
TL;DR: In this paper, a spectral analysis of the concentration field suggests that the formation of this inelastic microstructure is correlated with the magnitude of the total stresses in the flow, thus departing from the predictions of the theory that assumes spatial homogeneity and isotropy.
Abstract: Computer simulations of two‐dimensional rapid granular flows of uniform smooth inelastic disks under simple shear reveal a dynamic microstructure characterized by the local, spatially anisotropic agglomeration of disks. A spectral analysis of the concentration field suggests that the formation of this inelastic microstructure is correlated with the magnitude of the total stresses in the flow. The simulations confirm the theoretical results of Jenkins and Richman [J. Fluid Mech. 192, 313 (1988)] for the kinetic stresses in the dilute limit and for the collisional stresses in the dense limit, when the size of the periodic domain used in the simulations is a small multiple of the disk diameter. However, the kinetic and, to a lesser extent, collisional stresses both increase significantly with the size of the periodic domain, thus departing from the predictions of the theory that assumes spatial homogeneity and isotropy.
TL;DR: In this article, a subgrid model is developed and applied to a large-eddy simulation of the Kolmogorov inertial subrange, which is based directly on a model of the Navier-Stokes equation.
Abstract: A subgrid model is developed and applied to a large-eddy simulation of the Kolmogorov inertial subrange. The subgrid model is based directly on a model of the Navier-Stokes equation. The improved subgrid model contains two terms: an eddy viscosity and a stochastic force. Use of the subgrid model in a forced large-eddy simulation results in an energy spectrum that exhibits a clear k exp -5/3 power-law subrange with an approximate value K(o) = 2.1 of the Kolmogorov constant.
TL;DR: In this paper, it was shown that a necessary and sufficient condition for the scalar dissipation rate, conditioned on scalar value φ, to be independent of φ is that the one-point scalar probability distribution function (pdf) is Gaussian.
Abstract: It is shown that a necessary and sufficient condition for the scalar dissipation rate, conditioned on scalar value φ, to be independent of φ is that the one‐point scalar probability distribution function (pdf) is Gaussian. It is then shown that the amplitude mapping closure yields a closed‐form, separable expression for the φ dependence of the conditional dissipation rate in the case of an initial double‐delta scalar pdf. If the initial binary scalar field is located at φ=±1, the solution is exp{ − 2[erf−1(φ)]2}, a result that is strongly supported by earlier direct numerical simulations.
TL;DR: In this article, the authors investigated thermocapillary convection in cylindrical liquid bridges (floating zones) of liquids with Prandtl numbers Pr=1, 7, and 49.
Abstract: Thermocapillary convection (TC) in cylindrical liquid bridges (floating zones) of liquids with Prandtl numbers Pr=1, 7, and 49 is investigated experimentally. The zones have been heated from above or from below to study the influence of buoyant forces. Fourier analyses of temperature signals from zones covering systematically wide ranges of aspect ratios A and Marangoni numbers Ma have shown the existence of various forms of periodic and nonperiodic TC. This paper reports on periodic TC existing under certain conditions between the onset of time‐dependent TC at the critical Marangoni number Mac and 7×Mac. From the measurements of the onset of periodic TC the dependence is reported for the threshold Mac and the period near the threshold τc on the aspect ratio. The development of periodic TC when further increasing Ma is shown by typical examples from measurements of the frequency and the amplitude of the oscillations. By correlation analyses from three temperature signals, different structures of periodic ...
TL;DR: In this article, the authors derived a rigorous expression for the static fluid permeability k for flow through porous media to the electrical formation factor F (inverse of the dimensionless effective conductivity) and an effective length parameter L, i.e., k=L2/8F.
Abstract: A rigorous expression is derived that relates exactly the static fluid permeability k for flow through porous media to the electrical formation factor F (inverse of the dimensionless effective conductivity) and an effective length parameter L, i.e., k=L2/8F. This length parameter involves a certain average of the eigenvalues of the Stokes operator and reflects information about electrical and momentum transport. From the exact relation for k, a rigorous upper bound follows in terms of the principal viscous relation time Θ1 (proportional to the inverse of the smallest eigenvalue): k≤νΘ1/F, where ν is the kinematic viscosity. It is also demonstrated that νΘ1≤DT1, where T1 is the diffusion relaxation time for the analogous scalar diffusion problem and D is the diffusion coefficient. Therefore, one also has the alternative bound k≤DT1/F. The latter expression relates the fluid permeability on the one hand to purely diffusional parameters on the other. Finally, using the exact relation for the permeability, a ...
TL;DR: In this article, the authors used the large eddy simulation (LES) technique to simulate turbulent flow in a straight duct of square cross section and showed that both the Reynolds normal and shear stresses equally contribute to the production of mean streamwise vorticity.
Abstract: The fully developed turbulent flow in a straight duct of square cross section has been simulated using the large eddy simulation (LES) technique. A mixed spectral‐finite difference method has been used in conjunction with the Smagorinsky eddy‐viscosity model for the subgrid scales. The simulation was performed for a Reynolds number of 360 based on friction velocity (5810 based on bulk velocity) and duct width. The simulation correctly predicted the existence of secondary flows and their effects on the mean flow and turbulence statistics. The results are in good qualitative agreement with the experimental data available at much higher Reynolds numbers. It is observed that both the Reynolds normal and shear stresses equally contribute to the production of mean streamwise vorticity.
TL;DR: In this paper, the structure of the vorticity and passive scalar fields were examined by means of direct numerical simulations of homogeneous isotropic turbulence with 963 grid points and Rλ ≥ 60.
Abstract: Small‐scale structures of the vorticity and passive scalar fields have been examined by means of direct numerical simulations of homogeneous isotropic turbulence with 963 grid points and Rλ≊60. Both statistical and visual techniques have been used to examine the structure of certain quantities from the evolution equations for enstrophy and the scalar gradient. Tubelike regions of intense enstrophy contain large positive and sometimes large negative enstrophy production, and mostly moderate‐valued energy dissipation regions surround these tubes. The most intense regions of the scalar gradient are dissociated from the vortex tubes, and occur as large flat sheets. Within these sheets the scalar gradient production is large, the energy dissipation is small, and in their vicinity only moderate‐valued sheetlike enstrophy regions exist. The statistical techniques show that although activity in these intense regions is strong, on a volume normalized basis, by far the largest contributions to the terms in the evolution equations, along with the energy dissipation, are from low‐level ‘‘background’’ activity.
TL;DR: In this paper, the effect of anisotropic dispersion on nonlinear viscous fingering in miscible displacements is examined, and the dominance of finger interaction mechanisms that are essentially independent of details of the concentration fields and governed fundamentally by pressure fields is demonstrated.
Abstract: The effect of anisotropic dispersion on nonlinear viscous fingering in miscible displacements is examined. The formulation admits dispersion coefficient‐velocity field couplings (i.e., mechanical dispersivities) appropriate to both porous media and Hele–Shaw cells. A Hartley transform‐based scheme is used to numerically simulate unstable miscible displacement. Several nonlinear finger interactions were observed. Shielding, spreading, tip splitting, and pairing of viscous fingers were observed here, as well as in isotropic simulations. Multiple coalescence and fading were observed in simulations with weak lateral dispersion, but not for isotropic dispersion. Transversely and longitudinally averaged one‐dimensional concentration histories demonstrate the rate at which the mixing zone broadens and the increase in lateral scale as the fingers evolve when no tip splitting occurs. These properties are insensitive to both the dispersion anisotropy and the Peclet number at high Peclet number and long times. This suggests the dominance of finger interaction mechanisms that are essentially independent of details of the concentration fields and governed fundamentally by pressure fields.
TL;DR: The stability of stratified shear flows when the density interface is much thinner than, and displaced with respect to, the velocity interface is investigated in this article, where a row of spanwise vortex tubes forms at the level of maximum velocity gradient which, because of profile asymmetry, is displaced from the mean interface level.
Abstract: This study investigates the stability of stratified shear flows when the density interface is much thinner than, and displaced with respect to, the velocity interface. Theoretical results obtained from the Taylor–Goldstein equation are compared with experiments performed in mixing layer channels. In these experiments a row of spanwise vortex tubes forms at the level of maximum velocity gradient which, because of the profile asymmetry, is displaced from the mean interface level. As the bulk Richardson number is lowered from a high positive value the effects of these vortex tubes become more pronounced. Initially the interface cusps under their influence, then thin wisps of fluid are drawn from the cusps into asymmetric Kelvin–Helmholtz billows. At lower Richardson numbers increasingly more fluid is drawn into these billows. The inherent asymmetry of flows generated in mixing layer channels is shown to preclude an effective study of the Holmboe instability. Statically unstable flows (negative Richardson numbers) are subject to the Rayleigh–Taylor instability. However, if the absolute value of the Richardson number is sufficiently small the Kelvin–Helmholtz instability dominates initially.
TL;DR: In this article, the Cercignani-Lampis gas surface scattering kernel is extended to include two important cases not covered by the basic model, i.e., diffuse scattering with partial energy accommodation, and the accommodation of vibrational energy of a diatomic molecule with equally spaced energy levels.
Abstract: The Cercignani–Lampis gas–surface scattering kernel is extended to include two important cases not covered by the basic model. These are (a) diffuse scattering with partial energy accommodation, and (b) accommodation of vibrational energy of a diatomic molecule with equally spaced energy levels. Both extensions are easily implemented in direct simulation Monte Carlo (DSMC) calculations. The results of some test calculations are presented.
TL;DR: In this paper, a means of identifying and characterizing chaotic mixing regions by examining patterns of spatial variation of finite-time estimates of the Lyapunov exponents is proposed, and tested on a number of idealized cases.
Abstract: Some implications of chaotic advection for mixing of potential vorticity and chemical species by large‐scale, two‐dimensional, atmospheric flows are examined. It is argued that such mixing is important in the Earth’s atmosphere and in those of the other rapidly rotating planets, but that the essential features of the mixing cannot be captured by an effective diffusivity. A means of identifying and characterizing chaotic mixing regions by examining patterns of spatial variation of finite‐time estimates of the Lyapunov exponents is proposed, and tested on a number of idealized cases. Some preliminary results on application of the method to Northern Hemisphere atmospheric data are reported. The principal mixing zones, characteristic mixing time, and barriers to transport are identified.
TL;DR: In this article, up to two pairings of the dominant spanwise rollers have been simulated, and estimates for the degree of three-dimensionalality required for the pairing to initiate the mixing transition were obtained.
Abstract: Direct numerical simulations of time‐developing plane mixing layers have been performed using a variety of initial conditions. Up to two pairings of the dominant spanwise rollers have been simulated. When the flow is sufficiently three dimensional, a pairing can cause the mixing layer to undergo a transition to small‐scale turbulence. This small‐scale transition is accompanied by increased mixing of a passive scalar, similar to observations of the mixing transition in experiments. As part of the transition process, thin vortex sheets are generated by vortex stretching and roll up as in a two‐dimensional mixing layer. This higher‐order rollup is part of the cascade to small‐scale turbulence. Estimates are obtained for the degree of three‐dimensionality required for the pairing to initiate the transition.
TL;DR: In this paper, the authors investigated the stability of high-temperature boundary layers under the assumption of chemical equilibrium and this gas model is labeled as real gas model and found that real gas effects cause the first mode instability to stabilize while the second mode is made more unstable.
Abstract: High‐temperature effects alter the physical and transport properties of a gas, air in particular, due to vibrational excitation and gas dissociation, and thus the chemical reactions have to be considered in order to compute the flow field. Linear stability of high‐temperature boundary layers is investigated under the assumption of chemical equilibrium and this gas model is labeled here as ‘‘real gas model.’’ In this model, the system of stability equations remains of the same order as for the perfect gas and the effect of chemical reactions is introduced only through mean flow and gas property variations. Calculations are performed for Mach 10 and 15 boundary layers and the results indicate that real gas effects cause the first mode instability to stabilize while the second mode is made more unstable. It is also found that the second mode instability shifts to lower frequencies. There is a slight destabilizing influence of real gas on the Goertler instability as compared to the perfect gas results.
TL;DR: In this article, a lid-driven cavity (LDC) with a small amount of throughflow reveals multiple steady states at low cavity Reynolds numbers, which suggest that multiple stable steady states may also exist in closed LDCs.
Abstract: Flow visualization studies of a lid‐driven cavity (LDC) with a small amount of throughflow reveal multiple steady states at low cavity Reynolds numbers. These results show that the well‐known LDC flow, which consists of a primary eddy and secondary corner eddies, is only locally stable, becomes globally unstable, and competes with at least three other steady states before being replaced by a time‐periodic flow. The small amount of throughflow present in this system seems to have no qualitative effect on the fluid flow characteristics. These observations suggest that multiple stable steady states may also exist in closed LDC’s. Since stability properties of the closed LDC flows are virtually unexplored, we interpret our flow visualization results by first proposing an expected behavior of an idealized (free‐slip end walls) LDC and then treating the problem at hand as a perturbation of the ideal case. The results also suggest that there are nonunique and competing sequences of transitions that lead the flow in a LDC from laminar steady state toward turbulence.
TL;DR: In this paper, the fine structure maps of the instantaneous scalar energy dissipation rate field in a turbulent flow are presented in the form of spatial and temporally successive data planes from a sequence of such three-dimensional volumes.
Abstract: Results from highly resolved, four‐dimensional measurements of the fine structure of the fully space‐ and time‐varying Sc≫1 conserved scalar field and the associated scalar energy dissipation rate field in a turbulent flow are presented. The resolution achieved in all three spatial dimensions and in time reaches down to the local strain‐limited molecular diffusion scale in the flow, allowing all three components of the instantaneous scalar gradient vector field ∇ζ(x,t) and their time evolution at every point in the data space to be directly evaluated. Results are presented in the form of fine structure maps of the instantaneous dissipation field loge ∇ζ⋅∇ζ(x,t) in several spatially adjacent data planes within an individual three‐dimensional spatial data volume, as well as in several temporally successive data planes from a sequence of such three‐dimensional data volumes. The degree of anisotopy in the underlying scalar gradient field is characterized in terms of the joint distribution β(ϑ,φ) of spherical ...