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John Taylor - One of the best experts on this subject based on the ideXlab platform.
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testing linear marginal stability in stratified Shear Layers
Journal of Fluid Mechanics, 2018Co-Authors: Christopher Howland, John Taylor, C P CaulfieldAbstract:We use two-dimensional direct numerical simulations of Boussinesq stratified Shear Layers to investigate the influence of the minimum gradient Richardson number $Ri_{m}$ on the early time evolution of Kelvin–Helmholtz instability to its saturated ‘billow’ state. Even when the diffusion of the background velocity and density distributions is counterbalanced by artificial body forces to maintain the initial profiles, in the limit as $Ri_{m}\rightarrow 1/4$ , the perturbation growth rate tends to zero and the saturated perturbation energy becomes small. These results imply, at least for such canonical inflectional stratified Shear flows, that ‘marginally unstable’ flows with $Ri_{m}$ only slightly less than 1/4 are highly unlikely to become ‘turbulent’, in the specific sense of being associated with significantly enhanced dissipation, irreversible mixing and non-trivial modification of the background distributions without additional externally imposed forcing.
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nonlinear evolution of linear optimal perturbations of strongly stratified Shear Layers
Journal of Fluid Mechanics, 2017Co-Authors: Alexis Kaminski, C P Caulfield, John TaylorAbstract:The Miles–Howard theorem states that a necessary condition for normal-mode instability in parallel, inviscid, steady stratified Shear flows is that the minimum gradient Richardson number, , is less than somewhere in the flow. However, the non-normality of the Navier–Stokes and buoyancy equations may allow for substantial perturbation energy growth at finite times. We calculate numerically the linear optimal perturbations which maximize the perturbation energy gain for a stably stratified Shear layer consisting of a hyperbolic tangent velocity distribution with characteristic velocity and a uniform stratification with constant buoyancy frequency . We vary the bulk Richardson number (corresponding to ) between 0.20 and 0.50 and the Reynolds numbers between 1000 and 8000, with the Prandtl number held fixed at . We find the transient growth of non-normal perturbations may be sufficient to trigger strongly nonlinear effects and breakdown into small-scale structures, thereby leading to enhanced dissipation and non-trivial modification of the background flow even in flows where . We show that the effects of nonlinearity are more significant for flows with higher , lower and higher initial perturbation amplitude . Enhanced kinetic energy dissipation is observed for higher- and lower- flows, and the mixing efficiency, quantified here by where is the dissipation rate of density variance and is the dissipation rate of kinetic energy, is found to be approximately 0.35 for the most strongly nonlinear cases.
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transient growth in strongly stratified Shear Layers
Journal of Fluid Mechanics, 2014Co-Authors: Alexis Kaminski, C P Caulfield, John TaylorAbstract:We investigate numerically transient linear growth of three-dimensional perturbations in a stratified Shear layer to determine which perturbations optimize the growth of the total kinetic and potential energy over a range of finite target time intervals. The stratified Shear layer has an initial parallel hyperbolic tangent velocity distribution with Reynolds number and Prandtl number , where is the kinematic viscosity of the fluid and is the diffusivity of the density. The initial stable buoyancy distribution has constant buoyancy frequency , and we consider a range of flows with different bulk Richardson number , which also corresponds to the minimum gradient Richardson number at the midpoint of the Shear layer. For short target times, the optimal perturbations are inherently three-dimensional, while for sufficiently long target times and small the optimal perturbations are closely related to the normal-mode ‘Kelvin–Helmholtz’ (KH) instability, consistent with analogous calculations in an unstratified mixing layer recently reported by Arratia et al. (J. Fluid Mech., vol. 717, 2013, pp. 90–133). However, we demonstrate that non-trivial transient growth occurs even when the Richardson number is sufficiently high to stabilize all normal-mode instabilities, with the optimal perturbation exciting internal waves at some distance from the midpoint of the Shear layer.
C P Caulfield - One of the best experts on this subject based on the ideXlab platform.
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testing linear marginal stability in stratified Shear Layers
Journal of Fluid Mechanics, 2018Co-Authors: Christopher Howland, John Taylor, C P CaulfieldAbstract:We use two-dimensional direct numerical simulations of Boussinesq stratified Shear Layers to investigate the influence of the minimum gradient Richardson number $Ri_{m}$ on the early time evolution of Kelvin–Helmholtz instability to its saturated ‘billow’ state. Even when the diffusion of the background velocity and density distributions is counterbalanced by artificial body forces to maintain the initial profiles, in the limit as $Ri_{m}\rightarrow 1/4$ , the perturbation growth rate tends to zero and the saturated perturbation energy becomes small. These results imply, at least for such canonical inflectional stratified Shear flows, that ‘marginally unstable’ flows with $Ri_{m}$ only slightly less than 1/4 are highly unlikely to become ‘turbulent’, in the specific sense of being associated with significantly enhanced dissipation, irreversible mixing and non-trivial modification of the background distributions without additional externally imposed forcing.
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nonlinear evolution of linear optimal perturbations of strongly stratified Shear Layers
Journal of Fluid Mechanics, 2017Co-Authors: Alexis Kaminski, C P Caulfield, John TaylorAbstract:The Miles–Howard theorem states that a necessary condition for normal-mode instability in parallel, inviscid, steady stratified Shear flows is that the minimum gradient Richardson number, , is less than somewhere in the flow. However, the non-normality of the Navier–Stokes and buoyancy equations may allow for substantial perturbation energy growth at finite times. We calculate numerically the linear optimal perturbations which maximize the perturbation energy gain for a stably stratified Shear layer consisting of a hyperbolic tangent velocity distribution with characteristic velocity and a uniform stratification with constant buoyancy frequency . We vary the bulk Richardson number (corresponding to ) between 0.20 and 0.50 and the Reynolds numbers between 1000 and 8000, with the Prandtl number held fixed at . We find the transient growth of non-normal perturbations may be sufficient to trigger strongly nonlinear effects and breakdown into small-scale structures, thereby leading to enhanced dissipation and non-trivial modification of the background flow even in flows where . We show that the effects of nonlinearity are more significant for flows with higher , lower and higher initial perturbation amplitude . Enhanced kinetic energy dissipation is observed for higher- and lower- flows, and the mixing efficiency, quantified here by where is the dissipation rate of density variance and is the dissipation rate of kinetic energy, is found to be approximately 0.35 for the most strongly nonlinear cases.
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transient growth in strongly stratified Shear Layers
Journal of Fluid Mechanics, 2014Co-Authors: Alexis Kaminski, C P Caulfield, John TaylorAbstract:We investigate numerically transient linear growth of three-dimensional perturbations in a stratified Shear layer to determine which perturbations optimize the growth of the total kinetic and potential energy over a range of finite target time intervals. The stratified Shear layer has an initial parallel hyperbolic tangent velocity distribution with Reynolds number and Prandtl number , where is the kinematic viscosity of the fluid and is the diffusivity of the density. The initial stable buoyancy distribution has constant buoyancy frequency , and we consider a range of flows with different bulk Richardson number , which also corresponds to the minimum gradient Richardson number at the midpoint of the Shear layer. For short target times, the optimal perturbations are inherently three-dimensional, while for sufficiently long target times and small the optimal perturbations are closely related to the normal-mode ‘Kelvin–Helmholtz’ (KH) instability, consistent with analogous calculations in an unstratified mixing layer recently reported by Arratia et al. (J. Fluid Mech., vol. 717, 2013, pp. 90–133). However, we demonstrate that non-trivial transient growth occurs even when the Richardson number is sufficiently high to stabilize all normal-mode instabilities, with the optimal perturbation exciting internal waves at some distance from the midpoint of the Shear layer.
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the anatomy of the mixing transition in homogeneous and stratified free Shear Layers
Journal of Fluid Mechanics, 2000Co-Authors: C P Caulfield, W R PeltierAbstract:We investigate the detailed nature of the ‘mixing transition’ through which turbulence may develop in both homogeneous and stratified free Shear Layers. Our focus is upon the fundamental role in transition, and in particular the associated ‘mixing’ (i.e. small-scale motions which lead to an irreversible increase in the total potential energy of the flow) that is played by streamwise vortex streaks, which develop once the primary and typically two-dimensional Kelvin–Helmholtz (KH) billow saturates at finite amplitude.Saturated KH billows are susceptible to a family of three-dimensional secondary instabilities. In homogeneous fluid, secondary stability analyses predict that the stream-wise vortex streaks originate through a ‘hyperbolic’ instability that is localized in the vorticity braids that develop between billow cores. In sufficiently strongly stratified fluid, the secondary instability mechanism is fundamentally different, and is associated with convective destabilization of the statically unstable subLayers that are created as the KH billows roll up.We test the validity of these theoretical predictions by performing a sequence of three-dimensional direct numerical simulations of Shear layer evolution, with the flow Reynolds number (defined on the basis of Shear layer half-depth and half the velocity difference) Re = 750, the Prandtl number of the fluid Pr = 1, and the minimum gradient Richardson number Ri(0) varying between 0 and 0.1. These simulations quantitatively verify the predictions of our stability analysis, both as to the spanwise wavelength and the spatial localization of the streamwise vortex streaks. We track the nonlinear amplification of these secondary coherent structures, and investigate the nature of the process which actually triggers mixing. Both in stratified and unstratified Shear Layers, the subsequent nonlinear amplification of the initially localized streamwise vortex streaks is driven by the vertical Shear in the evolving mean flow. The two-dimensional flow associated with the primary KH billow plays an essentially catalytic role. Vortex stretching causes the streamwise vortices to extend beyond their initially localized regions, and leads eventually to a streamwise-aligned collision between the streamwise vortices that are initially associated with adjacent cores.It is through this collision of neighbouring streamwise vortex streaks that a final and violent finite-amplitude subcritical transition occurs in both stratified and unstratified Shear Layers, which drives the mixing process. In a stratified flow with appropriate initial characteristics, the irreversible small-scale mixing of the density which is triggered by this transition leads to the development of a third layer within the flow of relatively well-mixed fluid that is of an intermediate density, bounded by narrow regions of strong density gradient.
Tatsuya Hasegawa - One of the best experts on this subject based on the ideXlab platform.
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Combustion-induced local Shear Layers within premixed flamelets in weakly turbulent flows
Physics of Fluids, 2018Co-Authors: Andrei N. Lipatnikov, Vladimir Sabelnikov, Shinnosuke Nishiki, Tatsuya HasegawaAbstract:3D direct numerical simulation data obtained from statistically stationary, planar, weakly turbulent, premixed flames, which are characterized by two different density ratios (7.53 and 2.50) and are associated with the flamelet combustion regime, are analyzed to investigate differences between velocity and pressure variations (i) in flamelets in a weakly turbulent flow and (ii) in the counterpart laminar flame. Results show that while the thermo-chemical structure of the flamelets is weakly affected by turbulence under the studied conditions, the local velocity, vorticity, and pressure fields within the flamelets differ significantly from the velocity, vorticity, and pressure fields, respectively, within the laminar flame. In particular, local Shear Layers appear within flamelets in the turbulent flow because acceleration of a reacting mixture by the local pressure gradient is inversely proportional to the mixture density and, hence, depends on the mixture state. The Shear Layers are characterized by large velocity gradients (both the tangential gradient of the normal velocity with respect to the flamelet surface and the normal gradient of the tangential velocity), whose magnitudes may be comparable with the magnitude of the velocity gradient across the laminar flame. In flamelet zones characterized by a relatively large magnitude of the locally normal gradient of the tangential velocity, the local vorticity magnitude is also large and such zones contribute substantially to the overall generation of vorticity due to baroclinic torque. These results cast doubts on the validity of a simple common modeling approach that consists in directly invoking expressions derived for the laminar flames in order to describe the influence of combustion-induced thermal expansion on weakly turbulent velocity and pressure fields.
Sutanu Sarkar - One of the best experts on this subject based on the ideXlab platform.
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turbulent Shear Layers in a uniformly stratified background dns at high reynolds number
Journal of Fluid Mechanics, 2021Co-Authors: Alexandra Vandine, Hieu T Pham, Sutanu SarkarAbstract:Direct numerical simulations are performed to investigate a stratified Shear layer at high Reynolds number (. The dependence of mixing efficiency on buoyancy Reynolds number during the turbulence phase is qualitatively similar to homogeneous Sheared turbulence.
Michele Guala - One of the best experts on this subject based on the ideXlab platform.
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prograde vortices internal Shear Layers and the taylor microscale in high reynolds number turbulent boundary Layers
Journal of Fluid Mechanics, 2021Co-Authors: Michael Heisel, Charitha De Silva, N Hutchins, Ivan Marusic, Michele GualaAbstract:The statistical properties of prograde spanwise vortex cores and internal Shear Layers (ISLs) are evaluated for a series of high-Reynolds-number turbulent boundary Layers. The considered flows span a wide range of both Reynolds number and surface roughness. In each case, the largest spanwise vortex cores in the outer layer of the boundary layer have size comparable to the Taylor microscale . The same scaling parameters describe the average thickness and velocity difference across the ISLs. The results demonstrate the importance of the local large-eddy turnover time in determining the strain rate confining the size of the vortex cores and Shear Layers. The relevance of the turnover time, and more generally the Taylor microscale, can be explained by a stretching mechanism involving the mutual interaction of coherent velocity structures such as uniform momentum zones with the evolving Shear Layers separating the structures.
