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P H Diamond - One of the best experts on this subject based on the ideXlab platform.
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scale selection and feedback loops for patterns in drift wave zonal Flow Turbulence
Plasma Physics and Controlled Fusion, 2019Co-Authors: Weixin Guo, P H Diamond, David W Hughes, Lu Wang, Arash AshourvanAbstract:The scale selection and feedback loops for the formation and sustainment of a mesoscopic staircase profile structure are investigated for drift wave-zonal Flow Turbulence. A mean field model derived from the Hasegawa–Wakatani system and including the evolution of mean density, mean vorticity and perturbed potential enstrophy (PE) is used. It is found that a quasi-periodic zonal staircase forms from self-sharpening of modulation. The principle feedback loop is through the nonlinear dependence of mixing length on electron density gradient, which enters by way of the potential vorticity gradient. Counterintuitively, shearing is not effective. Moreover, the number of steps in the staircase is sensitive to both the drive (production rate of PE and initial density gradient) and damping (Flow viscosity and collisional diffusivity) factors. The minimal step scale is selected by competition between the initial density gradient and diffusive dissipation. Finite Turbulence spreading is necessary to form the staircase, but moderate enhancement of Turbulence spreading tends to wash out the pattern. The staircase retains a memory of its initial state. Both the mean shear and zonal shear affect the staircase evolution. A strong mean shear quenches the pattern by suppressing the drift wave Turbulence. The implications of these findings are also discussed.
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small scale coherent vortex generation in drift wave zonal Flow Turbulence
Physics of Plasmas, 2015Co-Authors: Z B Guo, T S Hahm, P H DiamondAbstract:We present a paradigm for the generation of small scale coherent vortex (SSCV) in drift wave-zonal Flow (DW-ZF) Turbulence. We demonstrate that phases of DWs can couple coherently, mediated by the ZF shearing. A SSCV is formed when the phases of the DWs are “attracted” to form a stable “phase cluster.” We show that the ZF shearing induces asymmetry between “attractive” and “repulsive” phase couplings, so that a net attractive phase coupling results. The turbulent DWs will (partially)synchronize into a stable SSCV at locations, where the attractive phase coupling induced by the ZF shearing exceeds the “detuning” effects by the DW dispersion and random phase scattering. We also discuss the “self-binding” effect of the newly formed SSCV.
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elasticity in drift wave zonal Flow Turbulence
Physical Review E, 2014Co-Authors: Z B Guo, Yusuke Kosuga, P H Diamond, O D GurcanAbstract:We present a theory of turbulent elasticity, a property of drift-wave--zonal-Flow (DW-ZF) Turbulence, which follows from the time delay in the response of DWs to ZF shears. An emergent dimensionless parameter ${|\ensuremath{\langle}v\ensuremath{\rangle}}^{\ensuremath{'}}|/\ensuremath{\Delta}{\ensuremath{\omega}}_{k}$ is found to be a measure of the degree of Fickian flux-gradient relation breaking, where ${|\ensuremath{\langle}v\ensuremath{\rangle}}^{\ensuremath{'}}|$ is the ZF shearing rate and $\ensuremath{\Delta}{\ensuremath{\omega}}_{k}$ is the Turbulence decorrelation rate. For ${|\ensuremath{\langle}v\ensuremath{\rangle}}^{\ensuremath{'}}|/\ensuremath{\Delta}{\ensuremath{\omega}}_{k}g1$, we show that the ZF evolution equation is converted from a diffusion equation, usually assumed, to a telegraph equation, i.e., the turbulent momentum transport changes from a diffusive process to wavelike propagation. This scenario corresponds to a state very close to the marginal instability of the DW-ZF system, e.g., the Dimits shift regime. The frequency of the ZF wave is ${\ensuremath{\Omega}}_{\mathrm{ZF}}=\ifmmode\pm\else\textpm\fi{}{\ensuremath{\gamma}}_{d}^{1/2}{\ensuremath{\gamma}}_{\mathrm{modu}}^{1/2}$, where ${\ensuremath{\gamma}}_{d}$ is the ZF friction coefficient and ${\ensuremath{\gamma}}_{\mathrm{modu}}$ is the net ZF growth rate for the case of the Fickian flux-gradient relation. This insight provides a natural framework for understanding temporally periodic ZF structures in the Dimits shift regime and in the transition from low confined mode to high confined mode in confined plasmas.
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coherent structure phenomena in drift wave zonal Flow Turbulence
Physical Review Letters, 2000Co-Authors: A I Smolyakov, P H Diamond, M A MalkovAbstract:Zonal Flows are azimuthally symmetric plasma potential perturbations spontaneously generated from small-scale drift-wave fluctuations via the action of Reynolds stresses. We show that, after initial linear growth, zonal Flows can undergo further nonlinear evolution leading to the formation of long-lived coherent structures which consist of self-bound wave packets supporting stationary shear layers. Such coherent zonal Flow structures constitute dynamical paradigms for intermittency in drift-wave Turbulence that manifests itself by the intermittent distribution of regions with a reduced level of anomalous transport.
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self regulating shear Flow Turbulence a paradigm for the l to h transition
Physical Review Letters, 1994Co-Authors: P H Diamond, Y M Liang, Benjamin A Carreras, P W TerryAbstract:A self-consistent model of the [ital L] to [ital H] transition is derived from coupled nonlinear envelope equations for the fluctuation level and radial electric field shear, [ital E][sub [ital r]][sup [prime]]. These equations exhibit a supercritical bifurcation between dual [ital L]-mode and [ital H]-mode fixed points. The transition occurs when the Turbulence level is large enough for the Reynolds stress drive to overcome the damping of the [bold E][times][bold B] Flow. This defines a power threshold for the transition, which is calculated and found to be consistent with experimental findings.
Richard R Kerswell - One of the best experts on this subject based on the ideXlab platform.
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minimal seeds for shear Flow Turbulence using nonlinear transient growth to touch the edge of chaos
Journal of Fluid Mechanics, 2012Co-Authors: Chris C T Pringle, Ashley P Willis, Richard R KerswellAbstract:We propose a general strategy for determining the minimal finite amplitude disturbance that triggers transition to Turbulence in shear Flows. This involves constructing a variational problem that searches over all disturbances of fixed initial amplitude which respect the boundary conditions, incompressibility and the Navier–Stokes equations, to maximize a chosen functional over an asymptotically long time period. The functional must be selected such that it identifies turbulent velocity fields by taking significantly enhanced values compared to those for laminar fields. We illustrate this approach using the ratio of the final to initial perturbation kinetic energies (energy growth) as the functional and the energy norm to measure amplitudes in the context of pipe Flow. Our results indicate that the variational problem yields a smooth converged solution provided that the initial amplitude is below the threshold for transition. This optimal is the nonlinear analogue of the well-studied (linear) transient growth optimal. At the critical threshold, the optimization seeks out a disturbance that is on the ‘edge’ of Turbulence during the period. Above this threshold, when disturbances trigger Turbulence by the end of the period, convergence is then practically impossible. The first disturbance found to trigger Turbulence as the amplitude is increased identifies the ‘minimal seed’ for the given geometry and forcing (Reynolds number). We conjecture that it may be possible to select a functional such that the converged optimal below threshold smoothly converges to the minimal seed at threshold. Our choice of the energy growth functional is shown to come close to this for the pipe Flow geometry investigated here.
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minimal seeds for shear Flow Turbulence using nonlinear transient growth to touch the edge of chaos
arXiv: Fluid Dynamics, 2011Co-Authors: Chris C T Pringle, Ashley P Willis, Richard R KerswellAbstract:We propose a general strategy for determining the minimal finite amplitude isturbance to trigger transition to Turbulence in shear Flows. This involves constructing a variational problem that searches over all disturbances of fixed initial amplitude, which respect the boundary conditions, incompressibility and the Navier--Stokes equations, to maximise a chosen functional over an asymptotically long time period. The functional must be selected such that it identifies turbulent velocity fields by taking significantly enhanced values compared to those for laminar fields. We illustrate this approach using the ratio of the final to initial perturbation kinetic energies (energy growth) as the functional and the energy norm to measure amplitudes in the context of pipe Flow. Our results indicate that the variational problem yields a smooth converged solution providing the amplitude is below the threshold amplitude for transition. This optimal is the nonlinear analogue of the well-studied (linear) transient growth optimal. At and above this threshold, the optimising search naturally seeks out disturbances that trigger Turbulence by the end of the period, and convergence is then practically impossible. The first disturbance found to trigger Turbulence as the amplitude is increased identifies the `minimal seed' for the given geometry and forcing (Reynolds number). We conjecture that it may be possible to select a functional such that the converged optimal below threshold smoothly converges to the minimal seed at threshold. This seems at least approximately true for our choice of energy growth functional and the pipe Flow geometry chosen here.
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using nonlinear transient growth to construct the minimal seed for shear Flow Turbulence
Physical Review Letters, 2010Co-Authors: Chris C T Pringle, Richard R KerswellAbstract:Linear transient growth analysis is commonly used to suggest the structure of disturbances which are particularly efficient in triggering transition to Turbulence in shear Flows. We demonstrate that the addition of nonlinearity to the analysis can substantially change the prediction made in pipe Flow from simple two-dimensional streamwise rolls to a spanwise and cross-stream localized three-dimensional state. This new nonlinear optimal is demonstrably more efficient in triggering Turbulence than the linear optimal indicating that there are better ways to design perturbations to achieve transition.
Jonathan B Freund - One of the best experts on this subject based on the ideXlab platform.
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the near field pressure radiated by planar high speed free shear Flow Turbulence
Journal of Fluid Mechanics, 2017Co-Authors: David Buchta, Jonathan B FreundAbstract:Jets with Mach numbers are well known to emit an intense, fricative, so-called crackle sound, having steep compressions interspersed with weaker expansions that together yield a positive pressure skewness . Its shock-like features are obvious hallmarks of nonlinearity, although a full explanation of the skewness is lacking, and wave steepening alone is understood to be insufficient to describe its genesis. Direct numerical simulations of high-speed free-shear Flows for Mach numbers , , and in the Reynolds number range are used to examine the mechanisms leading to such pressure signals, especially the pressure skewness. For and , the pressure immediately adjacent the Turbulence already has the large associated with jet crackle. It also has a surprisingly complex three-dimensional structure, with locally high pressures at compression-wave intersections. This structure is transient, and it simplifies as radiating waves subsequently merge through nonlinear mechanisms to form the relatively distinct and approximately two-dimensional Mach-like waves deduced from laboratory visualizations. A transport equation for is analysed to quantify factors affecting its development. The viscous dissipation that decreases is balanced by a particular nonlinear flux, which is (of course) absent in linear acoustic propagation and confirmed to be independent of the simulated Reynolds numbers. Together these effects maintain an approximately constant in the near acoustic field.
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near field shocks radiated by high speed free shear Flow Turbulence
AIAA CEAS Aeroacoustics Conference, 2014Co-Authors: David Buchta, Aaron T Anderson, Jonathan B FreundAbstract:Temporally developing turbulent planar free shear layers with Mach numbers M = 1.5, 2.5, and 3.5 are directly simulated to provide a geometrically simplified model of the generation of a peculiar sound, known as ‘crackle’. Sound-field pressure skewness for M = 2.5 and 3.5 cases exceed Sk(p ′) > 0.4, which has been correlated with perception of crackle. Statistics related to Mach wave angle and wave density indicate nonlinear interactions in the very near acoustic field in these same cases. Results show both merging of multiple waves and flattening of non-planar waves into approximately planar weak shocks.
Tobias M Schneider - One of the best experts on this subject based on the ideXlab platform.
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increasing lifetimes and the growing saddles of shear Flow Turbulence
Physical Review Letters, 2014Co-Authors: Tobias Kreilos, Bruno Eckhardt, Tobias M SchneiderAbstract:In linearly stable shear Flows, Turbulence spontaneously decays with a characteristic lifetime that varies with Reynolds number. The lifetime sharply increases with Reynolds number so that a possible divergence marking the transition to sustained Turbulence at a critical point has been discussed. We present a mechanism by which the lifetimes increase: in the system’s state space, turbulent motion is supported by a chaotic saddle. Inside this saddle a locally attracting periodic orbit is created and undergoes a traditional bifurcation sequence generating chaos. The formed new “ turbulent bubble” is initially an attractor supporting persistent chaotic dynamics. Soon after its creation, it collides with its own boundary, by which it becomes leaky and dynamically connected with the surrounding structures. The complexity of the chaotic saddle that supports transient Turbulence hence increases by incorporating the remnant of a new bubble. As a a result, the time it takes for a trajectory to leave the saddle and decay to the laminar state is increased. We demonstrate this phenomenon in plane Couette Flow and show that characteristic lifetimes vary nonsmoothly and nonmonotonically with Reynolds number.
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transition in localized pipe Flow Turbulence
Physical Review Letters, 2009Co-Authors: Fernando Mellibovsky, Alvaro Meseguer, Tobias M Schneider, Bruno EckhardtAbstract:Direct numerical simulation of transitional pipe Flow is carried out in a long computational domain in order to characterize the dynamics within the saddle region of phase space that separates laminar Flow from turbulent intermittency. For Reynolds numbers ranging from Re ¼ 1800 to 2800, a shoot and bisection method is used to compute critical trajectories. The chaotic saddle or edge state approached by these trajectories is studied in detail. For Re � 2000 the edge state and the corresponding intermittent puff are shown to share similar averaged global properties. For Re � 2200, the puff length grows unboundedly whereas the edge state varies only little with Re. In this regime, transition is shown to proceed in two steps: first the energy grows to produce a localized turbulent patch, which then, during the second stage, spreads out to fill the pipe.
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transition in localized pipe Flow Turbulence
Physical Review Letters, 2009Co-Authors: Fernando Mellibovsky, Alvaro Meseguer, Tobias M Schneider, Bruno EckhardtAbstract:Direct numerical simulation of transitional pipe Flow is carried out in a long computational domain in order to characterize the dynamics within the saddle region of phase space that separates laminar Flow from turbulent intermittency. For Reynolds numbers ranging from Re=1800 to 2800, a shoot and bisection method is used to compute critical trajectories. The chaotic saddle or edge state approached by these trajectories is studied in detail. For Re or =2200, the puff length grows unboundedly whereas the edge state varies only little with Re. In this regime, transition is shown to proceed in two steps: first the energy grows to produce a localized turbulent patch, which then, during the second stage, spreads out to fill the pipe.
Chris C T Pringle - One of the best experts on this subject based on the ideXlab platform.
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minimal seeds for shear Flow Turbulence using nonlinear transient growth to touch the edge of chaos
Journal of Fluid Mechanics, 2012Co-Authors: Chris C T Pringle, Ashley P Willis, Richard R KerswellAbstract:We propose a general strategy for determining the minimal finite amplitude disturbance that triggers transition to Turbulence in shear Flows. This involves constructing a variational problem that searches over all disturbances of fixed initial amplitude which respect the boundary conditions, incompressibility and the Navier–Stokes equations, to maximize a chosen functional over an asymptotically long time period. The functional must be selected such that it identifies turbulent velocity fields by taking significantly enhanced values compared to those for laminar fields. We illustrate this approach using the ratio of the final to initial perturbation kinetic energies (energy growth) as the functional and the energy norm to measure amplitudes in the context of pipe Flow. Our results indicate that the variational problem yields a smooth converged solution provided that the initial amplitude is below the threshold for transition. This optimal is the nonlinear analogue of the well-studied (linear) transient growth optimal. At the critical threshold, the optimization seeks out a disturbance that is on the ‘edge’ of Turbulence during the period. Above this threshold, when disturbances trigger Turbulence by the end of the period, convergence is then practically impossible. The first disturbance found to trigger Turbulence as the amplitude is increased identifies the ‘minimal seed’ for the given geometry and forcing (Reynolds number). We conjecture that it may be possible to select a functional such that the converged optimal below threshold smoothly converges to the minimal seed at threshold. Our choice of the energy growth functional is shown to come close to this for the pipe Flow geometry investigated here.
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minimal seeds for shear Flow Turbulence using nonlinear transient growth to touch the edge of chaos
arXiv: Fluid Dynamics, 2011Co-Authors: Chris C T Pringle, Ashley P Willis, Richard R KerswellAbstract:We propose a general strategy for determining the minimal finite amplitude isturbance to trigger transition to Turbulence in shear Flows. This involves constructing a variational problem that searches over all disturbances of fixed initial amplitude, which respect the boundary conditions, incompressibility and the Navier--Stokes equations, to maximise a chosen functional over an asymptotically long time period. The functional must be selected such that it identifies turbulent velocity fields by taking significantly enhanced values compared to those for laminar fields. We illustrate this approach using the ratio of the final to initial perturbation kinetic energies (energy growth) as the functional and the energy norm to measure amplitudes in the context of pipe Flow. Our results indicate that the variational problem yields a smooth converged solution providing the amplitude is below the threshold amplitude for transition. This optimal is the nonlinear analogue of the well-studied (linear) transient growth optimal. At and above this threshold, the optimising search naturally seeks out disturbances that trigger Turbulence by the end of the period, and convergence is then practically impossible. The first disturbance found to trigger Turbulence as the amplitude is increased identifies the `minimal seed' for the given geometry and forcing (Reynolds number). We conjecture that it may be possible to select a functional such that the converged optimal below threshold smoothly converges to the minimal seed at threshold. This seems at least approximately true for our choice of energy growth functional and the pipe Flow geometry chosen here.
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using nonlinear transient growth to construct the minimal seed for shear Flow Turbulence
Physical Review Letters, 2010Co-Authors: Chris C T Pringle, Richard R KerswellAbstract:Linear transient growth analysis is commonly used to suggest the structure of disturbances which are particularly efficient in triggering transition to Turbulence in shear Flows. We demonstrate that the addition of nonlinearity to the analysis can substantially change the prediction made in pipe Flow from simple two-dimensional streamwise rolls to a spanwise and cross-stream localized three-dimensional state. This new nonlinear optimal is demonstrably more efficient in triggering Turbulence than the linear optimal indicating that there are better ways to design perturbations to achieve transition.