9,422 research outputs found

    Optimal transient growth in thin-interface internal solitary waves

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    The dynamics of perturbations to large-amplitude Internal Solitary Waves (ISW) in two-layered flows with thin interfaces is analyzed by means of linear optimal transient growth methods. Optimal perturbations are computed through direct-adjoint iterations of the Navier-Stokes equations linearized around inviscid, steady ISWs obtained from the Dubreil-Jacotin-Long (DJL) equation. Optimal perturbations are found as a function of the ISW phase velocity cc (alternatively amplitude) for one representative stratification. These disturbances are found to be localized wave-like packets that originate just upstream of the ISW self-induced zone (for large enough cc) of potentially unstable Richardson number, Ri<0.25Ri < 0.25. They propagate through the base wave as coherent packets whose total energy gain increases rapidly with cc. The optimal disturbances are also shown to be relevant to DJL solitary waves that have been modified by viscosity representative of laboratory experiments. The optimal disturbances are compared to the local WKB approximation for spatially growing Kelvin-Helmholtz (K-H) waves through the Ri<0.25Ri < 0.25 zone. The WKB approach is able to capture properties (e.g., carrier frequency, wavenumber and energy gain) of the optimal disturbances except for an initial phase of non-normal growth due to the Orr mechanism. The non-normal growth can be a substantial portion of the total gain, especially for ISWs that are weakly unstable to K-H waves. The linear evolution of Gaussian packets of linear free waves with the same carrier frequency as the optimal disturbances is shown to result in less energy gain than found for either the optimal perturbations or the WKB approximation due to non-normal effects that cause absorption of disturbance energy into the leading face of the wave.Comment: 33 pages, 22 figure

    Symmetry Analysis in Linear Hydrodynamic Stability Theory: Classical and New Modes in Linear Shear

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    We present a symmetry classification of the linearised Navier-Stokes equations for a two-dimensional unbounded linear shear flow of an incompressible fluid. The full set of symmetries is employed to systematically derive invariant ansatz functions. The symmetry analysis grasps three approaches. Two of them are existing ones, representing the classical normal modes and the Kelvin modes, while the third is a novel approach and leads to a new closed-form solution of traveling modes, showing qualitatively different behaviour in energetics, shape and kinematics when compared to the classical approaches. The last modes are energy conserving in the inviscid case. They are localized in the cross-stream direction and periodic in the streamwise direction. As for the kinematics, they travel at constant velocity in the cross-stream direction, whilst in the streamwise direction they are accelerated by the base flow. In the viscous case, the modes break down due to damping of high wavenumber contributions

    Relaminarisation of Re_{\tau} = 100 channel flow with globally stabilising linear feedback control

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    The problems of nonlinearity and high dimension have so far prevented a complete solution of the control of turbulent flow. Addressing the problem of nonlinearity, we propose a flow control strategy which ensures that the energy of any perturbation to the target profile decays monotonically. The controller's estimate of the flow state is similarly guaranteed to converge to the true value. We present a one-time off-line synthesis procedure, which generalises to accommodate more restrictive actuation and sensing arrangements, with conditions for existence for the controller given in this case. The control is tested in turbulent channel flow (Reτ=100Re_\tau=100) using full-domain sensing and actuation on the wall-normal velocity. Concentrated at the point of maximum inflection in the mean profile, the control directly counters the supply of turbulence energy arising from the interaction of the wall-normal perturbations with the flow shear. It is found that the control is only required for the larger-scale motions, specifically those above the scale of the mean streak spacing. Minimal control effort is required once laminar flow is achieved. The response of the near-wall flow is examined in detail, with particular emphasis on the pressure and wall-normal velocity fields, in the context of Landahl's theory of sheared turbulence

    Relaminarisation of Re_Ï„=100 channel flow with globally stabilising linear feedback control

    Get PDF
    The problems of nonlinearity and high dimension have so far prevented a complete solution of the control of turbulent flow. Addressing the problem of nonlinearity, we propose a flow control strategy which ensures that the energy of any perturbation to the target profile decays monotonically. The controller’s estimate of the flow state is similarly guaranteed to converge to the true value. We present a one-time off-line synthesis procedure, which generalises to accommodate more restrictive actuation and sensing arrangements, with conditions for existence for the controller given in this case. The control is tested in turbulent channel flow (Re_τ = 100) using full-domain sensing and actuation on the wall-normal velocity. Concentrated at the point of maximum inflection in the mean profile, the control directly counters the supply of turbulence energy arising from the interaction of the wall-normal perturbations with the flow shear. It is found that the control is only required for the larger-scale motions, specifically those above the scale of the mean streak spacing. Minimal control effort is required once laminar flow is achieved. The response of the near-wall flow is examined in detail, with particular emphasis on the pressure and wall-normal velocity fields, in the context of Landahl’s theory of sheared turbulence
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