9,422 research outputs found
Optimal transient growth in thin-interface internal solitary waves
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
(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 ) of potentially
unstable Richardson number, . They propagate through the base wave
as coherent packets whose total energy gain increases rapidly with . 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 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
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
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 () 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
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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