1,250 research outputs found
Linear waves in sheared flows. Lower bound of the vorticity growth and propagation discontinuities in the parameters space
This study provides sufficient conditions for the temporal monotonic decay of
enstrophy for two-dimensional perturbations traveling in the incompressible,
viscous, plane Poiseuille and Couette flows. Extension of J. L. Synge's
procedure (1938) to the initial-value problem allowed us to find the region of
the wavenumber-Reynolds number map where the enstrophy of any initial
disturbance cannot grow. This region is wider than the kinetic energy's one. We
also show that the parameters space is split in two regions with clearly
distinct propagation and dispersion properties
Couette-Poiseuille flow experiment with zero mean advection velocity: Subcritical transition to turbulence
We present a new experimental set-up that creates a shear flow with zero mean
advection velocity achieved by counterbalancing the nonzero streamwise pressure
gradient by moving boundaries, which generates plane Couette-Poiseuille flow.
We carry out the first experimental results in the transitional regime for this
flow. Using flow visualization we characterize the subcritical transition to
turbulence in Couette-Poiseuille flow and show the existence of turbulent spots
generated by a permanent perturbation. Due to the zero mean advection velocity
of the base profile, these turbulent structures are nearly stationary. We
distinguish two regions of the turbulent spot: the active, turbulent core,
which is characterized by waviness of the streaks similar to traveling waves,
and the surrounding region, which includes in addition the weak undisturbed
streaks and oblique waves at the laminar-turbulent interface. We also study the
dependence of the size of these two regions on Reynolds number. Finally, we
show that the traveling waves move in the downstream (Poiseuille).Comment: 17 pages, 15 figure
Order-of-magnitude speedup for steady states and traveling waves via Stokes preconditioning in Channelflow and Openpipeflow
Steady states and traveling waves play a fundamental role in understanding
hydrodynamic problems. Even when unstable, these states provide the
bifurcation-theoretic explanation for the origin of the observed states. In
turbulent wall-bounded shear flows, these states have been hypothesized to be
saddle points organizing the trajectories within a chaotic attractor. These
states must be computed with Newton's method or one of its generalizations,
since time-integration cannot converge to unstable equilibria. The bottleneck
is the solution of linear systems involving the Jacobian of the Navier-Stokes
or Boussinesq equations. Originally such computations were carried out by
constructing and directly inverting the Jacobian, but this is unfeasible for
the matrices arising from three-dimensional hydrodynamic configurations in
large domains. A popular method is to seek states that are invariant under
numerical time integration. Surprisingly, equilibria may also be found by
seeking flows that are invariant under a single very large Backwards-Euler
Forwards-Euler timestep. We show that this method, called Stokes
preconditioning, is 10 to 50 times faster at computing steady states in plane
Couette flow and traveling waves in pipe flow. Moreover, it can be carried out
using Channelflow (by Gibson) and Openpipeflow (by Willis) without any changes
to these popular spectral codes. We explain the convergence rate as a function
of the integration period and Reynolds number by computing the full spectra of
the operators corresponding to the Jacobians of both methods.Comment: in Computational Modelling of Bifurcations and Instabilities in Fluid
Dynamics, ed. Alexander Gelfgat (Springer, 2018
The laminar generalized Stokes layer and turbulent drag reduction
This paper considers plane channel flow modified by waves of spanwise
velocity applied at the wall and travelling along the streamwise direction.
Laminar and turbulent regimes for the streamwise flow are both studied.
When the streamwise flow is laminar, it is unaffected by the spanwise flow
induced by the waves. This flow is a thin, unsteady and streamwise-modulated
boundary layer that can be expressed in terms of the Airy function of the first
kind. We name it the generalized Stokes layer because it reduces to the
classical oscillating Stokes layer in the limit of infinite wave speed.
When the streamwise flow is turbulent, the laminar generalized Stokes layer
solution describes well the space-averaged turbulent spanwise flow, provided
that the phase speed of the waves is sufficiently different from the turbulent
convection velocity, and that the time scale of the forcing is smaller than the
life time of the near-wall turbulent structures. Under these conditions, the
drag reduction is found to scale with the Stokes layer thickness, which renders
the laminar solution instrumental for the analysis of the turbulent flow.
A classification of the turbulent flow regimes induced by the waves is
presented by comparing parameters related to the forcing conditions with the
space and time scales of the turbulent flow.Comment: Accepted for publication on J. Fluid Mec
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