92 research outputs found
Multi-scale invariant solutions in plane Couette flow: a reduced-order model approach
Plane Couette flow at Re=1200 (based on the channel half-height and half the
velocity difference between the top and bottom plates) is investigated in the
minimal multi-scale flow unit (i.e. a flow unit with only two spanwise integral
length scales), a system for which the computation of invariant solutions that
are physically representative of the turbulent state has been understood to be
challenging. To address this challenge, our approach is to employ an accurate
reduced-order model with 600 degrees of freedom (Cavalieri & Nogueira, Phys.
Rev. Fluids, vol. 7, 2022, L102601). Using the two-scale energy budget and the
temporal cross-correlation of key observables, it is first demonstrated that
the model contains most of the multi-scale physical processes identified
recently (Doohan et al., J. Fluid Mech., vol. 913, 2021, A8): i.e. the large-
and small-scale self-sustaining processes, the energy cascade for turbulent
dissipation, and an energy-cascade mediated small-scale production mechanism.
Invariant solutions of the reduced-order model are subsequently computed,
including 96 equilibria and 43 periodic orbits. It is found that all the
computed equilibrium solutions are not able to reproduce sound energy balance
associated with the multi-scale dynamics of turbulent state. Incorporation of
unsteadiness into invariant solutions is seen to be essential for a sensible
description of the multi-scale turbulent dynamics and the related energetics,
at least in this type of flow, as periodic orbits with a sufficiently long
period are mainly able to describe the complex spatiotemporal dynamics
associated with the known multi-scale phenomena
Reduced-order Galerkin models of plane Couette flow
Reduced-order models were derived for plane Couette flow using Galerkin
projection, with orthonormal basis functions taken as the leading
controllability modes of the linearised Navier-Stokes system for a few low
wavenumbers. Resulting Galerkin systems comprise ordinary differential
equations, with a number of degrees of freedom ranging from 144 to 600, which
may be integrated to large times without sign of numerical instability. The
reduced-order models so obtained are also found to match statistics of direct
numerical simulations at Reynolds number 500 and 1200 with reasonable accuracy,
despite a truncation of orders of magnitude in the degrees of freedom of the
system. The present models offer thus an interesting compromise between
simplicity and accuracy in a canonical wall-bounded flow, with relatively few
modes representing coherent structures in the flow and their dominant dynamics.Comment: 10 pages, 4 figure
Jet-edge interaction tones
Motivated by the problem of jet-flap interaction noise, we study the tonal
dynamics that occur when a sharp edge is placed in the hydrodynamic nearfield
of an isothermal turbulent jet. We perform hydrodynamic and acoustic pressure
measurements in order to characterise the tones as a function of Mach number
and streamwise edge position. The distribution of spectral peaks observed, as a
function of Mach number, cannot be explained using the usual edge-tone
scenario, in which resonance is underpinned by coupling between
downstream-travelling Kelvin-Helmholtz wavepackets and upstream-travelling
sound waves. We show, rather, that the strongest tones are due to coupling
between the former and upstream-travelling jet modes recently studied by Towne
et al. (2017) and Schmidt et al. (2017). We also study the band-limited nature
of the resonance, showing a high-frequency cut-off to be due to the frequency
dependence of the upstream-travelling waves. At high Mach number these become
evanescent above a certain frequency, whereas at low Mach number they become
progressively trapped with increasing frequency, a consequence of which is
their not being reflected in the nozzle plane. Additionally, a weaker,
low-frequency, forced-resonance regime is identified that involves the same
upstream travelling jet modes but that couple, in this instance, with
downstream-travelling sound waves. It is suggested that the existence of two
resonance regimes may be due to the non-modal nature of wavepacket dynamics at
low-frequency.Comment: 21 pages, 15 figure
Wavepacket eduction in turbulent jets based on eigenmode decomposition of PIV data
The dynamics of large scale structures in unforced turbulent jets at subsonic speeds have been related to the generation of the peak noise radiated the aft direction. The utility of instability wavepackets computed by linear stability theory or parabolised stability equations (PSE) have been demonstrated for the modeling of the near-field pressure fluctuations associated with the coherent structures. In this paper, we investigate whether the velocity field corresponding to the wavepackets also represents adequately that of the coherent structures. Previous research showed remarkable agreement in the velocity field up to the end of the potential core, but the agreement is lost gradually downstream.
Locally-parallel linear stability theory (LST) of jet velocity profiles is revisited to further study the evolution of the wavepackets and the manner in which PSE models them. An adjoint-based eigenmode decomposition technique is used to project cross-sectional velocity profiles measured using time-resolved particle image velocimetry (PIV) on the Kelvin-Helmholtz eigenmode responsible for the wavepacket amplification. The instability wave thus extracted is then compared, both in amplification and shape, to the PSE wavepacket and to the dominant coherent structures obtained from the proper orthogonal decomposition of the PIV measurements. The comparisons between PSE models and POD-filtered fluctuations define three spatial regions along the streamwise direction that are explained in terms of changes in the LST eigenspectrum
Widest scales in turbulent channels
The widest spanwise scales in turbulent channel flows are studied through the
use of three periodic channel-flow simulations at friction Reynolds number
. The length and height of the channels are the same in
all cases ( and respectively), while the width is
progressively doubled: . The effects of
increasing the domain can not be determined with statistical significance in
our simulations, since the difference in the statistics between the simulations
is of the same order as the errors of convergence. A channel flow similar to
the smaller one (, vol. 500, 2004, pp. 135--144),
which was averaged over a very long time, was used as a reference. The
one-dimensional spanwise spectrum of the streamwise velocity is computed with
the aim of assessing the domain-size effect on the widest scales. Our results
indicate that of the total streamwise energetic fluctuations is
recovered without a significant influence of the size of the domain. The
remaining of the energy reflects that the widest scales in the outer
layer are the ones most significantly affected by the spanwise length of the
domain. The power-spectral density for remains constant even if the
size of the domain in the spanwise direction is increased up to 4 times the
standard spanwise length, indicating that wide, spanwise coherent structures
are not an artifact of domain truncation
Lift-up, Kelvin-Helmholtz and Orr mechanisms in turbulent jets
Three amplification mechanisms present in turbulent jets, namely lift-up, Kelvin–Helmholtz and Orr, are characterized via global resolvent analysis and spectral proper orthogonal decomposition (SPOD) over a range of Mach numbers. The lift-up mechanism was recently identified in turbulent jets via local analysis by Nogueira et al. (J. Fluid Mech., vol. 873, 2019, pp. 211–237) at low Strouhal number ( St ) and non-zero azimuthal wavenumbers ( m ). In these limits, a global SPOD analysis of data from high-fidelity simulations reveals streamwise vortices and streaks similar to those found in turbulent wall-bounded flows. These structures are in qualitative agreement with the global resolvent analysis, which shows that they are a response to upstream forcing of streamwise vorticity near the nozzle exit. Analysis of mode shapes, component-wise amplitudes and sensitivity analysis distinguishes the three mechanisms and the regions of frequency–wavenumber space where each dominates, finding lift-up to be dominant as St/m→0 . Finally, SPOD and resolvent analyses of localized regions show that the lift-up mechanism is present throughout the jet, with a dominant azimuthal wavenumber inversely proportional to streamwise distance from the nozzle, with streaks of azimuthal wavenumber exceeding five near the nozzle, and wavenumbers one and two most energetic far downstream of the potential core
Transition to chaos in a reduced-order model of a shear layer
The present work studies the non-linear dynamics of a shear layer, driven by
a body force and confined between parallel walls, a simplified setting to study
transitional and turbulent shear layers. It was introduced by Nogueira \&
Cavalieri (J. Fluid Mech. 907, A32, 2021), and is here studied using a
reduced-order model based on a Galerkin projection of the Navier-Stokes system.
By considering a confined shear layer with free-slip boundary conditions on the
walls, periodic boundary conditions in streamwise and spanwise directions may
be used, simplifying the system and enabling the use of methods of dynamical
systems theory. A basis of eight modes is used in the Galerkin projection,
representing the mean flow, Kelvin-Helmholtz vortices, rolls, streaks and
oblique waves, structures observed in the cited work, and also present in shear
layers and jets. A dynamical system is obtained, and its transition to chaos is
studied. Increasing Reynolds number leads to pitchfork and Hopf
bifurcations, and the latter leads to a limit cycle with amplitude modulation
of vortices, as in the DNS by Nogueira \& Cavalieri. Further increase of
leads to the appearance of a chaotic saddle, followed by the emergence of
quasi-periodic and chaotic attractors. The chaotic attractors suffer a merging
crisis for higher , leading to chaotic dynamics with amplitude modulation
and phase jumps of vortices. This is reminiscent of observations of coherent
structures in turbulent jets, suggesting that the model represents dynamics
consistent with features of shear layers and jets.Comment: 28 pages, 18 figure
- …