51,488 research outputs found
Linear non-normal energy amplification of harmonic and stochastic forcing in turbulent channel flow
The linear response to stochastic and optimal harmonic forcing of small coherent perturbations to the turbulent channel mean flow is computed for Reynolds numbers ranging from Re_tau=500 to Re_tau=20000. Even though the turbulent mean flow is linearly stable, it is nevertheless able to sustain large amplifications by the forcing. The most amplified structures consist of streamwise elongated streaks that are optimally forced by streamwise elongated vortices. For streamwise elongated structures, the mean energy amplification of the stochastic forcing is found to be, to a first approximation, inversely proportional to the forced spanwise wavenumber while it is inversely proportional to its square for optimal harmonic forcing in an intermediate spanwise wavenumber range. This scaling can be explicitly derived from the linearised equations under the assumptions of geometric similarity of the coherent perturbations and of logarithmic base flow. Deviations from this approximate power-law regime are apparent in the premultiplied energy amplification curves that reveal a strong influence of two different peaks. The dominant peak scales in outer units with the most amplified spanwise wavelength of while the secondary peak scales in wall units with the most amplified . The associated optimal perturbations are almost independent of the Reynolds number when respectively scaled in outer and inner units. In the intermediate wavenumber range the optimal perturbations are approximatively geometrically similar. Furthermore, the shape of the optimal perturbations issued from the initial value, the harmonic forcing and the stochastic forcing analyses are almost indistinguishable. The optimal streaks corresponding to the large-scale peak strongly penetrate into the inner layer, where their amplitude is proportional to the mean-flow profile. At the wavenumbers corresponding to the large-scale peak, the optimal amplifications of harmonic forcing are at least two orders of magnitude larger than the amplifications of the variance of stochastic forcing and both increase with the Reynolds number. This confirms the potential of the artificial forcing of optimal large-scale streaks for the flow control of wall-bounded turbulent flows
Analysis and optimal velocity control of a stochastic convective Cahn-Hilliard equation
A Cahn-Hilliard equation with stochastic multiplicative noise and a random
convection term is considered. The model describes isothermal phase-separation
occurring in a moving fluid, and accounts for the randomness appearing at the
microscopic level both in the phase-separation itself and in the flow-inducing
process. The call for a random component in the convection term stems naturally
from applications, as the fluid's stirring procedure is usually caused by
mechanical or magnetic devices. Well-posedness of the state system is addressed
and optimisation of a standard tracking type cost with respect to the velocity
control is then studied. Existence of optimal controls is proved and the
G\^ateaux-Fr\'echet differentiability of the control-to-state map is shown.
Lastly, the corresponding adjoint backward problem is analysed, and first-order
necessary conditions for optimality are derived in terms of a variational
inequality involving the intrinsic adjoint variables.Comment: 38 page
Stochastic Structural Stability Theory applied to roll/streak formation in boundary layer shear flow
Stochastic Structural Stability Theory (SSST) provides an autonomous,
deterministic, nonlinear dynamical system for evolving the statistical mean
state of a turbulent system. In this work SSST is applied to the problem of
understanding the formation of the roll/streak structures that arise from
free-stream turbulence (FST) and are associated with bypass transition in
boundary layers. Roll structures in the cross-stream/spanwise plane and
associated streamwise streaks are shown to arise as a linear instability of
interaction between the FST and the mean flow. In this interaction incoherent
Reynolds stresses arising from FST are organized by perturbation streamwise
streaks to coherently force perturbation rolls giving rise to an amplification
of the streamwise streak perturbation and through this feedback to an
instability of the combined roll/streak/turbulence complex. The dominant
turbulent perturbation structures involved in supporting the
roll/streak/turbulence complex instability are non-normal optimal perturbations
with the form of oblique waves. The cooperative linear instability giving rise
to the roll/streak structure arises at a bifurcation in the parameter of STM
excitation parameter. This structural instability eventually equilibrates
nonlinearly at finite amplitude and although the resulting statistical
equilibrium streamwise streaks are inflectional the associated flows are
stable. Formation and equilibration of the roll/streak structure by this
mechanism can be traced to the non-normality which underlies interaction
between perturbations and mean flows in modally stable systems.Comment: 16 pages, 24 figures, has been submitted for publication to Physics
of Fluid
A Stochastic Resource-Sharing Network for Electric Vehicle Charging
We consider a distribution grid used to charge electric vehicles such that
voltage drops stay bounded. We model this as a class of resource-sharing
networks, known as bandwidth-sharing networks in the communication network
literature. We focus on resource-sharing networks that are driven by a class of
greedy control rules that can be implemented in a decentralized fashion. For a
large number of such control rules, we can characterize the performance of the
system by a fluid approximation. This leads to a set of dynamic equations that
take into account the stochastic behavior of EVs. We show that the invariant
point of these equations is unique and can be computed by solving a specific
ACOPF problem, which admits an exact convex relaxation. We illustrate our
findings with a case study using the SCE 47-bus network and several special
cases that allow for explicit computations.Comment: 13 pages, 8 figure
Stochastic forcing of the Lamb–Oseen vortex
The aim of the present paper is to analyse the dynamics of the Lamb–Oseen vortex when continuously forced by a random excitation. Stochastic forcing is classically used to mimic external perturbations in realistic configurations, such as variations of atmospheric conditions, weak compressibility effects, wing-generated turbulence injected in aircraft wake, or free-stream turbulence in wind tunnel experiments. The linear response of the Lamb–Oseen vortex to stochastic forcing can be decomposed in relation to the azimuthal symmetry of the perturbation given by the azimuthal wavenumber m. In the axisymmetric case m = 0, we find that the response is characterised by the generation of vortex rings at the outer periphery of the vortex core. This result is consistent with recurrent observations of such dynamics in the study of vortex-turbulence interaction. When considering helical perturbations m = 1, the response at large axial wavelengths consists of a global translation of the vortex, a feature very similar to the phenomenon of vortex meandering (or wandering) observed experimentally, corresponding to an erratic displacement of the vortex core. At smaller wavelengths, we find that stochastic forcing can excite specific oscillating modes of the Lamb–Oseen vortex. More precisely, damped critical-layer modes can emerge via a resonance mechanism. For perturbations with higher azimuthal wavenumber m > 2, we find no structure that clearly dominates the response of the vortex
A Distributed Scheduling Algorithm to Provide Quality-of-Service in Multihop Wireless Networks
Control of multihop Wireless networks in a distributed manner while providing
end-to-end delay requirements for different flows, is a challenging problem.
Using the notions of Draining Time and Discrete Review from the theory of fluid
limits of queues, an algorithm that meets delay requirements to various flows
in a network is constructed. The algorithm involves an optimization which is
implemented in a cyclic distributed manner across nodes by using the technique
of iterative gradient ascent, with minimal information exchange between nodes.
The algorithm uses time varying weights to give priority to flows. The
performance of the algorithm is studied in a network with interference modelled
by independent sets
- …