1,368 research outputs found
Statistical State Dynamics: a new perspective on turbulence in shear flow
Traditionally, single realizations of the turbulent state have been the
object of study in shear flow turbulence. When a statistical quantity was
needed it was obtained from a spatial, temporal or ensemble average of sample
realizations of the turbulence. However, there are important advantages to
studying the dynamics of the statistical state (the SSD) directly. In highly
chaotic systems statistical quantities are often the most useful and the
advantage of obtaining these statistics directly from a state variable is
obvious. Moreover, quantities such as the probability density function (pdf)
are often difficult to obtain accurately by sampling state trajectories even if
the pdf is stationary. In the event that the pdf is time dependent, solving
directly for the pdf as a state variable is the only alternative. However,
perhaps the greatest advantage of the SSD approach is conceptual: adopting this
perspective reveals directly the essential cooperative mechanisms among the
disparate spatial and temporal scales that underly the turbulent state. While
these cooperative mechanisms have distinct manifestation in the dynamics of
realizations of turbulence both these cooperative mechanisms and the phenomena
associated with them are not amenable to analysis directly through study of
realizations as they are through the study of the associated SSD. In this
review a selection of example problems in the turbulence of planetary and
laboratory flows is examined using recently developed SSD analysis methods in
order to illustrate the utility of this approach to the study of turbulence in
shear flow.Comment: 27 pages, 18 figures. To appear in the book "Zonal jets:
Phenomenology, genesis, physics", Cambridge University Press, edited by B.
Galperin and P. L. Rea
Israeli Demolition of Palestinian Houses as a Punitive Measure: Application of International Law to Regulation 119
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
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