Interaction of forced Orr-Sommerfeld and Squire modes in a low-order representation of turbulent channel flow

  title={Interaction of forced Orr-Sommerfeld and Squire modes in a low-order representation of turbulent channel flow},
  author={Ryan Michael McMullen and Kevin T. Rosenberg and Beverley J. McKeon},
  journal={Physical Review Fluids},
A resolvent-based reduced-order representation is used to capture time-averaged second-order statistics in turbulent channel flow. The recently-proposed decomposition of the resolvent operator into two distinct families related to the Orr-Sommerfeld and Squire operators [K. Rosenberg and B. J. McKeon, Efficient representation of exact coherent states of the Navier-Stokes equations using resolvent analysis, Fluid Dynamics Research 51, 011401 (2019)] results in dramatic improvement in the ability… 
Resolvent analysis of stratification effects on wall-bounded shear flows
The interaction between shear driven turbulence and stratification is a key process in a wide array of geophysical flows with spatio-temporal scales that span many orders of magnitude. A quick
Energy transfer in turbulent channel flows and implications for resolvent modelling
Abstract We analyse the inter-scale transfer of energy for two types of plane Poiseuille flow: the P4U exact coherent state of Park & Graham (J. Fluid Mech., vol. 782, 2015, pp. 430–454) and
Closing the loop: nonlinear Taylor vortex flow through the lens of resolvent analysis
Abstract We present an optimization-based method to efficiently calculate accurate nonlinear models of Taylor vortex flow. Through the resolvent formulation of McKeon & Sharma (J. Fluid Mech., vol.
From bypass transition to flow control and data-driven turbulence modeling: An input-output viewpoint
A comprehensive summary of the tools that can be employed to probe the dynamics of fluctuations around a laminar or turbulent base flow in the presence of such stochastic or deterministic input forcing and how input-output techniques enhance resolvent analysis is described.
Resolvent Analysis of laminar and turbulent duct flows
This work applies resolvent analysis to incompressible flow through a rectangular duct, in order to identify dominant linear energy-amplification mechanisms present in such flows. In particular, we
Scaling of turbulence intensities up to Reτ=106 with a resolvent-based quasilinear approximation
Scaling of near-wall turbulence intensities has been a subject of many investigations over several decades. Emerging evidence suggests that the near-wall streamwise turbulence intensity may not


Resolvent-Based Modeling of Flows in a Channel
This thesis concerns the continued development of the resolvent framework (McKeon and Sharma, 2010) to model wall-bounded turbulent flows. Herein, we introduce novel modifications and extensions of
Efficient representation of exact coherent states of the Navier–Stokes equations using resolvent analysis
A resolvent analysis of exact coherent states (ECS) of the Navier–Stokes equations (NSE) in a low Reynolds number channel is performed. The resolvent framework recasts the NSE into an input/output
Model-based scaling of the streamwise energy density in high-Reynolds-number turbulent channels
Abstract We study the Reynolds-number scaling and the geometric self-similarity of a gain-based, low-rank approximation to turbulent channel flows, determined by the resolvent formulation of McKeon &
Low-dimensional representations of exact coherent states of the Navier-Stokes equations from the resolvent model of wall turbulence.
It is reported that many exact invariant solutions of the Navier-Stokes equations for both pipe and channel flows are well represented by just a few modes of the model of McKeon and Sharma, establishing a surprising new link between the two distinct approaches to understanding turbulence.
A foundation for analytical developments in the logarithmic region of turbulent channels
An analytical framework for studying the logarithmic region of turbulent channels is formulated. We build on recent findings (Moarref et al., J. Fluid Mech., 734, 2013) that the velocity fluctuations
On the shape of resolvent modes in wall-bounded turbulence
This work develops a methodology for approximating the shape of leading resolvent modes for incompressible, quasi-parallel, shear-driven turbulent flows using prescribed analytic functions. We
Role of parasitic modes in nonlinear closure via the resolvent feedback loop
We use the feedback loop of McKeon \& Sharma (2010), where the nonlinear term in the Navier-Stokes equations is treated as an intrinsic forcing of the linear resolvent operator, to educe the
Scaling and interaction of self-similar modes in models of high Reynolds number wall turbulence
  • A. Sharma, R. Moarref, B. McKeon
  • Physics
    Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences
  • 2017
It is shown that much of the turbulence scaling behaviour in the logarithmic region can be determined from a single arbitrarily chosen reference plane and the geometric scaling of the modes is impressed upon the nonlinear interaction between modes.
Coherent large-scale structures from the linearized Navier–Stokes equations
The wall-normal extent of the large-scale structures modelled by the linearized Navier–Stokes equations subject to stochastic forcing is directly compared to direct numerical simulation (DNS) data. A
Colour of turbulence
This paper addresses the problem of how to account for second-order statistics of turbulent flows using low-complexity stochastic dynamical models based on the linearized Navier–Stokes equations and develops models for coloured-in-time forcing using a maximum entropy formulation together with a regularization that serves as a proxy for rank minimization.