Binh K. Lieu

Self-sustaining turbulence in a restricted nonlinear model of plane Couette flow

This paper demonstrates the maintenance of self-sustaining turbulence in a restricted nonlinear (RNL) model of plane Couette flow. The RNL system is derived directly from the Navier-Stokes equations and permits higher resolution studies of the dynamical system associated with the stochastic structural stability theory (S3T) model, which is a second order approximation of the statistical state dynamics of the flow. The RNL model shares the dynamical restrictions of the S3T model but can be easily implemented by reducing a DNS code so that it retains only the RNL dynamics. Comparisons of turbulence arising from DNS and RNL simulations demonstrate that the RNL system supports self-sustaining turbulence with a mean flow as well as structural and dynamical features that are consistent with DNS. These results demonstrate that the simplified RNL system captures fundamental aspects of fully developed turbulence in wall-bounded shear flows and motivate use of the RNL/S3T framework for further study of wall-turbulence.

Worst-case amplification of disturbances in inertialess Couette flow of viscoelastic fluids

Amplification of deterministic disturbances in inertialess shear-driven channel flows of viscoelastic fluids is examined by analyzing the frequency responses from spatio-temporal body forces to the velocity and polymer stress fluctuations. In strongly elastic flows, we show that disturbances with large streamwise length scales may be significantly amplified even in the absence of inertia. For fluctuations without streamwise variations, we derive explicit analytical expressions for the dependence of the worst-case amplification (from different forcing to different velocity and polymer stress components) on the Weissenberg number (

Computation of frequency responses for linear time-invariant PDEs on a compact interval

We

Computation of the frequency responses for distributed systems with one spatial variable

), the maximum extensibility of the polymer chains (

Worst-case amplification of disturbances in inertialess flows of viscoelastic fluids

L

Model-based analysis of polymer drag reduction in a turbulent channel flow

), the viscosity ratio, and the spanwise wavenumber. For the Oldroyd-B model, the amplification of the most energetic components of velocity and polymer stress fields scales as

Turbulent drag reduction by streamwise traveling waves

We^2

Slow-fast decomposition of an inertialess flow of viscoelastic fluids

and

Spatially-localized optimal control of transition to turbulence

We^4

Controlling the onset of turbulence by streamwise travelling waves. Part 2. Direct numerical simulation

. On the other hand, finite extensibility of polymer molecules limits the largest achievable amplification even in flows with infinitely large Weissenberg numbers: in the presence of wall-normal and spanwise forces the amplification of the streamwise velocity and polymer stress fluctuations is bounded by quadratic and quartic functions of