16 research outputs found
Model-based scaling of the streamwise energy density in high-Reynolds-number turbulent channels
No full textWe study the Reynolds number scaling of a gain-based, low-rank approximation to turbulent channel flows, determined by the resolvent formulation of McKeon & Sharma (2010), in order to obtain a description of the streamwise turbulence intensity from direct consideration of the Navier-Stokes equations. Under this formulation, the velocity field is decomposed into propagating waves (with single streamwise and spanwise wavelengths and wave speed) whose wall-normal shapes are determined from the principal singular function of the corresponding resolvent operator. We establish that the resolvent formulation admits three classes of wave parameters that induce universal behavior with Reynolds number on the low-rank model, and which are consistent with scalings proposed throughout the wall turbulence literature. For the rank-1 model subject to broadband forcing, the integrated streamwise energy density takes a universal form which is consistent with the dominant near-wall turbulent motions. When the shape of the forcing is optimized to enforce matching with results from direct numerical simulations at low turbulent Reynolds numbers, further similarity appears. Representation of these weight functions using similarity laws enables prediction of the Reynolds number and wall-normal variations of the streamwise energy intensity at high Reynolds numbers (Re ? ? 10³-10¹?). Results from this low rank model of the Navier-Stokes equations compare favorably with experimental results in the literature
Model-based control of transitional and turbulent wall-bounded shear flows
No full textUniversity of Minnesota Ph.D. dissertation. January 2013. Major: Electrical Engineering. Advisor: Professor Mihailo R. Jovanovic. 1 computer file (PDF); xvii, 242 pages, appendices A-E.Moarref, Rashad. (2013). Model-based control of transitional and turbulent wall-bounded shear flows. Retrieved from the University Digital Conservancy, https://hdl.handle.net/11299/144896
Controlling the onset of turbulence by streamwise travelling waves. Part 2. Direct numerical simulation
No full textThis study builds on and confirms the theoretical findings of Part 1 of this paper (Moarref & Jovanović, J. Fluid Mech., 2010, doi:10.1017/S0022112010003393). We use direct numerical simulation of the Navier–Stokes equations to assess the efficacy of blowing and suction in the form of streamwise travelling waves for controlling the onset of turbulence in a channel flow. We highlight the effects of the modified base flow on the dynamics of velocity fluctuations and net power balance. Our simulations verify the theoretical predictions of Part 1 that the upstream travelling waves promote turbulence even when the uncontrolled flow stays laminar. On the other hand, the downstream travelling waves with parameters selected in Part 1 are capable of reducing the fluctuations' kinetic energy, thereby maintaining the laminar flow. In flows driven by a fixed pressure gradient, a positive net efficiency as large as 25 % relative to the uncontrolled turbulent flow can be achieved with downstream waves. Furthermore, we show that these waves can also relaminarize fully developed turbulent flows at low Reynolds numbers. We conclude that the theory developed in Part 1 for the linearized flow equations with uncertainty has considerable ability to predict full-scale phenomena.</jats:p
Controlling the onset of turbulence by streamwise travelling waves. Part 1. Receptivity analysis
No full textWe examine the efficacy of streamwise travelling waves generated by a zero-net-mass-flux surface blowing and suction for controlling the onset of turbulence in a channel flow. For small-amplitude actuation, we utilize a weakly nonlinear analysis to determine base-flow modifications and assess the resulting net power balance. Receptivity analysis of the velocity fluctuations around this base flow is then employed to design the travelling waves. Our simulation-free approach reveals that, relative to the flow with no control, the downstream travelling waves with properly designed speed and frequency can significantly reduce receptivity, which makes them well suited for controlling the onset of turbulence. In contrast, the velocity fluctuations around the upstream travelling waves exhibit larger receptivity to disturbances. Our theoretical predictions, obtained by perturbation analysis (in the wave amplitude) of the linearized Navier–Stokes equations with spatially periodic coefficients, are verified using full-scale simulations of the nonlinear flow dynamics in the companion paper (Lieu et al., J. Fluid Mech., 2010, doi:10.1017/S002211201000340X).</jats:p
Remarks on computing the H<inf>2</inf> norm of incompressible fluids using descriptor state-space formulation
No full textLow-dimensional representations of exact coherent states of the Navier-Stokes equations from the resolvent model of wall turbulence
No full textWe report that many exact invariant solutions of the Navier-Stokes equations for both pipe and channel flows are well represented by just few modes of the model of McKeon & Sharma J. Fl. Mech. 658, 356 (2010). This model provides modes that act as a basis to decompose the velocity field, ordered by their amplitude of response to forcing arising from the interaction between scales. The model was originally derived from the Navier-Stokes equations to represent turbulent flows and has been used to explain coherent structure and to predict turbulent statistics. This establishes a surprising new link between the two distinct approaches to understanding turbulence
A foundation for analytical developments in the logarithmic region of turbulent channels
No full textAn 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 in the logarithmic region can be decomposed into a weighted sum of geometrically self-similar resolvent modes. The resolvent modes and the weights represent the linear amplification mechanisms and the scaling influence of the nonlinear interactions in the Navier-Stokes equations (NSE), respectively (McKeon & Sharma, J. Fluid Mech., 658, 2010). Originating from the NSE, this framework provides an analytical support for Townsend’s attached-eddy model. Our main result is that self-similarity enables order reduction in modeling the logarithmic region by establishing a quantitative link between the self-similar structures and the velocity spectra. Specifically, the energy intensities, the Reynolds stresses, and the energy budget are expressed in terms of the resolvent modes with speeds corresponding to the top of the logarithmic region. The weights of the triad modes -the modes that directly interact via the quadratic nonlinearity in the NSE- are coupled via the interaction coefficients that depend solely on the resolvent modes (McKeon et al., Phys. Fluids, 25, 2013). We use the hierarchies of self-similar modes in the logarithmic region to extend the notion of triad modes to triad hierarchies. It is shown that the interaction coefficients for the triad modes that belong to a triad hierarchy follow an exponential function. The combination of these findings can be used to better understand the dynamics and interaction of flow structures in the logarithmic region. The compatibility of the proposed model with theoretical and experimental results is further discussed
