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This paper employs an input–output based approach to analyse the convective velocities and transport of fluctuations in turbulent channel flows. The convective velocity for a fluctuating quantity associated with streamwise–spanwise wavelength pairs at each wall-normal location is obtained through the maximization of the power spectral density associated with the linearized Navier–Stokes equations with a turbulent mean profile and delta-correlated Gaussian forcing. We first demonstrate that the mean convective velocities computed in this manner agree well with those reported previously in the literature. We then exploit the analytical framework to probe the underlying mechanisms contributing to the local convective velocity at different wall-normal locations by isolating the contributions of each streamwise–spanwise wavelength pair (flow scale). The resulting analysis suggests that the behaviour of the convective velocity in the near-wall region is influenced by large-scale structures further away from the wall. These structures resemble Townsend’s attached eddies in the cross-plane, yet show incomplete similarity in the streamwise direction. We then investigate the role of each linear term in the momentum equation to isolate the contribution of the pressure, mean shear, and viscous effects to the deviation of the convective velocity from the mean at each flow scale. Our analysis highlights the role of the viscous effects, particularly in regards to large channel spanning structures whose influence extends to the near-wall region. The results of this work suggest the promise of an input–output approach for analysing convective velocity across a range of flow scales using only the mean velocity profile.
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Turbulent Channel Flow
The turbulent channel flow database is produced from a direct numerical simulation (DNS) of wall bounded flow with periodic boundary conditions in the longitudinal and transverse directions, and no-slip conditions at the top and bottom walls. In the simulation, the Navier-Stokes equations are solved using a wall {normal, velocity {vorticity formulation. Solutions to the governing equations are provided using a Fourier-Galerkin pseudo-spectral method for the longitudinal and transverse directions and seventh-order Basis-splines (B-splines) collocation method in the wall normal direction. De-aliasing is performed using the 3/2-rule [3]. Temporal integration is performed using a low-storage, third-order Runge-Kutta method. Initially, the flow is driven using a constant volume flux control (imposing a bulk channel mean velocity of U = 1) until stationary conditions are reached. Then the control is changed to a constant applied mean pressure gradient forcing term equivalent to the shear stress resulting from the prior steps. Additional iterations are then performed to further achieve statistical stationarity before outputting fields.
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- Award ID(s):
- 2103874
- PAR ID:
- 10423313
- Publisher / Repository:
- Johns Hopkins Turbulence Databases
- Date Published:
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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