Turbulent boundary layers absent mean shear

Abstract

We perform an experimental study to investigate the turbulent boundary layer above a stationary solid glass bed in the absence of mean shear. High Reynolds number $(Re_{\unicode[STIX]{x1D706}}\sim 300)$ horizontally homogeneous isotropic turbulence is generated via randomly actuated synthetic jet arrays (RASJA – Variano & Cowen J. Fluid Mech. vol. 604, 2008, pp. 1–32). Each of the arrays is controlled by a spatio-temporally varying algorithm, which in turn minimizes the formation of secondary mean flows. One array consists of an $8\times 8$ grid of jets, while the other is a $16\times 16$ array. Particle image velocimetry measurements are used to study the isotropic turbulent region and the boundary layer formed beneath as the turbulence encounters a stationary wall. The flow is characterized with statistical metrics including the mean flow and turbulent velocities, turbulent kinetic energy, integral scales and the turbulent kinetic energy transport equation, which includes the energy dissipation rate, production and turbulent transport. The empirical constant in the Tennekes (J. Fluid Mech. vol. 67, 1975, pp. 561–567) model of Eulerian frequency spectra is calculated based on the dissipation results and temporal frequency spectra from acoustic Doppler velocimetry measurements. We compare our results to prior literature that addresses mean shear free turbulent boundary layer characterizations via grid-stirred tank experiments, moving-bed experiments, rapid-distortion theory and direct numerical simulations in a forced turbulent box. By varying the operational parameters of the randomly actuated synthetic jet array, we also find that we are able to control the turbulence levels, including integral length scales and dissipation rates, by changing the mean on-times in the jet algorithm.

Sediment suspension and bed morphology in a mean shear free turbulent boundary layer

“…The sunbathing algorithm randomly selects instantaneous on-times given user-input parameters and , the mean on-time of each jet and the mean percentage of jet activity, respectively, as described in Johnson & Cowen (2018). As was observed in Johnson (2016), does not have a significant influence on the r.m.s. velocity or turbulent kinetic energy, and so a single percentage of active jets is selected for each of the RASJAs.…”

“…A spatial local median filter (Westerweel 1994; Cowen & Monismith 1997) then removes data exceeding a threshold relative to the nearest neighbour local median. As described in Johnson (2016), spatial interpolation is used to fill in removed data only when spatial spectra (or statistics based upon spatial spectra) requiring a continuous dataset are computed; otherwise filtered uninterpolated data are used.…”

“…The angle brackets denote a temporal average and lower case letters represent fluctuations. According to 3-component velocity data in Johnson (2016), the flow is radially symmetric about the axis. Thus we only report statistics along the plane and are able to invoke radial symmetry and continuity to statistically address the out-of-plane dynamics.…”

“…Invoking radial symmetry from earlier acoustic Doppler velocimetry measurements (Johnson 2016) and continuity (Cowen & Monismith 1997; Doron et al. 2000), the dissipation rate can be computed directly as from two-dimensional PIV measurements.…”

“…In exploring the mean velocity gradients, shown in figure 13, and Reynolds stresses that comprise , , and are approximately equal to zero. As in the case of turbulence absent mean shear above a solid boundary, being weakly non-zero is amplified by and contributes to non-zero (Johnson 2016). Unlike in the solid boundary case, is also non-zero in the present experiments, due to the hydraulic conductivity of the sediment bed.…”