A minimal form of quasi-linear approximation (QLA), recently proposed with a stochastic forcing and POD modes (Hwang & Ekchardt, J. Fluid Mech., 2020, 894:A23), has been extended by employing a resolvent framework. A particular effort is made to reach an extremely high Reynolds number by carefully controlling the approximation without loss of the general scaling properties in the spectra, while setting out the main limitations and accuracy of the proposed QLA with possibility of further improvement. The QLA is subsequently applied to turbulent channel flow up to Reτ = 10 6 (Reτ is the friction Reynolds number). While confirming that the logarithmic wallnormal dependence in streamwise and spanwise turbulence intensities robustly appears, it reveals some non-trivial difference from the scaling of the classical attached eddy model based on inviscid flow assumption. Firstly, the spanwise wavenumber spectra do not show any well-visible inverselaw behaviour due to the viscous wall effect prevailing in a significant portion of the lower part of the logarithmic layer. Secondly, the near-wall peak streamwise and spanwise turbulence intensities are found to deviate from ln Reτ scaling for Reτ 10 4 . Importantly, the near-wall streamwise turbulence intensity is inversely proportional to 1/U + cl (U + cl is the inner-scaled channel centreline velocity), consistent with the scaling obtained from an asymptotic analysis of the Navier-Stokes equations (Monkewitz & Nagib, J. Fluid Mech. 2015, 783:474-503). The same behaviour was also observed for the streamwise turbulence intensity in the logarithmic region, as was predicted by the asymptotic analysis. Finally, the streamwise turbulence intensity in the logarithmic region is found to become greater than the near-wall one at Reτ O(10 5 ). It is shown that this behaviour originates from the near-wall spectra associated with large-scale inactive motions, the intensity of which gradually decays as Reτ → ∞.

The Deformable Mirror Demonstration Mission (DeMi) was recently selected by DARPA to demonstrate in-space operation of a wavefront sensor and Microelectromechanical system (MEMS) deformable mirror (DM) payload on a 6U CubeSat. Space telescopes designed to make high-contrast observations using internal coronagraphs for direct characterization of exoplanets require the use of high-actuator density deformable mirrors. These DMs can correct image plane aberrations and speckles caused by imperfections, thermal distortions, and diffraction in the telescope and optics that would otherwise corrupt the wavefront and allow leaking starlight to contaminate coronagraphic images. DeMi is provide on-orbit demonstration and performance characterization of a MEMS deformable mirror and closed loop wavefront sensing.The DeMi payload has two operational modes, one mode that images an internal light source and another mode which uses an external aperture to images stars. Both the internal and external modes include image plane and pupil plane wavefront sensing. The objectives of the internal measurement of the 140-actuator MEMS DM actuator displacement are characterization of the mirror performance and demonstration of closed-loop correction of aberrations in the optical path. Using the external aperture to observe stars of magnitude 2 or brighter, assuming 3-axis stability with less than 0.1 degree of attitude knowledge and jitter below 10 arcsec RMSE, per observation, DeMi will also demonstrate closed loop wavefront control on an astrophysical target. We present an updated payload design, results from simulations and laboratory optical prototyping, as well as present our design for accommodating high-voltage multichannel drive electronics for the DM on a CubeSat.