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1. Collision rate of bidisperse spheres settling in a compressional non-continuum gas flow

   https://doi.org/10.1017/jfm.2020.942  

   Dhanasekaran, Johnson; Roy, Anubhab; Koch, Donald L. (March 2021, Journal of Fluid Mechanics)

   null (Ed.)

   Collisions in a dilute polydisperse suspension of spheres of negligible inertia interacting through non-continuum hydrodynamics and settling in a slow uniaxial compressional flow are studied. The ideal collision rate is evaluated as a function of the relative strength of gravity and uniaxial compressional flow and it deviates significantly from a linear superposition of these driving terms. This non-trivial behaviour is exacerbated by interparticle interactions based on uniformly valid non-continuum hydrodynamics, that capture non-continuum lubrication at small separations and full continuum hydrodynamic interactions at larger separations, retarding collisions driven purely by sedimentation significantly more than those driven purely by the linear flow. While the ideal collision rate is weakly dependent on the orientation of gravity with the axis of compression, the rate including hydrodynamic interactions varies by more than $$100\,\%$$ with orientation. This dramatic shift can be attributed to complex trajectories driven by interparticle interactions that prevent particle pairs from colliding or enable a circuitous path to collision. These and other important features of the collision process are studied in detail using trajectory analysis at near unity and significantly smaller than unity size ratios of the interacting spheres. For each case analysis is carried for a large range of relative strengths and orientations of gravity to the uniaxial compressional flow, and Knudsen numbers (ratio of mean free path of the media to mean radius). 

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2. Shear rheology of a dilute suspension of thin rings

   https://doi.org/10.1122/8.0000628  

   Borker, Neeraj S.; Koch, Donald L. (April 2023, Journal of Rheology)

   The rheology of suspensions of rings (tori) rotating in an unbounded low Reynolds number simple shear flow is calculated using numerical simulations at dilute particle number densities ( n ≪ 1 ). Suspensions of non-Brownian rings are studied by computing pair interactions that include hydrodynamic interactions modeled using slender body theory and particle collisions modeled using a short-range repulsive force. Particle contact and hydrodynamic interactions were found to have comparable influences on the steady-state Jeffery orbit distribution. The average tilt of the ring away from the flow-vorticity plane increased during pairwise interactions compared to the tilt associated with Jeffery rotation and the steady-state orbit distribution. Particle stresses associated with the increased tilt during the interaction were found to be comparable to the stresses induced directly by particle contact forces and the hydrodynamic velocity disturbances of other particles. The hydrodynamic diffusivity coefficients in the gradient and vorticity directions were also obtained and were found to be two orders of magnitude larger than the corresponding values in fiber suspensions at the same particle concentrations. Rotary Brownian dynamics simulations of isolated Brownian rings were used to understand the shear rate dependence of suspension rheology. The orbit distribution observed in the regime of weak Brownian motion, P e ≫ ϕ T − 3, was surprisingly similar to that obtained from pairwise interaction calculations of non-Brownian rings. Here, the Peclet number P e is the ratio of the shear rate and the rotary diffusivity of the particle and ϕ T is the effective inverse-aspect ratio of the particle (approximately equal to 2 π times the inverse of its non-dimensional Jeffery time period). Thus, the rheology results obtained from pairwise interactions should retain accuracy even for weakly Brownian rings ( n ≪ 1 and ϕ T − 3 ≪ P e ). 

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3. Reynolds number dependency in supersonic spatially-developing turbulent boundary layers

   https://doi.org/10.2514/6.2020-0574  

   Araya, Guillermo; Lagares, Christian; Jansen, Kenneth E. (January 2020, 2020 AIAA SciTech Forum (AIAA 3247313) 6 - 10 January, Orlando, FL, 2020.)

   Direct Numerical Simulation (DNS) of compressible spatially-developing turbulent boundary layers (SDTBL) is performed at a Mach number of 2.5 and low/high Reynolds numbers over isothermal Zero-Pressure Gradient (ZPG) flat plates. Turbulent inflow information is generated via a dynamic rescaling-recycling approach (J. Fluid Mech., 670, pp. 581-605, 2011), which avoids the use of empirical correlations in the computation of inlet turbulent scales. The range of the low Reynolds number case is approximately 400-800, based on the momentum thickness, freestream velocity and wall viscosity. DNS at higher Reynolds numbers (~3,000, about four-fold larger) is also carried out with the purpose of analyzing the effect of Reynolds number on the transport phenomena in the supersonic regime. Additionally, low/high order flow statistics are compared with DNS of an incompressible isothermal ZPG boundary layer at similar low Reynolds numbers and the temperature regarded as a passive scalar. Peaks of turbulence intensities move closer to the wall as the Reynolds number increases in the supersonic flat plate. Furthermore, Reynolds shear stresses depict a much larger "plateau" (constant shear layer) at the highest Reynolds number considered in present study. 

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4. Prograde vortices, internal shear layers and the Taylor microscale in high-Reynolds-number turbulent boundary layers

   https://doi.org/10.1017/jfm.2021.478  

   Heisel, Michael; de Silva, Charitha M.; Hutchins, Nicholas; Marusic, Ivan; Guala, Michele (August 2021, Journal of Fluid Mechanics)

   null (Ed.)

   The statistical properties of prograde spanwise vortex cores and internal shear layers (ISLs) are evaluated for a series of high-Reynolds-number turbulent boundary layers. The considered flows span a wide range of both Reynolds number and surface roughness. In each case, the largest spanwise vortex cores in the outer layer of the boundary layer have size comparable to the Taylor microscale $$\lambda _T$$ , and the azimuthal velocity of these large vortex cores is governed by the friction velocity $${u_\tau }$$ . The same scaling parameters describe the average thickness and velocity difference across the ISLs. The results demonstrate the importance of the local large-eddy turnover time in determining the strain rate confining the size of the vortex cores and shear layers. The relevance of the turnover time, and more generally the Taylor microscale, can be explained by a stretching mechanism involving the mutual interaction of coherent velocity structures such as uniform momentum zones with the evolving shear layers separating the structures. 

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5. Wind- and Wave-Driven Reynolds Stress and Velocity Shear in the Upper Ocean for Idealized Misaligned Wind-Wave Conditions

   https://doi.org/10.1175/JPO-D-20-0157.1  

   Wang, Dong; Kukulka, Tobias (February 2021, Journal of Physical Oceanography)

   null (Ed.)

   Abstract This study investigates the dynamics of velocity shear and Reynolds stress in the ocean surface boundary layer for idealized misaligned wind and wave fields using a large-eddy simulation (LES) model based on the Craik–Leibovich equations, which captures Langmuir turbulence (LT). To focus on the role of LT, the LES experiments omit the Coriolis force, which obscures a stress–current-relation analysis. Furthermore, a vertically uniform body force is imposed so that the volume-averaged Eulerian flow does not accelerate but is steady. All simulations are first spun-up without wind-wave misalignment to reach a fully developed stationary turbulent state. Then, a crosswind Stokes drift profile is abruptly imposed, which drives crosswind stresses and associated crosswind currents without generating volume-averaged crosswind currents. The flow evolves to a new stationary state, in which the crosswind Reynolds stress vanishes while the crosswind Eulerian shear and Stokes drift shear are still present, yielding a misalignment between Reynolds stress and Lagrangian shear (sum of Eulerian current and Stokes drift). A Reynolds stress budgets analysis reveals a balance between stress production and velocity–pressure gradient terms (VPG) that encloses crosswind Eulerian shear, demonstrating a complex relation between shear and stress. In addition, the misalignment between Reynolds stress and Eulerian shear generates a horizontal turbulent momentum flux (due to correlations of along-wind and crosswind turbulent velocities) that can be important in producing Reynolds stress (due to correlations of horizontal and vertical turbulent velocities). Thus, details of the Reynolds stress production by Eulerian and Stokes drift shear may be critical for driving upper-ocean currents and for accurate turbulence parameterizations in misaligned wind-wave conditions. 

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