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1. Structured Input-Output Analysis of Oblique Turbulent Bands in Transitional Plane Couette-Poiseuille Flow

   Y. Shuai; C. Liu; D. F. Gayme (July 2022, Structured Input-Output Analysis of Oblique Turbulent Bands in Transitional Plane Couette-Poiseuille Flow)

   In this work, we apply structured input-output analysis to study optimal perturbations and dominant flow patterns in transitional plane Couette-Poiseuille flow. The results demonstrate that this approach predicts the high structured gain of perturbations with wavelengths corresponding to the oblique turbulent bands observed in experiments. The inclination angles of these structures and their Reynolds number dependence are also consistent with previously observed trends. Reynolds number scalings of the maximally amplified structures for an intermediate laminar profile that is equally balanced between plane Couette and Poiseuille flow show an exponent that is at the midpoint of previously computed values for these two flows. However, the dependence of these scaling exponents on the shape of laminar flow as the relative contribution moves from predominately plane Couette to Poiseuille flow is not monotonic and our analysis indicates the emergence of different optimal perturbation structures through the parameter regime. Finally we adapt our approach to estimate the advection speeds of oblique turbulent bands in plane Couette flow and Poiseuille flow by computing their phase speed. The results show good agreement with prior predictions of the convection speeds of these structures from direct numerical simulations, which suggests that this framework has further potential in examining the dynamics of these structures. 

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2. Effect of external shear flow on sperm motility

   https://doi.org/10.1039/c9sm00717b  

   Kumar, Manish; Ardekani, Arezoo M. (August 2019, Soft Matter)

   The trajectory of sperm in the presence of background flow is of utmost importance for the success of fertilization, as sperm encounter background flow of different magnitude and direction on their way to the egg. Here, we have studied the effect of an unbounded simple shear flow as well as a Poiseuille flow on the sperm trajectory. In the presence of a simple shear flow, the sperm moves on an elliptical trajectory in the reference frame advecting with the local background flow. The length of the major-axis of this elliptical trajectory decreases with the shear rate. The flexibility of the flagellum and consequently the length of the major axis of the elliptical trajectories increases with the sperm number. The sperm number is a dimensionless number representing the ratio of viscous force to elastic force. The sperm moves downstream or upstream depending on the strength of background Poiseuille flow. In contrast to the simple shear flow, the sperm also moves toward the centerline in a Poiseuille flow. Far away from the centerline, the cross-stream migration velocity of the sperm increases as the transverse distance of the sperm from the centerline decreases. Close to the centerline, on the other hand, the cross-stream migration velocity decreases as the sperm further approaches the center. The cross-stream migration velocity of the sperm also increases with the sperm number. 

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3. Revisiting steady viscous flow of a generalized Newtonian fluid through a slender elastic tube using shell theory

   https://doi.org/10.1002/zamm.201900309  

   Anand, Vishal; Christov, Ivan C. (August 2020, ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik)

   Abstract A flow vessel with an elastic wall can deform significantly due to viscous fluid flow within it, even at vanishing Reynolds number (no fluid inertia). Deformation leads to an enhancement of throughput due to the change in cross‐sectional area. The latter gives rise to a non‐constant pressure gradient in the flow‐wise direction and, hence, to a nonlinear flow rate–pressure drop relation (unlike the Hagen–Poiseuille law for a rigid tube). Many biofluids are non‐Newtonian, and are well approximated by generalized Newtonian (say, power‐law) rheological models. Consequently, we analyze the problem of steady low Reynolds number flow of a generalized Newtonian fluid through a slender elastic tube by coupling fluid lubrication theory to a structural problem posed in terms of Donnell shell theory. A perturbative approach (in the slenderness parameter) yields analytical solutions for both the flow and the deformation. Using matched asymptotics, we obtain a uniformly valid solution for the tube's radial displacement, which features both a boundary layer and a corner layer caused by localized bending near the clamped ends. In doing so, we obtain a “generalized Hagen–Poiseuille law” for soft microtubes. We benchmark the mathematical predictions against three‐dimensional two‐way coupled direct numerical simulations (DNS) of flow and deformation performed using the commercial computational engineering platform by ANSYS. The simulations show good agreement and establish the range of validity of the theory. Finally, we discuss the implications of the theory on the problem of the flow‐induced deformation of a blood vessel, which is featured in some textbooks. 

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4. Numerical Investigation of Flow Inside the Collector of a Solar Chimney Power Plant

   https://doi.org/10.2514/6.2021-0367  

   Hasan, Md Kamrul; Gross, Andreas; Bahrainirad, Ladan; Fasel, Hermann F. (January 2021, AIAA Scitech 2021 Forum)

   null (Ed.)

   The flow through the collector of a solar chimney power plant model on the roof of the Aerospace and Mechanical Engineering building at the University of Arizona was investigated numerically for the conditions of the experiment. The measured wall temperature and inflow velocity for a representative day were chosen for the simulation. The simulation was performed with a newly developed higher-order-accurate compact finite difference code. The code employs fifth-order-accurate biased compact finite differences for the convective terms and fourth-order-accurate central compact finite differences for the viscous terms. A fourth-order-accurate Runge-Kutta method was employed for time integration. Unsteady random disturbances are introduced at the inflow boundary and the downstream evolution of the resulting waves was investigated based on the Fourier transforms of the unsteady flow data. Steady azimuthal waves with a wavenumber of roughly four based on the channel half-height are the most amplified as a result of Rayleigh-Benard-Poiseuille instability. Different from plane Rayleigh-Benard-Poiseuille flow, these waves appear to merge in the streamwise direction. Oblique waves are also amplified. The growth rates are however lower than for the steady modes. Because of the strong streamwise flow acceleration, the growth rates decrease in the downstream direction. 

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5. Stationary Structures Near the Kolmogorov and Poiseuille Flows in the 2d Euler Equations

   https://doi.org/10.1007/s00205-023-01842-3  

   Coti Zelati, Michele; Elgindi, Tarek M.; Widmayer, Klaus (February 2023, Archive for Rational Mechanics and Analysis)

   Abstract We study the behavior of solutions to the incompressible 2dEuler equations near two canonical shear flows with critical points, the Kolmogorov and Poiseuille flows, with consequences for the associated Navier–Stokes problems. We exhibit a large family of new, non-trivial stationary states that are arbitrarily close to the Kolmogorov flow on the square torus$$\mathbb {T}^2$$ $T^2$in analytic regularity. This situation contrasts strongly with the setting of some monotone shear flows, such as the Couette flow: there the linearized problem exhibits an “inviscid damping” mechanism that leads to relaxation of perturbations of the base flows back to nearby shear flows. Our results show that such a simple description of the long-time behavior is not possible for solutions near the Kolmogorov flow on$$\mathbb {T}^2$$ $T^2$. Our construction of the new stationary states builds on a degeneracy in the global structure of the Kolmogorov flow on$$\mathbb {T}^2$$ $T^2$, and we also show a lack of correspondence between the linearized description of the set of steady states and its true nonlinear structure. Both the Kolmogorov flow on a rectangular torus and the Poiseuille flow in a channel are very different. We show that the only stationary states near them must indeed be shears, even in relatively low regularity. In addition, we show that this behavior is mirrored closely in the related Navier–Stokes settings: the linearized problems near the Poiseuille and Kolmogorov flows both exhibit an enhanced rate of dissipation. Previous work by us and others shows that this effect survives in the full, nonlinear problem near the Poiseuille flow and near the Kolmogorov flow on rectangular tori, provided that the perturbations lie below a certain threshold. However, we show here that the corresponding result cannot hold near the Kolmogorov flow on$${\mathbb T}^2$$ $T^2$. 

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