Related papers: Modified Reynolds equation for steady flow through…
Using various techniques from dynamical systems theory, we rigorously study an experimentally validated model by [Barkley et al., Nature, 526:550-553, 2015], which describes the rise of turbulent pipe flow via a PDE system of reduced…
A new scaling is derived that yields a Reynolds number independent profile for all components of the Reynolds stress in the near-wall region of wall bounded flows, including channel, pipe and boundary layer flows. The scaling demonstrates…
Equilibrium, traveling wave, and periodic orbit solutions of pipe, channel, and plane Couette flows can now be computed precisely at Reynolds numbers above the onset of turbulence. These invariant solutions capture the complex dynamics of…
The steady motion of a viscous incompressible fluid through a sieve (that is, a wall perforated with a large number of small holes), in a pipe of finite length, is modeled through the Navier-Stokes equations under mixed boundary conditions…
We review works on the asymptotic stability of the Couette flow. The majority of the paper is aimed towards a wide range of applied mathematicians with an additional section aimed towards experts in the mathematical analysis of PDEs.
We investigated the pressure-driven flow in curved channels at low aspect ratio, the latter being the ratio between the channel height (along the axial direction) and width (along the radial direction). The dynamics was studied numerically,…
Using the Lagrangian transport of momentum, the Reynolds stress can be expressed in terms of basic turbulence parameters. The Reynolds stress gradient represents the lateral transport of stream-wise momentum, balanced by the u2 transport,…
Viscous flows through pipes and channels are steady and ordered until, with increasing velocity, the laminar motion catastrophically breaks down and gives way to turbulence. How this apparently discontinuous change from low- to…
In this paper, we study nonlinear stability of the 3D plane Couette flow $(y,0,0)$ at high Reynolds number ${Re}$ in a finite channel $\mathbb{T}\times [-1,1]\times \mathbb{T}$. It is well known that the plane Couette flow is linearly…
We study flow driven through a finite-length planar rigid channel by a fixed upstream flux, where a segment of one wall is replaced by a pre-stressed elastic beam subject to uniform external pressure. The steady and unsteady systems are…
We present an asymptotic theory for analytical characterization of the high-Reynolds-number incompressible flow of a Newtonian fluid past a shear-free circular cylinder. The viscosity-induced modifications to this flow are localized and…
In this study, new turbulence closure equations are derived in the light of turbulence as a continuous phase transition phenomenon. Closed-form Reynolds averaged Navier-Stokes equations due to those closure equations are solved numerically…
The Reynolds equation from lubrication theory and the Stokes equations for zero Reynolds number flows are distinct models for an incompressible fluid with negligible inertia. Here we investigate the sensitivity of the Reynolds equation to…
The fluctuations of turbulence intensity in a pipe flow around the critical Reynolds number is difficult to study but important because they are related to turbulent-laminar transitions. We here propose a rare-event sampling method to study…
We show a method, for direct numerical simulations, to trigger and maintain turbulent bands directly at low Reynolds numbers in channel flow. The key is to impose a moving localised force which induces a local flow with sufficiently strong…
A necessary and sufficient condition for linear stability of inviscid parallel shear flow is formulated by a novel variational method, where the velocity profile is assumed to be monotonic and analytic. Unstable eigenvalues of the Rayleigh…
We solve the Stokes equations for the flow around two parallel translating and rotating cylinders using tools from complex analysis and conformal mapping. By considering cylinders of arbitrary size and separation, we generalise the…
The energy method, also known as the Reynolds-Orr equation, is widely utilized in predicting the unconditional stability threshold of shear flows owing to the zero contribution of nonlinear terms to the time derivative of perturbation…
Iterative coarse-graining procedure based on Wyld's perturbation expansion is applied to the problem of Navier-Stokes turbulence. It is shown that the low-order calculation gives the fixed-point Reynolds number $ Re_{fp}$ (coupling…
The increased friction caused by turbulence is a significant contributor to energy consumption in the fluid-transport and piping industries. Here we describe a passive approach to reduce friction: we show that a local increase in streamwise…