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The estimation of the permeability of porous media to fluids is of fundamental importance in fields as diverse as oil and gas industry, agriculture, hydrology and medicine. Despite more than 150 years since the publication of Darcy's linear…
For the incompressible Navier--Stokes equation, the Reynolds number ($\mathrm{Re}$) is a dimensionless parameter quantifying the relative importance of inertial over viscous forces. In the low-$\mathrm{Re}$ regime ($\mathrm{Re} \ll 1$), the…
This article investigates the intrinsic link between skewness and statistical intermittency in velocity and temperature increments within homogeneous isotropic turbulence. The theoretical framework builds upon the author's previously…
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…
In the present treatise, a stability analysis of the bottom boundary layer under solitary waves based on energy bounds and nonmodal theory is performed. The instability mechanism of this flow consists of a competition between streamwise…
Turbulent flows driven by a vertically invariant body force were proven to become exactly two-dimensional above a critical rotation rate, using upper bound theory. This transition in dimensionality of a turbulent flow has key consequences…
Wall-bounded turbulence is relevant for many engineering and natural science applications, yet there are still aspects of its underlying physics that are not fully understood, particularly at high Reynolds numbers. In this study, we…
The recent theoretical discovery of families of travelling wave solutions in pipe flow at Reynolds numbers lower than the transitional range naturally raises the question of their relevance to the turbulent transition process. Here a series…
The onset of shear flow turbulence is characterized by turbulent patches bounded by regions of laminar flow. At low Reynolds numbers localized turbulence relaminarises, raising the question of whether it is transient in nature or it becomes…
Intermittency is one of central obstacles for understanding small-scale dynamics in the fully developed hydrodynamic turbulence. The modern approach is largely based on the multifractal theory of Parisi and Frisch which is, however,…
We interpret measurements of the Reynolds number dependence of the torque in Taylor-Couette flow by Lewis and Swinney [Phys. Rev. E 59, 5457 (1999)] and of the pressure drop in pipe flow by Smits and Zagarola, [Phys. Fluids 10, 1045 (1998)]…
We study the behaviour of the streamwise velocity variance in turbulent wall-bounded flows using a DNS database of pipe flow up to $Re_{\tau} \approx 12000$. The analysis of the spanwise spectra in the viscous near-wall region strongly…
If a fluid flow is driven by a weak Gaussian random force, the nonlinearity in the Navier-Stokes equations is negligibly small and the resulting velocity field obeys Gaussian statistics. Nonlinear effects become important as the driving…
We consider the flow of a Newtonian fluid in a three-dimensional domain, rotating about a vertical axis and driven by a vertically invariant horizontal body-force. This system admits vertically invariant solutions that satisfy the 2D…
The transition of the flow in a duct of square cross-section is studied. Like in the similar case of the pipe flow, the motion is linearly stable for all Reynolds numbers; this flow is thus a good candidate to investigate the 'bypass' path…
Following the recent observation that turbulent pipe flow can be relaminarised by a relatively simple modification of the mean velocity profile, we here carry out a quantitative experimental investigation of this phenomenon. Our study…
A computational study of three-dimensional instability of steady flows in a helical pipe of arbitrary curvature and torsion is carried out for the first time. The problem is formulated in Germano coordinates in two equivalent but different…
Relaminarization of wall-bounded turbulent flows by means of external static magnetic fields is a long-known phenomenon in the physics of electrically conducting fluids at low magnetic Reynolds numbers. Despite the large literature on the…
Turbulence generally arises in shear flows if velocities and hence inertial forces are sufficiently large. In striking contrast, viscoelastic fluids can exhibit disordered motion even at vanishing inertia. Intermediate between these cases,…
A hydrodynamic model of active, low Reynolds number suspensions, shows the emergence of an asymptotic state with a universal spectral scaling and non-Gaussian (intermittent) fluctuations in the velocity field. Such states arise when these…