In this work, we study the nonlinear instability of two-dimensional (2D) wallbounded shear flows from the large deviation point of view. The main idea is to consider the Navier–Stokes equations perturbed by small noise in force and then examine the noise-induced transitions between the two coexisting stable solutions due to the subcritical bifurcation. When the amplitude of the noise goes to ze...

Relying on the rugosity effect, we analyse the drag minimization problem in relation with the micro-structure of the surface of a given obstacle. We construct a mathematical framework for the optimization problem, prove the existence of an optimal solution by Γ-convergence arguments and analyse the stability of the drag with respect to the micro-structure. For Stokes flows we justify why rugosi...

Traditional TCP traffic modeling has focused on “micro-scale” modeling of TCP, i.e., detailed modeling of a single TCP flow. While micro-scale models of TCP are suitable for understanding the precise behavior of individual flows, they are not well suited to the situation when a large number of TCP flows interact with each other as is the case in realistic networks. In this survey, we present se...

We consider the flow of a class of incompressible fluids which are constitutively defined by the symmetric part of the velocity gradient being a function, which can be nonmonotone, of the deviator of the stress tensor. These models are generalizations of the stress power-law models introduced and studied by J. Málek, V. Pr̊uša, K.R. Rajagopal : Generalizations of the Navier-Stokes fluid from a n...

Velocity fields for Poiseuille flow through tubes having general cross section are calculated using a path integral method involving the first-passage times of random walks in the interior of the cross sectional domain B of the pipe. This method is applied to a number of examples where exact results are available and to more complicated geometries of practical interest. These examples include a...

In this paper, a number of methods are described that allow for more accurate and more efficient computation of viscous flow effects with the CFD tool COMFLOW. The intended application area is the offshore environment, where flows are characterized by Reynolds numbers of at least O(106). A symmetry-preserving regularization model will be used to model turbulence. In the near-wall region, an ext...

Recent efforts by the present authors have focused on the fundamental multiscaling behaviors of the time averaged dynamical equations of wall-turbulence. These efforts have generated a number of new results relating to dynamical structure, as well as a new mathematical foundation. Central to this has been the development of the so-called method of scaling patches. This method provides a formali...

The statistical properties of fully developed planar turbulent Couette–Poiseuille flow result from the simultaneous imposition of a mean wall shear force together with a mean pressure force. Despite the fact that pure Poiseuille flow and pure Couette flow are the two extremes of Couette–Poiseuille flow, the statistical properties of the latter have proved resistant to scaling approaches that co...

Viscoelastic plane Poiseuille flow is shown to become linearly unstable in the absence of inertia, limit high elasticities, for ultradilute polymer solutions. While inertialess elastic instabilities have been predicted curvilinear shear flows, this first ever report a purely linear instability rectilinear flow. The novel continues up Reynolds number (Re) $O(1000)$, corresponding recently identi...