Related papers: Relationship between the methods of bounding time …
The background method is a widely used technique to bound mean properties of turbulent flows rigorously. This work reviews recent advances in the theoretical formulation and numerical implementation of the method. First, we describe how the…
Invariant solutions of the Navier-Stokes equations play an important role in the spatiotemporally chaotic dynamics of turbulent shear flows. Despite the significance of these solutions, their identification remains a computational…
Through a discussion of some typical unsteady hydrodynamic flows, we argue that the time averaged hydrodynamic functions at each point give a rather sparse filling of the local jet space. This situation then suggests a set of time dependent…
Bounds on turbulent averages in shear flows can be derived from the Navier--Stokes equations by a mathematical approach called the background method. Bounds that are optimal within this method can be computed at each Reynolds number Re by…
We investigate a steady flow of incompressible fluid in the plane. The motion is governed by the Navier-Stokes equations with prescribed velocity $u_\infty$ at infinity. The main result shows the existence of unique solutions for arbitrary…
The steady compressible Navier--Stokes--Fourier system is considered, with either Dirichlet or Navier boundary conditions for the velocity and the heat flux on the boundary proportional to the difference of the temperature inside and…
We consider incompressible flows between two transversely vibrating solid walls and construct an asymptotic expansion of solutions of the Navier-Stokes equations in the limit when both the amplitude of vibrations and the thickness of the…
We consider the Navier--Stokes equations in a half-plane with a drift term parallel to the boundary and a small source term of compact support. We provide detailed information on the behavior of the velocity and the vorticity at infinity in…
We extend the Doering-Constantin approach to upper bounds on energy dissipation in turbulent flows by introducing a balance parameter into the variational principle. This parameter governs the relative weight of different contributions to…
We investigate spatial and temporal cross-correlations between streamwise and normal velocity components in three shear flows: a low-dimensional model for vortex-streak interactions, direct numerical simulations for a nearly homogeneous…
Many physical systems of interest involve the close interaction of a flow in a domain with complex, time-varying boundaries. Treatment of boundaries of this nature is cumbersome due to the difficulty in explicitly tracking boundaries that…
The auxiliary function method allows computation of extremal long-time averages of functions of dynamical variables in autonomous nonlinear ordinary differential equations via convex optimization. For dynamical systems defined by autonomous…
When studying fluid mechanics in terms of instability, bifurcation and invariant solutions one quickly finds out how little can be done by pen and paper. For flows on sufficiently simple domains and under sufficiently simple boundary…
We use a method based on the lubrication approximation in conjunction with a residual-based mass-continuity iterative solution scheme to compute the flow rate and pressure field in distensible converging-diverging tubes for Navier-Stokes…
We study the stability of Couette flow in the 3d Navier-Stokes equations with rotation, as given by the Coriolis force. Hereby, the nature of linearized dynamics near Couette flow depends crucially on the force balance between background…
The background method is adapted to derive rigorous limits on surface speeds and bulk energy dissipation for shear stress driven flow in two and three dimensional channels. By-products of the analysis are nonlinear energy stability results…
In this paper axisymmetric solutions of the Navier-Stokes equations governing the flow induced by a half-line source when the fluid domain is bounded by a conical wall are discussed. Two types of boundary conditions are identified; one in…
We study a nonlinear coupled fluid-structure system modelling the blood flow through arteries. The fluid is described by the incompressible Navier-Stokes equations in a 2D rectangular domain where the upper part depends on a structure…
We show theoretically that the mean turbulent dynamics can be described by a kinetic theory representation with a single free relaxation time that depends on space and time. A proper kinetic equation is constructed from averaging the…
Wall-bounded turbulent shear flows are known to exhibit universal small-scale dynamics that are modulated by large-scale flow structures. Strong pressure gradients complicate this characterization, however; they can cause significant…