Related papers: Steady Prandtl Layers over a Moving Boundary: Non-…
We investigate the Reynolds-shear-stress carrying structures in the outer layer of non-equilibrium pressure-gradient turbulent boundary layers using four direct numerical simulation databases, two cases of non-equilibrium pressure-gradient…
In this paper we study the equations governing the unsteady motion of an incompressible homogeneous generalized second grade fluid subject to periodic boundary conditions. We establish the existence of global-in-time strong solutions for…
A basic example of shear flow was introduced by DiPerna and Majda to study the weak limit of oscillatory solutions of the Euler equations of incompressible ideal fluids. In particular, they proved by means of this example that weak limit of…
A Lagrangian relativistic approach to the non--linear dynamics of cosmological perturbations of an irrotational collisionless fluid is considered. Solutions are given at second order in perturbation theory for the relevant fluid and…
In this paper, we prove the linear damping for the 2-D Euler equations around a class of shear flows under the assumption that the linearized operator has no embedding eigenvalues. For the symmetric flows, we obtain the explicit decay…
In this paper, we study the back flow of the two-dimensional unsteady Prandtl boundary layer under an adverse pressure gradient. The occurrence of back flow is an important physical event in the evolution of boundary layer, which eventually…
We consider the binormal flow equation, which is a model for the dynamics of vortex filaments in Euler equations. Geometrically it is a flow of curves in three dimensions, explicitly connected to the 1-D Schr\"odinger map with values on the…
The properties of confined granular flows are studied through discrete numerical simulations. Two types of flows with different boundaries are compared: (i) gravity-driven flows topped with a free surface and over a base where erosion…
We consider a non-Newtonian fluid flow in a thin domain with thickness $\eta_\varepsilon$ and an oscillating top boundary of period $\varepsilon$. The flow is described by the 3D incompressible Navier-Stokes system with a nonlinear…
This paper concerns the structural stability of smooth cylindrically symmetric transonic flows in a concentric cylinder. Both cylindrical and axi-symmetric perturbations are considered. The governing system here is of mixed…
A nontrivial smooth steady incompressible Euler flow in three dimensions with compact support is constructed. Another uncommon property of this solution is the dependence between the Bernoulli function and the pressure.
Consider the flow of a thin layer of non-Newtonian fluid over a solid surface. I model the case of a viscosity that depends nonlinearly on the shear-rate; power law fluids are an important example, but the analysis here is for general…
The three-dimensional dynamics of a single non-Brownian flexible fiber in shear flow is evaluated numerically, in the absence of inertia. A wide range of ratios A of bending to hydrodynamic forces and hundreds of initial configurations are…
Using the flow governing equation approach to similarity, Weyburne (D. Weyburne, arXiv:1701.02364, 2016) recently showed that for 2-D turbulent boundary layer flows, the Prandtl Plus scalings are NOT, in general, the proper similarity…
The dynamics along the particle trajectories for the 3D axisymmetric Euler equations are considered. It is shown that if the inflow is rapidly increasing (pushy) in time, the corresponding laminar profile of the incompressible Euler flow is…
A little complement concerning the dynamics of non-metric manifolds is provided, by showing that any flow on an $\omega$-bounded surface with non-zero Euler character has a fixed point.
In this article, we study the 2D incompressible steady Navier-Stokes equation in a channel $(-L,0)\times(-1,1)$ with the no-slip boundary condition on $\{Y = \pm 1\}$, and consider the inviscid limit $\varepsilon \to 0$. In the special case…
Non-monotonic velocity profiles are an inherent feature of mixing flows obeying non-slip boundary conditions. There are, however, few known models of laminar mixing which incorporate this feature and have proven mixing properties. Here we…
In this paper we address the question of the pointwise almost everywhere limit of nonlinear Schr\"odinger flows to the initial data, in both the continuous and the periodic settings. Then we show how, in some cases, certain smoothing…
An explicit expression is obtained for the sectional curvature in the plane spanned by two stationary flows, cos(k, x) and cos(l, x). It is shown that for certain values of the wave vectors k and l the curvature becomes positive for alpha >…