Estimating maximum scour depth is normally required in order to determine the depth of  bridge piles. The present paper uses the SSIIM Software which considers flow and sediment equations in a three dimensional manner. The software models flow field around circular bridge pile by resolving Navier-Stokes three-dimensional equations and k-  method, and by temporary solution of flow field and cont...

We obtain a pointwise, a priori bound for the vorticity of axis symmetric solutions to the 3 dimensional Navier-Stokes equations. The bound is in the form of a reciprocal of a power of the distance to the axis of symmetry. This seems to be the first general pointwise estimate established for the axis symmetric Navier-Stokes equations.

In this paper we establish the local exact internal controllability of steady state solutions for the Navier-Stokes equations in three-dimensional bounded domains, with the Navier slip boundary conditions. The proof is based on a Carlemantype estimate for the backward Stokes equations with the same boundary conditions, which is also established here.

In the last decade or so, the lattice Boltzmann (LB) method has emerged as a new and effective numerical technique of computational fluid dynamics (CFD).(1-5) Modeling of the incompressible Navier-Stokes equation is among many of its wide applications. Indeed, the lattice Boltzmann equation (LBE) was first proposed to simulate the incompressible NavierStokes equations.(1) The incompressible Nav...

— We prove that the Navier-Stokes, the Euler and the Stokes equations admit a Lagrangian structure using the stochastic embedding of Lagrangian systems. These equations coincide with extremals of an explicit stochastic Lagrangian functional, i.e. they are stochastic Lagrangian systems in the sense of [6].

To our knowledge, most numerical methods for solving discretizations of the Stokes equations depend on the Schur complement and thus the convergence rate depends on the aspect ratio of the domain. We present a preconditioner for a staggered grid discretization of the Stokes equations which is proven to be independent of the aspect ratio. Finally numerical experiments confirm the robustness of t...

— We prove that the Navier-Stokes, the Euler and the Stokes equations admit a Lagrangian structure using the stochastic embedding of Lagrangian systems. These equations coincide with extremals of an explicit stochastic Lagrangian functional, i.e. they are stochastic Lagrangian systems in the sense of [6].

We present a second-order accurate method for computing the coupled motion of a viscous fluid and an elastic material interface with zero thickness. The fluid flow is described by the Navier-Stokes equations, with a singular force due to the stretching of the moving interface. We decompose the velocity into a “Stokes” part and a “regular” part. The first part is determined by the Stokes equatio...

In [4] the authors consider the two dimensional Navier-Stokes equations in the exterior of an obstacle shrinking to a point and determine the limit velocity. Here we consider the same problem in the three dimensional case, proving that the limit velocity is a solution of the Navier-Stokes equations in the full space.

In this paper we consider the three–dimensional Navier–Stokes equations subject to periodic boundary conditions or in the whole space. We provide sufficient conditions, in terms of one direction derivative of the velocity field, namely, uz , for the regularity of strong solutions to the three-dimensional Navier–Stokes equations.