33,977 research outputs found
PROTEUS two-dimensional Navier-Stokes computer code, version 1.0. Volume 3: Programmer's reference
A new computer code was developed to solve the 2-D or axisymmetric, Reynolds-averaged, unsteady compressible Navier-Stokes equations in strong conservation law form. The thin-layer or Euler equations may also be solved. Turbulence is modeled using an algebraic eddy viscosity model. The objective was to develop a code for aerospace applications that is easy to use and easy to modify. Code readability, modularity, and documentation were emphasized. The equations are written in nonorthogonal body-fitted coordinates, and solved by marching in time using a fully-coupled alternating-direction-implicit procedure with generalized first- or second-order time differencing. All terms are linearized using second-order Taylor series. The boundary conditions are treated implicitly, and may be steady, unsteady, or spatially periodic. Simple Cartesian or polar grids may be generated internally by the program. More complex geometries require an externally generated computational coordinate system. The documentation is divided into three volumes. Volume 3 is the Programmer's Reference, and describes the program structure, the FORTRAN variables stored in common blocks, and the details of each subprogram
Degenerate pullback attractors for the 3D Navier-Stokes equations
As in our previous paper, the 3D Navier-Stokes equations with a
translationally bounded force contain pullback attractors in a weak sense.
Moreover, those attractors consist of complete bounded trajectories. In this
paper, we present a sufficient condition under which the pullback attractors
are degenerate. That is, if the Grashof constant is small enough, the pullback
attractor will be a single point on a unique, complete, bounded, strong
solution. We then apply our results to provide a new proof of the existence of
a unique, strong, periodic solution to the 3D Navier-Stokes with a small,
periodic forcing term
Dynamic Stability of the 3D Axi-symmetric Navier-Stokes Equations with Swirl
In this paper, we study the dynamic stability of the 3D axisymmetric
Navier-Stokes Equations with swirl. To this purpose, we propose a new
one-dimensional (1D) model which approximates the Navier-Stokes equations along
the symmetry axis. An important property of this 1D model is that one can
construct from its solutions a family of exact solutions of the 3D
Navier-Stokes equations. The nonlinear structure of the 1D model has some very
interesting properties. On one hand, it can lead to tremendous dynamic growth
of the solution within a short time. On the other hand, it has a surprising
dynamic depletion mechanism that prevents the solution from blowing up in
finite time. By exploiting this special nonlinear structure, we prove the
global regularity of the 3D Navier-Stokes equations for a family of initial
data, whose solutions can lead to large dynamic growth, but yet have global
smooth solutions
Turbulence properties and global regularity of a modified Navier-Stokes equation
We introduce a modification of the Navier-Stokes equation that has the
remarkable property of possessing an infinite number of conserved quantities in
the inviscid limit. This new equation is studied numerically and turbulence
properties are analyzed concerning energy spectra and scaling of structure
functions. The dissipative structures arising in this new equation are curled
vortex sheets contrary to vortex tubes arising in Navier-Stokes turbulence. The
numerically calculated scaling of structure functions is compared with a
phenomenological model based on the She-L\'ev\^eque approach. Finally, for this
equation we demonstrate global well-posedness for sufficiently smooth initial
conditions in the periodic case and in . The key feature is the
availability of an additional estimate which shows that the -norm of the
velocity field remains finite
Weak-inertial flow between two rough surfaces
âOseenâPoiseuilleâ equations are developed from an asymptotic formulation of the three-dimensional NavierâStokes equations in order to study the influence of weak inertia on flows between rough surfaces. The impact of the first correction on macroscopic flow due to inertia has been determined by solving these equations numerically. From the numerical convergence of the asymptotic expansion to the three-dimensional NavierâStokes flows, it is shown that, at the macroscopic scale, the quadratic correction to the Reynolds equation in the weak-inertial regime vanishes generalizing a similar result in porous media
Parameter Estimation for the Stochastically Perturbed Navier-Stokes Equations
We consider a parameter estimation problem to determine the viscosity
of a stochastically perturbed 2D Navier-Stokes system. We derive several
different classes of estimators based on the first Fourier modes of a
single sample path observed on a finite time interval. We study the consistency
and asymptotic normality of these estimators. Our analysis treats strong,
pathwise solutions for both the periodic and bounded domain cases in the
presence of an additive white (in time) noise.Comment: to appear in SP
Parametrization of global attractors experimental observations and turbulence
This paper is concerned with rigorous results in the theory of turbulence and fluid flow. While derived from the abstract theory of attractors in infinite-dimensional dynamical systems, they shed some light on the conventional heuristic theories of turbulence, and can be used to justify a well-known experimental method.
Two results are discussed here in detail, both based on parametrization of the attractor. The first shows that any two fluid flows can be distinguished by a sufficient number of point observations of the velocity. This allows one to connect rigorously the dimension of the attractor with the LandauâLifschitz ânumber of degrees of freedomâ, and hence to obtain estimates on the âminimum length scale of the flowâ using bounds on this dimension. While for two-dimensional flows the rigorous estimate agrees with the heuristic approach, there is still a gap between rigorous results in the three-dimensional case and the Kolmogorov theory.
Secondly, the problem of using experiments to reconstruct the dynamics of a flow is considered. The standard way of doing this is to take a number of repeated observations, and appeal to the Takens time-delay embedding theorem to guarantee that one can indeed follow the dynamics âfaithfullyâ. However, this result relies on restrictive conditions that do not hold for spatially extended systems: an extension is given here that validates this important experimental technique for use in the study of turbulence.
Although the abstract results underlying this paper have been presented elsewhere, making them specific to the NavierâStokes equations provides answers to problems particular to fluid dynamics, and motivates further questions that would not arise from within the abstract theory itself
- âŠ