Turbulence In Incompressible Fluid Research Articles

Two-layer turbulent flow over a rough rotating surface

A model of turbulent incompressible fluid flow over a rough surface under the action of the Coriolis force with a turbulent transfer coefficient corresponding to the Prandtl mixing length is proposed. A solution of the problem, asymptotic in the small Coriolis parameter, is presented for horizontally uniform steady-state flow. It is shown that for a small Coriolis parameter the velocity profile and the turbulent transfer coefficient can differ substantially from the limiting expressions known from Prandtl theory. The smaller the roughness coefficient, the greater the difference.

Direct Numerical Simulation of Isotropic Turbulence by Upstream-Shifted Interpolation Method.

A direct numerical simulation of three-dimensional isotropic turbulence of incompressible fluid was performed in order to examine an upstream-shifted interpolation (USI) method and a modified upstream-biased finite difference (UBD) method. These upstream techniques, which have been proposed by the present author, are based on an appropriate central finite difference method. In comparison with the 3rd- or 5th-order UBD method, the USI method agrees reasonably with a reliable central difference method and a spectral method. USI shows better consistency, especially for higher-order statistics of turbulence than the UBD method.

The renormalization group method in statistical hydrodynamics

This paper gives a first principles formulation of a renormalization group (RG) method appropriate to study of turbulence in incompressible fluids governed by Navier–Stokes equations. The present method is a momentum-shell RG of Kadanoff–Wilson type based upon the Martin–Siggia–Rose (MSR) field-theory formulation of stochastic dynamics. A simple set of diagrammatic rules are developed which are exact within perturbation theory (unlike the well-known Ma–Mazenko prescriptions). It is also shown that the claim of Yakhot and Orszag (1986) is false that higher-order terms are irrelevant in the ε expansion RG for randomly forced Navier–Stokes (RFNS) with power-law force spectrum F̂(k)=D0k−d+(4−ε). In fact, as a consequence of Galilei covariance, there are an infinite number of higher-order nonlinear terms marginal by power counting in the RG analysis of the power-law RFNS, even when ε≪4. The difficulty does not occur in the Forster–Nelson–Stephen (FNS) RG analysis of thermal fluctuations in an equilibrium NS fluid, which justifies a linear regression law for d≳2. On the other hand, the problem occurs also at the nontrivial fixed point in the FNS Model A, or its Burgers analog, when d<2. The marginal terms can still be present at the strong-coupling fixed point in true NS turbulence. If so, infinitely many fixed points may exist in turbulence and be associated to a somewhat surprising phenomenon: nonuniversality of the inertial-range scaling laws depending upon the dissipation-range dynamics.

Universality and scaling in fully developed turbulence

Abstract The small scale velocity fluctuations in high Reynolds number incompressible fluid turbulence exhibit universal scaling properties independent of the large scale flow structures. The evidence for this universality and scaling from experiment and direct numerical simulation, which has considerably improved in recent years, is reviewed in this article. The emphasis is on those features which are independent of any particular statistical theory. Some attempt is made to link this phenomenological picture to Navier-Stokes dynamics, but this is necessarily quite incomplete since a fundamental theoretical understanding is still lacking.

Flow Features to Control Thermally Induced Convection in a Vertical Laminar Flow Cleanroom

This paper presents results of a flow simulation study of convection heat currents above a heat source in a vertical laminar flow (VLF) cleanroom as determined both experimentally and computationally. Typical clcanroom operations have numerous pieces of equipment that generate heat— thus the importanec of this study. The experiment was carried out in a full-scale mockup of a cleanroom. Temperature distributions above an electrical hot plate were measured for 12 airflow velocities and four heat source levels. The results showed that when the mean downward airflow velocity was 0.20 m/s or greater, the plume of heated air was completely suppressed and rose only 30 cm above the heat source. The relation between the convection current zone and the Richardson number was determined. Computer models simulating the turbulent incompressible fluid flow in a Cartesian coordinate system were applid to analyze the three-dimensional heat currents inside the VLF cleanroom and to prediet the temperature and velocity distributions. The velocity distributions clearly indicated the magnitude of the area within which the heat current disturbed the vertical flow. Comparisons between the experimental findings and the calculated results provided significant information on how to apply the computer simulation to a practical design.

Cluster statistics of homogeneous fluid turbulence.

The intermittent property is investigated for numerically simulated incompressible three-dimensional fluid turbulence at Taylor microscale Reynolds number ${\mathit{R}}_{\ensuremath{\lambda}}$\ensuremath{\sim}100, 120, and 180. Cluster statistics applied to energy dissipation and velocity (spatial-) derivative fields characterize several intermittent properties, such as the degrees of concentration and the connectivity of regions of large magnitude. Some power-law behavior with a universal exponent appears in the statistics of the energy-dissipation field. Cluster statistics for the derivative field confirm the well-known experimental result that a higher-order derivative field is more intermittent. Moreover, the longitudinal- and the lateral-derivative velocity fields show some differences in the statistics: The former field has smaller concentration, and its cluster pattern is more spotty than the latter field.

The local structure of turbulence in incompressible viscous fluid for very large Reynolds numbers

§1. We shall denote by u α ( P ) = u α ( x 1 , x 2 , x 3 , t ), α = 1, 2, 3, the components of velocity at the moment t at the point with rectangular cartesian coordinates x 1 , x 2 , x 3 . In considering the turbulence it is natural to assume the components of the velocity u α ( P ) at every point P = ( x 1 , x 2 , x 3 , t ) of the considered domain G of the four-dimensional space ( x 1 , x 2 , x 3 , t ) are random variables in the sense of the theory of probabilities (cf. for this approach to the problem Millionshtchikov (1939) Denoting by Ᾱ the mathematical expectation of the random variable A we suppose that ῡ 2 α and (d u α /d x β ) 2 ― are finite and bounded in every bounded subdomain of the domain G .

Turbulent incompressible fluid flow in a channel with unilateral mass transfer

Turbulent incompressible fluid flow in a channel with unilateral mass transfer

Conditional averaging procedure for the elimination of the small-scale modes from incompressible fluid turbulence at high Reynolds numbers.

Conditional averaging procedure for the elimination of the small-scale modes from incompressible fluid turbulence at high Reynolds numbers.

Etude numérique du transfert thermique métal-fluide dans un conduit rectangulaire en régime instationnaire

Numerical results of the determination, by the finite difference method, of the temperature profile in a parallel plates duct containing an incompressible laminar or turbulent fluid in forced convection is presented. Different heat transfer conditions are considered as well as a time-dependent heat flux condition on the top metal plate. The coupling between conduction and convection is carried by the ‘solid-fluid’ interface. The heat transfer coefficient between plate and fluid is found at each point and time by a heat balance equation on the top plate. The results are compared with those found employing a simplified model MS and proved by the infra-red thermography results.

Large-scale vortices in helical turbulence of incompressible fluid

Abstract The interaction of a mean flow with a random fluctuation field is considered. This interaction is described by the averaged Navier-Stokes equation in which terms nonlinear in the fluctuation field are expressed in terms of the mean flow and the statistical properties of the fluctuation field, which is assumed to be homogeneous, isotropic, and helical. Averaged equations are derived using a functional technique. These equations are solved for a mean background flow that depends linearly on the position vector. The solutions show that large-scale vortices may arise in this system.

Spectrum, dimension, and polymer analogies in fluid turbulence.

The relation between fractal dimension and intertial exponents in three-dimensional incompressible fluid turbulence is analyzed. Several polymer analogies are explained, and an application to the numerical modeling of turbulence is presented.

On the theory of turbulence for incompressible fluids

On the theory of turbulence for incompressible fluids

Numerical and physical modeling of turbulent flow around a plate with two transverse ribs

Results are presented of a numerical and experimental investigation of turbulent incompressible fluid flow near a horizontal plate on which one and two interceptors are installed.

A technique to solve incompressible non-Newtonian flow problems

A finite difference numerical technique is presented to solve equations of Navier—Stokes type when coupled with a stress equation. Steady planar two-dimensional flows of incompressible non-Newtonian and turbulent fluid models are considered. The system of nonlinear equations that results is solved iteratively using a successive substitution approach that introduces a set of linear equations and a combination of inner and outer iterations. The convergence of the iteration and the stability of the difference scheme are analysed for a forward-facing step problem. Particular attention is paid to the dependence of the outer iteration upon the relevant material parameters. Results are presented for the second-order non-Newtonian model.

Theoretical basis for self-similarity in the decay of incompressible fluid turbulence.

Theoretical basis for self-similarity in the decay of incompressible fluid turbulence.

A phenomenological model for the passive scalar variance transformation in a turbulent fluid

The exact transport equation for the passive contaminant concentration variance in incompressible turbulent fluid, derived by Corrsin, J. appl. Phys. 23,113–118 (1952), is expressed in the integro-differential form. The phenomenological integro-differential model equation for the variance space-time transformation and the general form of its solution are proposed. On the grounds of a few simple special cases it is shown that the solutions of the model equation follow some previously derived general restrictions [ J. Fluid Mech. 91,337–355 (1979); 94, 83–101 (1979)]. Relying on the constructed model some earlier approaches [ J. appl. Phys. 23, 113–118 (1982); Adv. Geophys. 6, 117–137 (1959)] to the problem can be reinterpreted. The model is in good agreement with the available data of field and laboratory experiments.

Analysis of the drag of two discs in a turbulent incompressible fluid flow

The effect of reducing the drag of two discs is investigated by using difference modeling of their flow by using the two-parameter k — ɛ turbulence model.

Numerical Simulation of Turbulent Flows

Computational models of turbulence in incompressible Newtonian fluids governed by the Navier-Stokes equations are reviewed. The governing equations are presented, and both direct and large-eddy-simulations are examined. Resolution requirements and numerical techniques of spatial representation, definition of initial and boundary conditions, and time advancement are considered. Results of simulations of homogeneous turbulence in uniform shear, the evolution of a turbulent mixing layer, and turbulent channel flow are presented graphically and discussed.

Functional integrals in Navier–Stokes incompressible fluid turbulence

A variational principle is formulated for the dynamical evolution of the Hopf characteristic functional Φ=Φ[y(x),t] by employing an appropriate functional integral over all parameter fields y(x). It follows that the ratio of functional integrals Γ≡∫Φ*ΦD(y)/∫‖Φ‖2D(y) is an exact constant of the motion during the decay of boundary‐free Navier–Stokes incompressible fluid turbulence. Bearing the physical dimensions of inverse time, the constant of the motion Γ is a scalar function of the multipoint velocity correlation tensors embodied in Φ. For statistical situations such that the probability measure over the velocity‐field ensemble is semi‐Gaussian (i.e., the real part of ln Φ is a quadratic functional of y), Γ is evaluated explicitly in terms of the two‐point velocity correlation tensor.