摘要:

Natural convection in a differentially heated horizontal cylinder is investigated numerically and analytically. Particular attention is paid to the structure of steady convection, the nature of the transients and the onset of unsteadiness for a range of Prandtl numbers extending from 0.7 to infinity. The numerical algorithm integrates the 2-D Navier-Stokes equations in velocity-pressure formulation with a Chebyshev-Fourier spatial approximation. A gradual shift from the conduction to the boundary layer regime is observed for increasing Rayleigh number and the steady flow structure becomes rapidly independent ofPr. Whereas classical scalings are obtained for the azimuthal velocity and the thermal boundary layer thickness, the dynamic boundary layer thickness is found to be independent of the Prandtl number. A simplified semi-analytical model derived from projecting the governing equations on the lowest Fourier modes is proposed, which explains this property. Its solutions are in good quantitative agreement with the full nonlinear solutions in particular for large Prandtl numbers. For large enough Rayleigh values, the transients are found to be dominated by internal waves and the approach to steady state is achieved in an oscillatory manner by decay of internal wave motion. In the steady boundary layer regime, the average Nusselt number classically scales likeRa1/4and a correlation valid over the range of Prandtl numbers considered is 0.28Ra1/4. The onset of unsteadiness is investigated either by direct numerical integration or by linear stability analysis which combines Newton’s iterations to determine the unstable steady states and Arnoldi’s method to compute the eigenvalues of largest real part of the linearized evolution operator about a steady state. It is thus found that the steady state solution undergoes a Hopf bifurcation and that depending on the Prandtl number the most unstable eigenvector may break or keep the symmetry of the base flow. The critical Rayleigh number is found to achieve an asymptotic value for large enough Prandtl number. The location of the hottest point is also shown to have a very large effect on the critical value. Finally, time integration of the unsteady nonlinear equations indicates that the Hopf bifurcation seems of supercritical type for values of the Prandtl number up to 9 and possibly subcritical for largerPrvalues. ©1997 American Institute of Physics.

ISSN:1070-6631    

DOI:10.1063/1.869197

出版商:AIP    

年代:1997

数据来源: AIP

摘要:

We investigate large Rayleigh number(106–109)and large Prandtl number(102–103)thermal convection in glycerol in an aspect ration one cubic cell. The kinematic viscosity of the fluid strongly depends upon the temperature. The symmetry between the top and bottom boundary layers is thus broken, the so-called non-Boussinesq regime. In a previous paper Wu and Libchaber have proposed that in such a state the two thermal boundary layers adjust their length scales so that the mean hot and cold temperature fluctuations are equal in the center of the cell. We confirm this equality. A simplified two-dimensional model for the mean center temperature based on an equation for the thermal boundary layer is presented and compared with the experimental results. The conclusion is that the central temperature adjusts itself so that heat fluxes from boundaries are equal, temperature fluctuations at the center symmetrical, at a cost of very different temperature drops and Rayleigh number for each boundary. ©1997 American Institute of Physics.

ISSN:1070-6631    

DOI:10.1063/1.869198

出版商:AIP    

年代:1997

数据来源: AIP

摘要:

In the past five years, working largely independently, five groups of researchers have proposed low-dimensional models of the behavior of parallel shear flows at high Reynolds numbers. These models are compared, and it is found that they are more similar than their authors have recognized. Among other similarities, most of them exhibit a threshold amplitude&egr;=O(R&agr;)asR→∞for some &agr;<−1, whereRis the Reynolds number, for perturbations of the laminar state that may excite transition to turbulence. The reason for this behavior in each case is an interaction of non-normal linear effects with quadratic nonlinearities. ©1997 American Institute of Physics.

ISSN:1070-6631    

DOI:10.1063/1.869199

出版商:AIP    

年代:1997

数据来源: AIP

摘要:

Minimal channel flow is analyzed by means of the Karhunen–Loe´ve (KL) decomposition. It is shown that the most energetic modes are streamwise rollers followed by outward tilted quasi-streamwise vortices. Both of these mode types have a strong similarity to structures seen in physical experiments. Temporal plots of roll energy, propagating energy, bulk velocity, and representational entropy have been obtained. Study of the evolution of these variables shows a consistent pattern of growth and decay in which entropy plays a key role in describing the events in the turbulent process. The roll and propagating modes are also shown to make independent contributions to the Reynolds stress with the roll modes dominating the profile near the walls and the propagating modes having larger values towards the channel center. A comparison of the KL dimension of this flow and a full channel flow shows that the dimension scales with box size, i.e., it confirms the assertion that dimension is an extensive variable. ©1997 American Institute of Physics.

ISSN:1070-6631    

DOI:10.1063/1.869323

出版商:AIP    

年代:1997

数据来源: AIP

摘要:

A Galilean invariant weak-equilibrium turbulence hypothesis that is sensitive to streamline curvature is proposed. The hypothesis leads to a fully explicit algebraic expression for Reynolds stress in terms of the mean velocity field and kinetic energy and dissipation of turbulence. The model is tested in curved homogeneous shear flow which is a homogeneous idealization of the circular streamline flow. The agreement is excellent with Reynolds stress closure model and adequate with available experimental data.

ISSN:1070-6631    

DOI:10.1063/1.869200

出版商:AIP    

年代:1997

数据来源: AIP

摘要:

We present an analytical scheme, easily implemented numerically, to generate synthetic Gaussian turbulent flows by using a linear Langevin equation, where the noise term acts as a stochastic stirring force. The characteristic parameters of the velocity field are well introduced, in particular the kinematic viscosity and the spectrum of energy. As an application, the diffusion of a passive scalar is studied for two different energy spectra. Numerical results are compared favorably with analytical calculations. ©1997 American Institute of Physics.

ISSN:1070-6631    

DOI:10.1063/1.869201

出版商:AIP    

年代:1997

数据来源: AIP

摘要:

A model for inhomogeneous turbulence is constructed that provides an exact representation of rapidly distorted homogeneous turbulence (RDT). The fundamental quantity modeled is the joint PDF of the velocity and wave vector which is related to the unit wavenumber vector. This joint PDF provides a model equation for the evolution of thedirectional spectrum, the integral over the wavenumber magnitude of the velocity spectrum. At this level the rapid pressure–rate-of-strain correlation is closed yielding exact equations in RDT. For decaying turbulence, the return-to-isotropy terms are modeled by stochastic diffusion equations for the velocity and wave vector. A general model of this type is constructed along with four simplified versions. The decay models are combined with the RDT model to give complete models for homogeneous turbulence, which are tested for several flows. The homogeneous models are then extended in a general manner to inhomogeneous turbulence. ©1997 American Institute of Physics.

ISSN:1070-6631    

DOI:10.1063/1.869195

出版商:AIP    

年代:1997

数据来源: AIP

摘要:

A shock driven material interface between two fluids of different density is unstable. This instability is known as Richtmyer–Meshkov (RM) instability. In this paper, we present a quantitative nonlinear theory of compressible Richtmyer–Meshkov instability in two dimensions. Our nonlinear theory contains no free parameter and provides analytical predictions for the overall growth rate, as well as the growth rates of the bubble and spike, from early to later times for fluids of all density ratios. The theory also includes a general formulation of perturbative nonlinear solutions for incompressible fluids (evaluated explicitly through the fourth order). Our theory shows that the RM unstable system goes through a transition from a compressible and linear one at early times to a nonlinear and incompressible one at later times. Our theoretical predictions are in excellent agreement with the results of full numerical simulations from linear to nonlinear regimes. ©1997 American Institute of Physics.

ISSN:1070-6631    

DOI:10.1063/1.869202

出版商:AIP    

年代:1997

数据来源: AIP

摘要:

Experimental observations show that the presence of small tabs on the edge of a hot, compressible jet exiting into a slower moving, colder ambient flow can increase the rate of spreading of the jet. This suggests that the rate of mixing of the jet and the ambient fluid is also increased. In order to elucidate the physical mechanism responsible for the increased spreading rate a set of calculations was carried out within the framework of the compressible three dimensional Navier–Stokes equations. A series of grid refinements were made to assess the accuracy of the results. We first simulated the flow without the tabs, obtaining reasonable agreement with experimental measurements of the velocity. We then simulated the flow, without tabs, over a range of values of the convective Mach number in order to determine the dependence of the mixing on this parameter. Simulations with modeled tabs were also carried out. In these calculations the effect of the tabs on the flow was modeled by pairs of counter-rotating vortices. The results of these calculations indeed show that the presence of the tabs increase the spreading rate of the jet. The basic physical mechanism responsible for the enhanced spreading rate is discussed and qualitative comparisons with flow visualizations are made. ©1997 American Institute of Physics.

ISSN:1070-6631    

DOI:10.1063/1.869203

出版商:AIP    

年代:1997

数据来源: AIP

摘要:

A uniform supersonic flow of a rarefied gas past a flat plate at zero angle of attack is considered, and the steady behavior of the gas around the plate is investigated numerically on the basis of the Boltzmann–Krook–Welander equation (or the so-called BGK model) and the diffuse reflection boundary condition. An accurate finite-difference analysis, which gives the correct description of the discontinuity of the velocity distribution function of the gas molecules occurring in the gas, is carried out, and the features of the flow field (the velocity distribution function and the macroscopic variables such as the density, temperature, and flow velocity of the gas), in particular, those around the leading and trailing edges, are clarified for a wide range of the Knudsen number. The drag acting on the plate and the energy transferred to it are also obtained accurately. In addition, on the basis of the results for small Knudsen numbers, the behavior of the gas around the leading edge of a semi-infinite plate is investigated in detail. ©1997 American Institute of Physics.

ISSN:1070-6631    

DOI:10.1063/1.869204

出版商:AIP    

年代:1997

数据来源: AIP