摘要:

Recent progress made in nonlinear stability theory of viscous, incompressible flows is discussed. First, progress made by means of the energy method is considered. In some cases the stability bounds obtained with the energy method coincide or nearly coincide with the critical values given by the linear stability theory. Further, a survey of recent mathematical investigations on the branching of steady solutions at the critical Reynolds (or Rayleigh) numbers is given. Finally, numerical methods solving the steady Navier—Stokes equations by finite differences are briefly mentioned.

ISSN:0031-9171    

DOI:10.1063/1.1762472

出版商:AIP    

年代:1967

数据来源: AIP

摘要:

A review is presented of some experimental results on transition from laminar to turbulent flow in a boundary layer of an incompressible fluid on a flat plate with no pressure gradient. In the absence of large disturbing influences, transition involves the sequence of processes occurring in the following order: The amplification of weak disturbances; the nonlinear development of disturbances; the development of high‐shear layer and high‐frequency disturbances; and the development of turbulent randomness. The interpretation of these processes is reviewed and brought up to date.

ISSN:0031-9171    

DOI:10.1063/1.1762423

出版商:AIP    

年代:1967

数据来源: AIP

摘要:

The principal assumptions used by Kraichnan in formulating a theory of turbulence are reviewed, and their meaning is examined in the light of a mathematical model. A regression function is defined and used to evaluate the triple correlations. The importance of the fourth‐order cumulants is discussed. The merits of the theory are illustrated by comparison with experimental results—in the case of the mathematical model—of grid turbulence (skewness factor) and of turbulence at very large Reynolds number.

ISSN:0031-9171    

DOI:10.1063/1.1762439

出版商:AIP    

年代:1967

数据来源: AIP

摘要:

The turbulent boundary layer can be subdivided into four distinct regions, sublayer, turbulent wall layer, outer region, and superlayer. Each one of these regions is briefly discussed and recent theoretical approaches dealing with the Reynolds stress are examined.

ISSN:0031-9171    

DOI:10.1063/1.1762462

出版商:AIP    

年代:1967

数据来源: AIP

摘要:

The specific features of atmospheric boundary‐layer turbulence are described. The small‐scale properties of atmospheric turbulence depend very little on the peculiarities of its large‐scale components and obey approximately the laws of locally isotropic turbulence. It is shown that turbulence is locally axisymmetric in respect to the vertical direction and depends upon the buoyancy parameter. Large‐scale turbulence obeys a similarity theory based upon the ``external'' parameters such as the geostrophic wind velocity, potential temperature difference across the boundary layer, roughness height of the underlying surface, the Coriolis parameter and the buoyancy parameter. The dynamic equations for the first‐ and second‐order statistical moments of turbulence are formulated and analyzed.

ISSN:0031-9171    

DOI:10.1063/1.1762491

出版商:AIP    

年代:1967

数据来源: AIP

摘要:

The handover of the vertical fluxes of momentum, heat, etc., from the small‐scale turbulence close to the earth's surface into the larger‐scale motions above is becoming an important question in the context of numerical treatment of atmospheric dynamics. In convective conditions, a decoupling of heat flow from the surface value is suggested at a height of some 5 to 10 times the Obukhov scale height, at times lower. Some changes in regime are already well documented below this level. Above it, the need for direct measurement of the eddy heat flux on the cumulus scale, and location of the roots of these circulations, is emphasized. For momentum flux the handover from microscale direct into the synoptic scale is considered primarily. At a level where the microscale flux has fallen from its surface value &tgr;0to &tgr;, the vertical motion in unaccelerated flow is &rgr;w= curl [(&tgr;0− &tgr;)/f], wherefis the Coriolis parameter. When this is viewed as a component of eddy motion on the global scale, the resultant eddy transport of momentum is found to be insignificant. But the asymmetry of acceleration patterns in the westerlies, particularly that broadly associated with the transient frontal systems, appears to yield significant momentum flux in the required direction. This defines the need for a clearer identification of the typical acceleration patterns and for numerical solutions of the appropriately modified boundary layer equations. The momentum flux attributable to thermal wind and the handover into mean meridional circulation are also discussed.

ISSN:0031-9171    

DOI:10.1063/1.1762502

出版商:AIP    

年代:1967

数据来源: AIP

摘要:

Within the last decade there has been a great increase in the sophistication of ideas on wave generation, but the more complex observational data required to check these theoretical ideas are still lacking. Such data as do exist seem to support, at least qualitatively, the Phillips idea of the nature of the initial wave generation mechanism, but indications are that the Miles mechanism of wave generation at later stages is inadequate to explain the observed increase of wave energy. New ideas involving the effect of the turbulence in the air, and of different flow configurations from that proposed by Miles, are being proposed. The available observations are still inadequate to test these ideas. Of particular importance to the theory are measurements in the air below the level of the wave creasts.

ISSN:0031-9171    

DOI:10.1063/1.1762504

出版商:AIP    

年代:1967

数据来源: AIP

摘要:

A rigorous mathematical description is given for the physical concept of the cascade process of sequential breakdown of turbulent eddies. It is assumed that the probability distribution for the ratio of typical values of turbulent fluctuations averaged over a small volumevto those averaged over a surrounding larger volumeVis invariant under the group of space similarity transformations, provided that the length scales of both volumes are much smaller than the external scale of turbulence and much larger than the Kolmogoroff scale. This assumption is in general agreement with the conclusions of Kolmogoroff and Obukhov and with the existing measurements of the power spectrum for the square of the velocity derivative. Some measurements of probability distributions for smallscale turbulent fluctuations are also discussed.

ISSN:0031-9171    

DOI:10.1063/1.1762505

出版商:AIP    

年代:1967

数据来源: AIP

摘要:

Two expressions are obtained for the turbulent viscosity associated with the transfer of mean‐square vorticity across the spectrum. Both involve the three‐dimensional energy‐spectrum functionEand on equating them, a differential equation for the spectrum is obtained. For small wavenumber magnitudes and at high Reynolds number,E= (27/3/3) &egr;2/3k−5/3, where &egr; is the time rate of kinetic energy dissipation per unit mass, andkis the wavenumber magnitude. Thus the universal constant in Kolmogoroff's law for the inertial subrange is (27/3/3) = 1.679 &cellip;. The solution of the differential equation for the high wavenumber magnitude end of the spectrum is yet to be found, but it is clear from the equation that a pure power function is not a solution, and thus Heisenberg'sk−7law is not supported.

ISSN:0031-9171    

DOI:10.1063/1.1762506

出版商:AIP    

年代:1967

数据来源: AIP

摘要:

R(x, r, t) is the Eulerian correlation function in the space with zero mean motion.R(t), the Lagrangian correlation function, may be found from the correlation functionR'(x, r, t) based on the sub‐ensemble of ``Eulerian trials'' for which the fluid particle at (x, r, t) is the same as that at (0, 0, 0). The hypothesis thatRmay be substituted forR'yields a connection betweenR(t) andR(x, r, t). The Lagrangian time scale is found to be about one‐third the Eulerian time scale. TheapparentEulerian time scale depends on the intensity of turbulence. Data on the ratio of Lagrangian toapparentEulerian time scales agree farily well with the analysis.

ISSN:0031-9171    

DOI:10.1063/1.1762507

出版商:AIP    

年代:1967

数据来源: AIP