摘要:

Numerical simulations of the early transition process in periodic grooved‐channel flow are presented. For Reynolds numbers,R<Rc,1=O(100), the two‐dimensional steady flow is stable to all disturbances; atR=Rc,1the flow undergoes a supercritical Hopf bifurcation to a nonlinear two‐dimensional steady‐periodic state; forR>Rc,2>Rc,1the wavy two‐dimensional flow is unstable to a classical linear three‐dimensional secondary instability; and for some range of Reynolds number aboveRc,2the secondary instability saturates in a steady‐periodic, three‐dimensional, low‐order equilibrium. The three‐dimensional equilibria owe their existence and stability to thenarrowbandnature of grooved‐channel‐flow secondary instability, which in turn reflects the low‐Reynolds‐numbersupercriticalform of the grooved‐channel‐flow primary bifurcation. The contrast between the low‐order, weak transition in ‘‘inflectional’’ complex‐geometry channels and the abrupt, snap‐through transition in (subcritical‐primary broadband‐secondary) planar channels illustrates the important role of primary criticality in the early transition process.

ISSN:0899-8213    

DOI:10.1063/1.857473

出版商:AIP    

年代:1989

数据来源: AIP

摘要:

Direct numerical simulation is used to study the curvature of material surfaces in isotropic turbulence. The Navier–Stokes equation is solved by a 643pseudospectral code for constant‐density homogeneous isotropic turbulence, which is made statistically stationary by low‐wavenumber forcing. The Taylor‐scale Reynolds number is 39. An ensemble of 8192 infinitesimal material surface elements is tracked through the turbulence. For each element, a set of exact ordinary differential equations is integrated in time to determine, primarily, the two principal curvaturesk1andk2. Statistics are then deduced of the mean‐square curvatureM= (1)/(2) (k21+k22), and of the mean radius of curvatureR=(k21+k22)−1/2. Curvature statistics attain an essentially stationary state after about 15 Kolmogorov time scales. Then the area‐weighted expectation ofRis found to be 12&eegr;, where &eegr; is the Kolmogorov length scale. For moderate and small radii (less than 10&eegr;) the probability density function (pdf) ofRis approximately uniform, there being about 5% probability ofRbeing less than &eegr;. The uniformity of the pdf ofR, for smallR, implies that the expectation ofMis infinite. It is found that the surface elements with large curvatures are nearly cylindrical in shape (i.e., ‖k1‖≫‖k2‖ or ‖k2‖≫‖k1‖), consistent with the folding of the surface along nearly straight lines. Nevertheless the variance of the Gauss curvatureK=k1k2is infinite.

ISSN:0899-8213    

DOI:10.1063/1.857474

出版商:AIP    

年代:1989

数据来源: AIP

摘要:

Tennekes [J. Fluid Mech.67, 561 (1975)] estimated the time decorrelation of inertial‐range excitation in isotropic turbulence by assuming effective statistical independence of the one‐time distributions of inertial‐range and energy‐range excitation. This picture has been challenged by Yakhot, Orszag, and She [Phys. Fluids A1, 184 (1989)], who studied forced turbulence by renormalization‐group (RNG) methods. The analysis given in the present paper leads to the conclusion that (a) precise coherence between energy‐range and inertial‐range excitation is needed to inhibit sweeping effects; (b) in the case of randomly forced turbulence, this coherence is impossible and Tennekes’ picture is unavoidable; and (c) the RNG analysis does not demonstrate inhibition of sweeping; instead, it discards sweeping effects at the outset. To augment the present study, an advected passive scalar is examined by computer simulation. Sweeping effects on small scales survive even in the case of long‐time advection by a frozen velocity field. The observed probability distributions resemble those for the alignment of vorticity and velocity observed in flow simulations.

ISSN:0899-8213    

DOI:10.1063/1.857475

出版商:AIP    

年代:1989

数据来源: AIP

摘要:

The dynamics of helical decaying homogeneous turbulence is investigated in direct numerical simulations at moderate Reynolds numbers. A new initialization procedure is presented that allows one to control both the energy and the helicity spectral density of the initial flow field. It is observed that large initial helicity impedes the transfer of energy toward smaller scales, inhibits the buildup of enstrophy, and reduces dissipation for several turnover times. Also, the skewness and flatness of the velocity derivatives reach values typical of turbulence much later than in comparable flows without helicity. However, these effects are significant only if the helicity of the flow is quite high. In simulations with small or vanishing initial helicity it is found that the fluctuations of the average helicity and the helicity spectral density lie within the range suggested by a quasi‐Gaussian approximation. This suggests that at moderate Reynolds number spontaneous fluctuations of helicity are not large enough to directly influence the energy transfer.

ISSN:0899-8213    

DOI:10.1063/1.857476

出版商:AIP    

年代:1989

数据来源: AIP

摘要:

Data obtained from the two‐dimensional numerical simulation of a plane mixing layer have been used to study the feasibility of tagging one side of the flow by a passive scalar and using the instantaneous concentration of the scalar to detect the typical coherent events in the flow. The study has shown that this technique works quite satisfactorily and yields results similar to those obtained by using the instantaneous vorticity as a detection criterion. The contribution from the coherent events to the time‐averaged turbulent momentum and scalar transport has been estimated. It is found that this contribution is of the same order as the time‐mean transport during most of the dynamical evolution of the coherent structure. However, it may attain very large values for short periods of time in the neighborhood of pairing. The increase is particularly spectacular in the case of the Reynolds shear stress. While the present findings obtained from a two‐dimensional simulation seem to support earlier results obtained from actual experiments, it is desirable to conduct additional studies with three‐dimensional simulations when they become available.

ISSN:0899-8213    

DOI:10.1063/1.857477

出版商:AIP    

年代:1989

数据来源: AIP

摘要:

The Poiseuille and thermal transpiration flows of a rarefied gas between two parallel plates are investigated on the basis of the linearized Boltzmann equation for hard‐sphere molecules and diffuse reflection boundary condition. The velocity distribution functions of the gas molecules as well as the gas velocity and heat flow profiles and mass fluxes are obtained for the whole range of the Knudsen number with good accuracy by the numerical method recently developed by the authors.

ISSN:0899-8213    

DOI:10.1063/1.857478

出版商:AIP    

年代:1989

数据来源: AIP

摘要:

Existing Chapman–Enskog solution procedures for binary mixtures of hard, perfectly elastic spheres are extended to hard, slightly dissipative spheres, and the associated constitutive relations are calculated. Then a steady, homogeneous shear flow is analyzed and the behavior of the mixture viscosity is determined as the diameter ratio, volume ratio, and total volume fraction are varied.

ISSN:0899-8213    

DOI:10.1063/1.857479

出版商:AIP    

年代:1989

数据来源: AIP

摘要:

The problem of shallow water waves propagating over slowly varying topography is considered. The fluid is assumed to be weakly viscous and the effects of viscosity can be considered only in the boundary layer on the bottom. By the methods of multiple scales and matched asymptotics, the Boussinesq theory is extended for this problem and a unified Kadomtsev–Petviashvili equation is obtained, in which viscous, topographic, and transverse modulational effects are incorporated.

ISSN:0899-8213    

DOI:10.1063/1.857480

出版商:AIP    

年代:1989

数据来源: AIP

摘要:

It is theoretically established that energy transfer in nonhomogeneous turbulence occurs in two distinct scale‐independent ‘‘modes.’’ The physical significance of these modes is examined. Further, evidence is presented that suggests the existence of a conservation principle that governs the transfer of energy between turbulence eddies of differing size. A possible algebraic form of such a principle is formulated.

ISSN:0899-8213    

DOI:10.1063/1.857481

出版商:AIP    

年代:1989

数据来源: AIP