摘要:

Using a two‐layer fluid model, Korteweg–de Vries (KdV) equations modified by viscosity are derived that describe weakly nonlinear long waves propagating along a channel of uniform but arbitrary cross section. Equations are deduced for both surface waves and internal waves. The case of high Reynolds number is considered, and the method of matched asymptotic expansion is employed. The coefficients of the KdV equation, which depend on the geometry of the channel cross section, are determined exactly for a rectangular cross section. Some particular cases including the Boussinesq limit are considered.

ISSN:0031-9171    

DOI:10.1063/1.865915

出版商:AIP    

年代:1986

数据来源: AIP

摘要:

Measurements have been made of the size of the region of secondary flow in a linearly stratified fluid, with Brunt–Va¨isa¨la¨ frequencies in the range of 0.65–3.23 rad/sec, caused by a rotationally oscillating shearing stress. The stress was generated by the surfaces of a disk of radiusr=5.078 cm undergoing torsional oscillations of angular frequency &ohgr;=1.50 rad/sec inside cylindrical boundaries with radii in the range 6.95–10.75 cm. The kinematic viscosity in the vicinity of the disk was approximately constant, &ngr;=1.08 centistokes. Several features of the flow are similar to the secondary flow described by Scranton and Lindberg [Phys. Fluids26, 1198 (1983)] as occurring in annular tank experiments to model geophysical turbulent mixing. For constant Ekman numberEk=&ngr;/&ohgr;r2, the size of the secondary flow region depends on the Brunt–Va¨isa¨la¨ frequency and the boundary radius; an empirical correlation of the data is presented.

ISSN:0031-9171    

DOI:10.1063/1.866001

出版商:AIP    

年代:1986

数据来源: AIP

摘要:

By introducing a suitable fluid rest frame, it is possible to simplify considerably the form of the Rankine–Hugoniot relations for relativistic magnetohydrodynamics. General solutions can then be found that are independent of the problem geometry. In this article, solutions for fast magnetoacoustic shocks in a Synge gas are discussed.

ISSN:0031-9171    

DOI:10.1063/1.865916

出版商:AIP    

年代:1986

数据来源: AIP

摘要:

In the collapse of a spherical cavity surrounded by a perfect gas initially at rest, the velocityR˙ of the free gas boundary has an initial valve of −2c0/(&ggr;−1) (c0is the speed of sound in the undisturbed gas and &ggr; is the adiabatic exponent). HereafterR˙ remains practically constant untilRbecomes a certain fraction &xgr;(&ggr;) of the initial radiusR0. Finally, forR<&xgr;R0,R˙ approaches the asymptotic behaviorR˙∼R−&tgr;(&ggr;)predicted by self‐similar solutions. The function &xgr;(&ggr;), which has been obtained numerically, decreases as &ggr; decreases and vanishes for a certain value of &ggr; near 1.5. This fact, together with the analogous behavior of &tgr;(&ggr;), suggests that there exists a certain value &ggr;cr≊1.5 of the adiabatic exponent such that, for 1<&ggr;<&ggr;crthe velocityR˙ of the free boundary is strictly a constant during the entire collapse. This behavior seems to be closely related to the results obtained by Lazarus [Phys. Fluids25, 1146 (1982)] who demonstrates that a degenerate stable, asymptotic solution, withR˙=const, exists for &ggr;<3/2.

ISSN:0031-9171    

DOI:10.1063/1.865917

出版商:AIP    

年代:1986

数据来源: AIP

摘要:

In this paper it is shown that the value of the similarity exponent &agr; derived analytically by Fujimoto and Mishkin [J. Fluid Mech.89, 61 (1978); Phys. Fluids21, 1933 (1978)] is exactly the same as that found by Stanyukovich [Unsteady Motion of Continuous Media, (Academic, New York, 1960)]. Since the result found by Stanyukovich is an approximation to &agr;, Fujimoto and Mishkin’s claim to have an exact expression of &agr; is false. The two methods are outlined and Stanyukovich’s result is simplified to show its equivalence to the work of Fujimoto and Mishkin.

ISSN:0031-9171    

DOI:10.1063/1.865918

出版商:AIP    

年代:1986

数据来源: AIP

摘要:

An asymptotic theory is presented for predicting the sound field generated by small‐amplitude instability waves in low‐speed boundary‐layer flows. A Tollmien–Schlichting wave of fixed frequency, which evolves spatially in a Blasius boundary layer, is considered, and the associated far‐field acoustic radiation is calculated. It is found that the directional dependence of the radiation intensity is of the dipole type. This result is discussed in connection with the superdirective acoustic fields caused by instability waves, which were recently observed in low‐Mach‐number jets.

ISSN:0031-9171    

DOI:10.1063/1.865919

出版商:AIP    

年代:1986

数据来源: AIP

摘要:

The compressible Rayleigh–Taylor instability of a supersonic accelerated contact discontinuity between two gases is studied by numerically solving the two‐dimensional Euler equations. The computed solutions exhibit a complicated set of nonlinear waves comprised of spike and bubble bow shocks, terminal shocks within the spike and bubble, Kelvin–Helmholtz rollup of the spike tip, and contact surface waves. The spike appears to attain a finite growth of aspect ratio approximately equal to 2. The propagation of a supersonic slab jet is also studied numerically, in order to compare and contrast the jet wave structure with that of the supersonic accelerated surface.

ISSN:0031-9171    

DOI:10.1063/1.865920

出版商:AIP    

年代:1986

数据来源: AIP

摘要:

Drag measurements for a flat plate equipped with passive boundary layer turbulence manipulators, the so‐called Large Eddy Break Up (LEBU) devices, have been carried out in a towing tank at plate length Reynolds numbers of 5–20 million. The towing tank facility allowed direct drag measurements as opposed to indirect methods based on, e.g., measurement of momentum loss thickness of the boundary layer. The LEBU devices consisted of two hydrofoils arranged in tandem, with a spacing of five to eight boundary layer thicknesses at the manipulator position (&dgr;m) and a height in the boundary layer of 0.5&dgr;m–0.9&dgr;m. Four different manipulator configurations were tested, with and without a trip wire on the test plate. The LEBU foil section was 10% thick and symmetric. The ratio between the LEBU chord and &dgr;mranged from 0.8 to 1.1, and the chord Reynolds number ranged from 25 000 to 100 000. Only for the lowest Reynolds number was a 2% drag reduction obtained. However, the main body of the experiments showed no drag reduction in contrast to previously reported experiments.

ISSN:0031-9171    

DOI:10.1063/1.865921

出版商:AIP    

年代:1986

数据来源: AIP

摘要:

The inertial range structure of turbulence is studied on the basis of an approximation derived by a systematic method of Lagrangian renormalized expansions. This method is also applied to the problem of a passive scalar field convected by turbulence, and some of its consequences are examined. Numerical values are obtained for various dimensionless constants in the inertial range including those in thek−5/3spectrum law for the turbulent energy and the scalar field.

ISSN:0031-9171    

DOI:10.1063/1.865922

出版商:AIP    

年代:1986

数据来源: AIP

摘要:

Measurements of Reynolds shear stress profiles and lateral heat flux profiles in the nearly self‐preserving region of the turbulent wake of a heated circular cylinder are compared with calculations obtained from the mean momentum and mean enthalpy equations. Two types of self‐preserving scales are used. The first uses the free‐stream velocityU1and the length scale [(x−x0)d]1/2, wherexis the distance from the cylinder,x0is the virtual origin, anddthe cylinder diameter. The second uses the centerline velocity defectU0and the velocity defect half‐widthL. Consistent results are obtained with both types of scales. In particular, the comparisons do not support the need for determining a new virtual origin, as suggested by Haririetal. [Phys. Fluids25, 1964 (1982)].

ISSN:0031-9171    

DOI:10.1063/1.865923

出版商:AIP    

年代:1986

数据来源: AIP