摘要:

Spectra of bounded and unbounded basins are calculated on an asymptotic approximation based on smallness of the seabed slopes. This leads to the geometrical optics theory of surface waves of Keller, which is used to extend the known, exact result for an idealized beach to the prediction of the spectra of a variety of more natural water bodies. Attention is directed to cylindrically symmetrical and two‐dimensional topographies corresponding, respectively, to islands and to continental slopes and laboratory channels. Marked differences are found in the character of the spectra for these two types of topography.

ISSN:0031-9171    

DOI:10.1063/1.1691819

出版商:AIP    

年代:1968

数据来源: AIP

摘要:

Turbulent mixing of passive scalar properties such as temperature or concentration is discussed. From physical and geometrical considerations it is concluded that the smallest scale features of a steady‐state turbulent scalar distribution are primarily determined by the number and distribution of points in the fluid for which the scalar gradient vector is zero, and surfaces for which the gradient magnitude is minimal. Mechanisms for the production, destruction, and motion of such “zero gradient points” and “minimal gradient surfaces” are examined. Initially, zero gradient points must be produced from regions of uniform scalar gradient, but the vast majority result from secondary splitting due to strain induced eccentricities of the closed isoscalar surfaces surrounding maximum or minimum points. An expression for the velocity of surfaces of constant scalar value is derived and used to interpret the Obukhov‐Corrsin length scale(D3/&egr;)14as the minimum size eddy capable of generating a zero gradient point from a region of uniform gradient, whereDis the molecular diffusivity of the scalar and &egr; is the mean viscous dissipation rate. A steady‐state separation distance between zero gradient points of order(D/&ggr;)12is inferred for scalar fields of arbitrary diffusivity where &ggr; is the root mean square rate of strain of the fluid. Previous theories such as that of Batchelor, Howells, and Townsend have assumed the local strain rate has no effect on scalar structure for large Prandtl number fields.

ISSN:0031-9171    

DOI:10.1063/1.1691820

出版商:AIP    

年代:1968

数据来源: AIP

摘要:

Universal similarity hypotheses are proposed based on the local straining mechanisms, Kolmogoroff's local isotropy theory, and the mixing theories of Obukhov, Corrsin, and Batchelor. Three sets of similarity coordinates follow from the hypotheses depending on five fundamental parameters of turbulent mixing: &egr;, the turbulence dissipation rate; &khgr;, the scalar variance dissipation rate; &ggr;, the local strain rate; &ngr;, the kinematic viscosity; andD, the molecular diffusivity of the scalar. Transformations between coordinate systems are shown to depend only onPr ≡ &ngr;/Das a mapping parameter. A unified spectral array with convergence properties required by the hypotheses is produced when the similarity hypotheses are used to predict the scalar spectrum function &Ggr;. The inertial subrange (&Ggr; ∼ k−5/3,kis the wavenumber) of Obukhov and Corrsin and the large Pr value viscous‐convective(&Ggr; ∼ k−1)subrange of Batchelor are reproduced. However, for small Pr values, a new inertial‐diffusive subrange arises with&Ggr; ∼ k−3and cutoff at wavenumber(&ggr;/D)12. Bounds for the universal subrange constants and functional forms for arbitrary Pr values are inferred using Batchelor's diffusive cutoff function, and compared with available experimental measurements.

ISSN:0031-9171    

DOI:10.1063/1.1691821

出版商:AIP    

年代:1968

数据来源: AIP

摘要:

The Lagrangian history direct interaction approximation is applied to isotropic turbulent mixing of a second‐order chemical reaction, the resulting closed sets of equations are presented, and an a‐bridgement of them is carried out. It is shown that in the limit of a stochastically distributed second‐order reaction the equations reduce to those of direct interaction. It is also demonstrated that the approximation preserves an important property of the exact equations; namely, that in the absence of molecular diffusion, the decay of single point statistical functions of the concentration field is independent of the turbulence.

ISSN:0031-9171    

DOI:10.1063/1.1691822

出版商:AIP    

年代:1968

数据来源: AIP

摘要:

The hydrodynamic theory of light scattering is generalized by using the linearized Burnett equations instead of the linearized Navier‐Stokes equations. It is emphasized that this is necessary if one is interested in phenomena which are of second order inlK, withlthe mean free path andKthe magnitude of the change in optical wave vector. The principal results are expressions for the initial dispersion (Kdependence) of the Brillouin shift and Landau‐Placzek ratio.

ISSN:0031-9171    

DOI:10.1063/1.1691823

出版商:AIP    

年代:1968

数据来源: AIP

摘要:

Trimodal solutions are given for the structure of a strong shock in a gas of spherocylindrical molecules. The trimodal theory includes rotational relaxation effects by setting up a kinetic theory for diatomic particles and adding a third equilibrium form to the monatomic bimodal distribution function of Mott‐Smith. Spherocylinders are characterized by two parameters. They are associated with (1) the eccentricity of the force field and (2) the ability to transfer energy between the translational and rotational modes. Virial coefficient experiments suggest that a value of one‐third for the eccentricity parameter is typical of several gases. Using this value, special emphasis is placed on the effects of the Mach number and the conversion parameter. Verification is provided for the absence of an internal temperature overshoot and for the predicted limitations of the theory. Shock profile and thickness curves are given that are comprehensive enough to be compared with data taken for widely varying Mach numbers and relaxation rates. Thus far, the only data on rotational relaxation are for nitrogen. Comparisons with the trimodal results show that spherocylinders with eccentricities of one‐third and conversion parameters of 0.025 would simulate the shock thickness behavior of nitrogen molecules. Profile displacement considerations, however, indicate that eccentricities other than one‐third must be investigated to simultaneously satisfy displacement and thickness data.

ISSN:0031-9171    

DOI:10.1063/1.1691824

出版商:AIP    

年代:1968

数据来源: AIP

摘要:

Formulas are derived for the amplitudes of waves that diverge from a shock as a result of any given incident disturbance. For strong shocks, that is the Mach number (M) is large, in an ideal gas it is shown that the pressure amplitude and the component of the energy flux normal to the shock of a transmitted sound wave are ofO (M2greater than those in the incident sound wave. Furthermore, if the impinging sound wave is incident near the critical angle the ratio of the pressure amplitude of the transmitted sound wave to that of the incident one is ofO (M3). On the other hand, if a sound wave is normally incident upon the back of the shock, only about 1% of the acoustic energy flux is reflected in the form of sound waves. It is also shown that incident entropy‐vorticity waves can generate intense sound waves behind a strong shock. The dependence of the transmission, reflection, and generation coefficients for sound waves on the Mach number and the angle of incidence is depicted in a series of graphs. The results are applied to the amplification of small disturbances in the solar wind on passage through the bow shock of the earth.

ISSN:0031-9171    

DOI:10.1063/1.1691825

出版商:AIP    

年代:1968

数据来源: AIP

摘要:

The structure of an ionizing shock front in a monatomic gas is described. Both atom‐atom and electron‐atom collisional ionization are considered. The ionization rates for either of these processes is assumed to be controlled by the rate of excitation from the ground state to the first excited level. In the front part of the shock, called the atom‐atom shock, atom collisional dissipative mechanisms (viscosity and thermal conductivity) determine the shock structure. A bimodal Mott‐Smith velocity distribution function is assumed for the atoms in this region, which has a thickness of the order of the atom‐atom viscosity mean free path. In the rear part of the shock front, called the relaxation zone, the collisional ionization processes determine the structure. For this region, which has a thickness proportional to the electron‐atom ionization mean free path, Maxwellian velocity distributions are assumed for the electrons, ions, and atoms. It was found that for Mach numbers of 30 or more the atom‐atom shock is of comparable thickness to the relaxation zone and the degree of ionization behind the atom‐atom shock is the order of10−1.

ISSN:0031-9171    

DOI:10.1063/1.1691826

出版商:AIP    

年代:1968

数据来源: AIP

摘要:

The propagation of a detonation wave in a tube containing a single stream of 2600‐&mgr;‐diam diethylcyclohexane droplets dispersed in gaseous oxygen has been studied with streak and space resolved photography, special pressure transducers, and thin‐film heat‐transfer gauges. The detonation wave, which reached a velocity of 4100 ft/sec, consisted of a planar shock front followed by secondary shocks and a gradual decrease in pressure as heat is added. A detailed history of an individual drop within the reaction zone is presented. Under the observed conditions a 2600‐&mgr;‐drop disintegrates continuously over a period of 500 &mgr;sec. Combustion is initiated in the wake of the drops at 65 &mgr;sec after the passage of the shock with the reaction zone considered completed in 670 &mgr;sec. One‐dimensional equations for a two‐phase Chapman‐Jouguet detonation wave with mass and heat addition within the reaction zone, and momentum and heat transfer out of the reaction zone are derived. Comparison of the experiments with the theoretical prediction yields a reasonable agreement.

ISSN:0031-9171    

DOI:10.1063/1.1691827

出版商:AIP    

年代:1968

数据来源: AIP

摘要:

The role of diffusion in the steady conduction process in dielectric fluids is developed. The relation of initial conditions to the mode of conduction is discussed and necessary conditions for the space‐charge‐limited mode are established. A generalized voltage‐current characteristic for the space‐charge‐limited mode and for a diffusion controlled mode is obtained and properties of the charge density, field, body force, and potential profiles calculated. Certain constraints on integration constants are obtained together with their implications for material and process parameters. The constraints enable us to derive an equation for the volume charge density at a surface of the fluid. For the space‐charge‐limited mode, aside from material parameters, this is found to be proportional to the two‐thirds power of the current density and independent of the thickness of the fluid.

ISSN:0031-9171    

DOI:10.1063/1.1691828

出版商:AIP    

年代:1968

数据来源: AIP