摘要:

Numerical solutions are presented for finite‐amplitude interfacial waves. Only symmetric waves are calculated. Two cases are considered. In the first case the waves are free‐surface solitary waves propagating on a basic flow with uniform vorticity. Large‐amplitude waves of extreme form are calculated for a range of values of the basic vorticity. In the second case the waves are propagating on the interface between two homogeneous fluids of different densities, which are otherwise at rest. Again large‐amplitude waves of extreme form are calculated for a range of values of the basic density ratio. In particular, in the Boussinesq limit when the density ratio is nearly unity, solitary waves of apparently unlimited amplitude can be found.

ISSN:0031-9171    

DOI:10.1063/1.866922

出版商:AIP    

年代:1988

数据来源: AIP

摘要:

When a liquid drop impacts on a pool, the drop will either coalesce into the host liquid, with the creation of a vortex ring below the surface and little splashing above, or will splash, producing a cavity in the host liquid that collapses inward, producing an upward jet of fluid. It is found that there is a critical Weber number, Wec=U(&rgr;D/T)1/2&bartil;8, below which vortex rings are formed and above which a jet is produced for drops falling into the identical fluid. Here,Uis the drop speed at impact,Dis the drop diameter, and &rgr; andTare density and surface tension, respectively. The Weber number criterion is compared with experiments using water and mercury.

ISSN:0031-9171    

DOI:10.1063/1.866872

出版商:AIP    

年代:1988

数据来源: AIP

摘要:

The first Landau constant of a free shear layer with parallel velocity profileU=tanh yis calculated numerically according to the amplitude expansion formulation proposed by Herbert [J. Fluid Mech.126, 167 (1983)]. The numerical results strongly support Gotoh’s asymptotic expression [J. Phys. Soc. Jpn.24, 1137 (1968)] of the first Landau constant &lgr;1for large Reynolds numberRwhen the amplification factorciis smaller thanR−1/3: &lgr;1=−8.177R1/3(1+0.25Rci). It is also concluded that the third‐order nonlinear term in the Landau equation acts as the stabilizing effect throughout the parameter range where the numerical calculation was performed.

ISSN:0031-9171    

DOI:10.1063/1.866873

出版商:AIP    

年代:1988

数据来源: AIP

摘要:

The one‐dimensional stability of detonation waves characterized by one‐step irreversible Arrhenius kinetics is examined. The description of the steady structure in the limit of infinite activation energy is well known, and an examination is made of the linear unsteady perturbation equations in the same limit. The spectrum contains both a single real positive eigenvalue that vanishes in the limit and an infinite number of nonvanishing eigenvalues that define a growth rate which is an increasing function of frequency. Plausible qualitative extrapolation to finite activation energies provides an explanation of experimental results obtained by Alpert and Toong [Astronaut. Acta17, 539 (1972)].

ISSN:0031-9171    

DOI:10.1063/1.866874

出版商:AIP    

年代:1988

数据来源: AIP

摘要:

The nonlinear spectral dynamics of a transitioning flow in the wake of a flat plate is experimentally studied at different downstream positions with a two‐point method. The measurement setup consists of two sensors, which are separated in the downstream direction. The quadratically nonlinear transfer function between the two points is then estimated from the digitized fluctuation data. Such transfer functions permit one to quantify the quadratically nonlinear spectral dynamics occurring between the two sensor points. The method used to estimate the transfer functions and local bicoherency for non‐Gaussian input and output signals, by means of digital spectral analysis techniques, is briefly discussed. The measured quadratic transfer function of the experimental data changes gradually with downstream distance, but its main features are unchanged. The observed appearance of progressively higher harmonics of the fundamental mode and the filling in of the spectral valleys over short downstream distances are, thus, mainly caused by spectral redistribution of energy that is available in the interacting modes and not caused by abrupt changes in the coupling properties. This result is supported by the local bicoherency measurements.

ISSN:0031-9171    

DOI:10.1063/1.866875

出版商:AIP    

年代:1988

数据来源: AIP

摘要:

A second‐order, single‐point closure model for calculating the transport of momentum and passive scalar quantities in turbulent flows is described. Of the unknown terms that appear in the Reynolds stress and scalar flux balance equations, it is those which involve the fluctuating pressure that exert a dominant influence in the majority of turbulent flows. A closure approximation (linear in the Reynolds stress) has been formulated for the velocity‐pressure gradient correlation appearing in the Reynolds stress equation. When this is used in conjunction with previous proposals for the other unknown terms in the stress equation, the proposed model closely simulates most of the data on high Reynolds number homogeneous turbulent flows. For the fluctuating scalar‐pressure gradient correlation appearing in the scalar flux equation, an approximation has been devised that satisfies the linear transformation properties of the exact equation. Additional characteristics of the fluctuating scalar field are obtained from the solution of modeled balance equations for the scalar variance and its ‘‘dissipation’’ rate. The resulting complete scalar field model is capable of reproducing measured data in decaying scalar grid turbulence and strongly sheared, nearly homogeneous flow in the presence of a mean scalar gradient. In addition, applications to the thermal mixing layer developing downstream from a partially heated grid and to a slightly heated plane jet issuing into stagnant surrounds result in calculated profiles in close agreement with those measured.

ISSN:0031-9171    

DOI:10.1063/1.866876

出版商:AIP    

年代:1988

数据来源: AIP

摘要:

Results from a flow visualization study of Dean vortex flow are presented. These were obtained over a range of Dean numbers from 40 to 220 using a transparent channel with mild curvature, an aspect ratio of 40 to 1, and an inner to outer radius ratio of 0.979. Observations and photographs show evidence of pairs of counter‐rotating Dean vortices indicated by mushroom‐shaped smoke patterns for Dean numbers greater than 64 and angular positions at least 85° from the start of curvature. Photographs showing nonsymmetric Dean vortices with rocking motion are presented and believed to be evidence of a twisting mode of oscillations. Dean vortices with oscillations mostly in the radial direction are also observed, which are believed to strongly depend on the small amplitude disturbances that trigger initial vortex development. Photographic evidence of small secondary vortex pairs, and vortices with simultaneous radial and spanwise oscillations are also given along with a domain map showing the experimental conditions for different types of vortex behavior.

ISSN:0031-9171    

DOI:10.1063/1.866877

出版商:AIP    

年代:1988

数据来源: AIP

摘要:

A theoretical study is made of thermophoresis of a solid sphere in a rarefied gas in which a uniform temperature gradient and a uniform velocity at infinity exist. The analysis is carried out on the basis of the linearized Bhatnager–Gross–Krook (BGK) equation, from which simultaneous integral equations for the density, flow velocity, and temperature are derived. These equations are solved numerically over a wide range of Knudsen numbers covering the area from the slip flow to the nearly free molecular flow. A formula for the variation of the thermophoretic force acting on the sphere versus the Knudsen number is obtained for any value of thermal conductivity of the sphere when there is no imposed flow at infinity. The thermophoretic velocity of a suspended sphere in a gas is also calculated. The flow patterns as well as the distributions of temperature are shown.

ISSN:0031-9171    

DOI:10.1063/1.866878

出版商:AIP    

年代:1988

数据来源: AIP

摘要:

A general theory is developed for obtaining the tangential and normal derivatives of thermodynamic and kinematic properties just downstream of a curved, unsteady shock wave. The flow upstream of the shock need not be steady or uniform and the gas need not be thermally or calorically perfect. Because of the complexity of the results, explicit formulas are provided for the above derivatives when the flow is steady and two‐dimensional or axisymmetric, and the gas is perfect.

ISSN:0031-9171    

DOI:10.1063/1.866879

出版商:AIP    

年代:1988

数据来源: AIP

摘要:

The dynamics of a compressible magnetofluid plasma with a polytropic equation of state are considered in the limit of low plasma frame acoustic Mach number. The relationship between the equations describing the low Mach number flow and the equations of idealized incompressible magnetohydrodynamics is investigated using a multiple time scale asymptotic expansion procedure, which is justified by appealing to several rigorous theorems concerning both hydrodynamics and magnetohydrodynamics. When appropriate assumptions are adopted concerning the degree of departure from incompressibility, the lowest‐order behavior is that of incompressible magnetohydrodynamics, associated with order Mach number‐squared ‘‘pseudosound’’ density fluctuations. The first corrections to incompressible flow take the form of magnetoacoustic fluctuations, with associated pressure fluctuations at the same order as the pseudosound pressure. Resumming the asymptotic series gives rise to a simple set of equations that describes ‘‘nearly incompressible magnetohydrodynamics.’’ The theory provides a justification for the turbulent density spectrum theory of Montgomery, Brown, and Matthaeus [J. Geophys. Res.92, 282 (1987)] and clarifies several issues pertaining to Alfve´n wave turbulence in the solar wind. The nearly incompressible description may also be useful in other theoretical contexts, particularly in extensions of incompressible magnetohydrodynamic turbulence theory, since it is expected to be valid for finite times (until possible shock structures form) when the global Mach number is sufficiently small.

ISSN:0031-9171    

DOI:10.1063/1.866880

出版商:AIP    

年代:1988

数据来源: AIP