摘要:

Four different numerical methods are used to determine the velocity and temperature of a viscous fluid in the boundary layer on a semi‐infinite vertical flat plate whose temperature is suddenly increased from that of the surrounding fluid. All the numerical results show a departure from the unsteady one‐dimensional solution before the theoretically predicted time. Further, the decrease in the mesh size does not seem to show the results to be the tending to a smooth limit; rather that the time of transition from the one‐dimensional unsteady solution to the steady state solution decreases and appears to be tending to zero. This suggests that the mathematical solution of the boundary layer equations may be one in which the solution changes discontinuously from the unsteady one‐dimensional solution to the steady state solution.

ISSN:0031-9171    

DOI:10.1063/1.862129

出版商:AIP    

年代:1978

数据来源: AIP

摘要:

Two anomalous phenomena in dilute polymer solution flows are reviewed: the pressure defect in Pitot tube readings and the pressure increase in orifice flow. Re‐analysis of data available in the open literature shows that anomalous effects occur beyond particular values of the strain rate (onset) and that the magnitude of the effects is proportional to the strain rate in excess of the onset value. This substantiates the hypothesis that dilute polymer solutions can be characterized by a single relaxation time and a single anomalous stress magnitude both concentration dependent, the latter proportional to concentration for dilute solutions.

ISSN:0031-9171    

DOI:10.1063/1.862130

出版商:AIP    

年代:1978

数据来源: AIP

摘要:

A two‐timing perturbation technique is applied in order to investigate the mutual interaction between a Stokes wave train on the water surface and long, low‐frequency, internal waves in a two‐layer model. The set of equations derived conserves energy in the system of surface and internal waves. This conservation is attributable to the coupling terms that appear in both the internal‐wave equations and the surface‐wave equations and that describe the energy transfer between both wave families. In addition to the coupling and nonlinear effects included in the surface‐wave equations (which are part of the interaction equations), a higher order, linear effect, attributable to the slow variations in surface‐wave properties, is also included. Because of the availability of a rigorously ordered description of the interaction processes, it has been possible to assess the relative influence of the nonlinear, finite‐amplitude terms, the coupling terms, and the higher order linear terms in the complete set of governing equations for a given set of conditions.

ISSN:0031-9171    

DOI:10.1063/1.862131

出版商:AIP    

年代:1978

数据来源: AIP

摘要:

The problem of horizontally propagating gravity waves impinging on a vertical shear layer which forms the boundary between uniform currents is isomorphic to an acoustic problem solved by Miles and by Ribner. The consequences of over‐reflection for a spatially growing instability are pointed out. The long wave reflection problem is solved for free surface and internal waves on a thin layer in an otherwise deep fluid. Over‐reflection is found possible for Froude numbers in excess of two; infinite over‐reflection will occur for certain angles of impingement.

ISSN:0031-9171    

DOI:10.1063/1.862132

出版商:AIP    

年代:1978

数据来源: AIP

摘要:

The inflow of a fluid of different density into an ambient fluid of uniform density and finite depth is studied numerically using the full Navier–Stokes and diffusion equations. The problem is posed as an initial‐boundary‐value problem. In both the overflow (lighter buoyant inflow) and underflow (heavier inflow) cases, a gravity current is established with a pronounced headwave. A significant feature of the flows is the presence of strong downwelling (overflow case) and upwelling (underflow case) activity near the front. The overflow case has been applied by Kao, Park, and Pao to the study of small‐scale oceanic fronts formed by the river discharge into the coastal region. The present paper deals with the fluid mechanical and numerical aspects of the overall problem in addition to presenting the results of the underflow case. It is found that the characteristics of the flow in the near field of the inflow are mainly governed by an inflow densimetric Froude number,Fe. In particular, the flow regime in the near field gradually changes from a plume‐like to a jet‐like behavior asFechanges from less than to greater than unity. For the overflow case the local densimetric Froude numberFdof the current is shown to be a constant and a similarity solution is found in the far field behind the headwave giving a universal result for the density and velocity structure in the vertical for the range of parameters explored.

ISSN:0031-9171    

DOI:10.1063/1.862133

出版商:AIP    

年代:1978

数据来源: AIP

摘要:

The classical unified theory of relaxation phenomena in hot fully ionized gases is applied to multicomponent gas mixtures composed of electrons and several types of ions. The theoretical expressions containing exact numerical factors in the arguments of Coulomb logarithms are developed for the bracket integrals needed in the computations of the third approximations to the thermal and the electrical conductivities, and the diffusion coefficients of multicomponent gas mixtures at intermediate and full ionization within the framework of the Chapman–Enskog–Burnett method.

ISSN:0031-9171    

DOI:10.1063/1.862134

出版商:AIP    

年代:1978

数据来源: AIP

摘要:

The self‐similar solution of spherically imploding shock waves is derived analytically for a perfect gas with a constant ratio &ggr; =cp/cv. The basic conservation equations are reduced to a first‐order differential equation in thex‐yplane. The requirement of a maximum for the pressure curve dictates the values of the self‐similar exponent &agr;m. These values are compared with the previously derived numerical values of &agr;m. When &ggr;=2+&sqrt;3, the maximum of the pressure occurs at the shock front. The pressure curve then decreases monotonically.

ISSN:0031-9171    

DOI:10.1063/1.862135

出版商:AIP    

年代:1978

数据来源: AIP

摘要:

The development of transverse magnetohydrodynamic shock waves has been studied in an electromagnetic shock tube for both parallel and antiparallel bias shock waves. Radial magnetic field profiles indicate an essentially flat shock front is formed in both cases. The shock and piston behavior is modeled by a simple snowplow model with a resistive arc across the launching endplate of the shock tube. Mass leakage through the piston is necessary to explain the observed high shock speeds. The method of characteristics is used to compute magnetic field profiles in excellent agreement with those observed experimentally.

ISSN:0031-9171    

DOI:10.1063/1.862136

出版商:AIP    

年代:1978

数据来源: AIP

摘要:

Shock wave analyses and shielding models pertaining to pellet ablation phenomena are reviewed. Some inconsistencies are shown to exist in some of the studies available. Models are developed and estimates are given for pellet ablation rates in hot plasmas with and without magnetic fields present. The possible existence of a self‐regulating ablation mechanism is indicated.

ISSN:0031-9171    

DOI:10.1063/1.862137

出版商:AIP    

年代:1978

数据来源: AIP

摘要:

The one‐dimensional self‐similar motion of an initially cold, half‐space plasma of electron densityn0, produced by the (anomalous) absorption of a laser pulse of irradiation &fgr; =&fgr;0t/&tgr; (0<t⩽&tgr;) at the critical densitync(nc/n0≡&egr;≪1), is considered. The analysis allows for electron heat conduction and ion‐electron energy exchange and retains three dimensionless numbers: &egr;,Zi(ion charge number), and &agr;= (9k/4mi) (&tgr;k2n20/&fgr;0K¯e)2/3, wherek,miare Boltzmann’s constant and the ion mass, and K¯e× (electron temperature)5/2= heat conductivity. If &agr; ≫&egr;−4/3, a deflagration wave separates an isentropic compression with a shock bounding the undisturbed plasma, and an isentropic expansion flow to the vacuum. The structures of these three regions are completely determined; in particular, the Chapman–Jouguet condition is proved and the density behind the deflagration is found. The deflagration‐compression thickness ratio is large (small) for &agr;≪&egr;−5/3(&agr;≫&egr;−5/3). The compression to expansion ratio for both energy and thickness isO(&egr;1/2). ForZilarge, a deflagration exists even if &agr;∼&egr;−4/3. Condition &agr;≫&egr;−4/3may be applied to pulses that are not linear.

ISSN:0031-9171    

DOI:10.1063/1.862138

出版商:AIP    

年代:1978

数据来源: AIP