摘要:

The mechanism of vortex reconnection is investigated by solving the Navier–Stokes equation numerically starting with a closed knotted vortex tube, which gives a nonzero helicity. A new type of vortex reconnection mechanism—bridging—is observed. Small regions of high vorticity bursting out of the vortex tube become larger and bridge different portions of the tube. A relation between the change of the helicity and the mechanism of the vortex reconnection is discussed.

ISSN:0031-9171    

DOI:10.1063/1.866066

出版商:AIP    

年代:1987

数据来源: AIP

摘要:

Direct numerical simulations of turbulent spots in plane Poiseuille and boundary‐layer flows are performed. Mature, self‐similar spots are obtained. The propagation velocities and spreading angles are found to compare well with corresponding experiments. The difference in shape of the two spots is also clearly discernible: the turbulent parts are contained within arrowhead regions that point in opposite directions for the two cases. The wing‐tip region of the Poiseuille spot is also found to consist of a large‐amplitude semiturbulent wave packet.

ISSN:0031-9171    

DOI:10.1063/1.866067

出版商:AIP    

年代:1987

数据来源: AIP

摘要:

A method is presented for obtaining lower bounds on the permeability of a porous medium. It is applied to media composed of periodic and random configurations of spheres and cylinders.

ISSN:0031-9171    

DOI:10.1063/1.866068

出版商:AIP    

年代:1987

数据来源: AIP

摘要:

The attenuation of a compressional sound wave propagating through a fluid bounded by a solid surface of fractal dimension 2≤df<3 is studied. At high sound wave frequency &ohgr;, the attenuation is caused primarily by the viscous dissipation within a boundary layer near the solid surface of thickness &dgr;=(&mgr;/&rgr;&ohgr;)1/2, where &mgr; is the viscosity and &rgr; the density of the fluid. Because the surface area ‘‘seen’’ by the boundary layer increases with decreasing &dgr;, one might expect the attenuation &ggr; to scale in a self‐similar manner with &dgr;, i.e., &ggr;∼&dgr;2‐da, where 2≤da<3. A multiple scales analysis based on a wide separation in the length scales of successively smaller levels of surface structure is used to determine the dependence of the attenuation on the boundary layer thickness. While the possibility of a self‐similar scaling of the attenuation is confirmed, the attenuation exponentdais generally quite different from the fractal dimensiondf. In fact the presence of a fractal surface areadf≠2 is neither a necessary nor sufficient criterion for a self‐similar scaling of the attenuationda≠2.

ISSN:0031-9171    

DOI:10.1063/1.866069

出版商:AIP    

年代:1987

数据来源: AIP

摘要:

The linear stability of certain displacement processes in porous media for two‐dimensional radial flows induced by a point source is examined. Both two‐phase, immiscible displacement and single‐phase miscible displacement in the presence of equilibrium adsorption are discussed. In agreement with Tan and Homsy [Phys. Fluids30, 1239 (1987)], it is found that disturbances grow or decay algebraically in time. Via appropriate transformations the eigenvalue problems are shown to be identical to those in rectilinear flow geometries with suitably modified base states and parameters. Thus several stability features are inferred directly from the analysis in rectilinear geometries. The results indicate the existence of critical values for the capillary (NCa) or Peclet (Pe) number, above which the displacement is unstable for wavenumbers in a band of finite width. For largeNCaor Pe the most dangerous and the highest cutoff modes scale linearly withNCaor Pe. The different scaling found by Tan and Homsy [Phys. Fluids30, 1239 (1987)] follows directly as a singular limit of the miscible displacement problem in the absence of adsorption.

ISSN:0031-9171    

DOI:10.1063/1.866070

出版商:AIP    

年代:1987

数据来源: AIP

摘要:

An experimental study of the flow over a shallow rectangular cavity indicates that, between the states of periodic and fully developed turbulent flow, three different regimes of fluid motion occur as the Reynolds number increases. In the first regime, regime I, the time trace from a pressure transducer, located at the downstream corner of the cavity, varies weakly in amplitude. The frequency spectrum of the trace shows that a single frequency, its’ first harmonic, and a second frequency are selectively amplified. In the second regime, regime II, there is intermittency in the pressure time trace and the two incommensurate frequencies are further apart from each other than in regime I. The primary frequency is the result of a shear‐layer instability but the secondary frequency is believed to depend on a transverse wave on the primary cavity vortex. The exchange of fluid between this vortex and the free stream is enhanced when the two waves are constructively interfering and the exchange is attenuated when the two waves are destructively interfering. If the amplitude of the transverse wave is sufficiently large and the two waves are in phase, fluid from the primary vortex is observed to burst through the shear layer giving rise to a period of apparently random motion. In the third regime, regime III, the pressure oscillations vary strongly with time, and include frequent periods of intense irregular behavior. At times, the pressure cycles have double peaks when the vortices that form in the shear layer are partially clipped by the downstream edge of the cavity. This clipping does not, however, coincide with a decay in the shear‐layer oscillations, as it does in regime II.

ISSN:0031-9171    

DOI:10.1063/1.866071

出版商:AIP    

年代:1987

数据来源: AIP

摘要:

The higher spatial‐stability eigenmodes for the Blasius boundary layer are examined by using asymptotic theory and an infinite number of modes are found. The asymptotic results are shown to be in close agreement with results from a direct numerical solution of the Orr–Sommerfeld problem. The asymptotic theory would therefore provide an efficient tool in exploratory searches for the eigenvalues.

ISSN:0031-9171    

DOI:10.1063/1.866072

出版商:AIP    

年代:1987

数据来源: AIP

摘要:

A formulation of inviscid fluid dynamics based on the densityF(x,v,t) in asingle‐particlephasespace[x=(x1,x2,x3),v=(v1,v2,v3)] is presented. This density evolves in time according to a Poisson bracket ofFwithH(x,v,t)—a Hamiltonian in the same single‐particle phase space. Compressible flows of barotropic fluid and homogeneous, incompressible flows are disscussed. The main advantage of the phase space density formulation over either Euler or Lagrange formulations is the algebraic and conceptual ease in making fully Hamiltonian approximations to the flow by alteringH(x,v,t) and the Poisson brackets appropriately. The example of a shallow layer of rapidly rotating fluid where a Rossby number expansion is desired will be discussed in some detail. Changes of phase space coordinates that give an approximateH(expanded in Rossby number) andexactPoisson brackets will be exhibited. The resulting quasigeostrophic equations forFare two‐dimensional partial differential equations to every order in Rossby number. The extension to multiple layers will be presented.

ISSN:0031-9171    

DOI:10.1063/1.866073

出版商:AIP    

年代:1987

数据来源: AIP

摘要:

The stability of two adjoining vortex layers with constant vorticity of opposite sign is analyzed. Linear stability analysis shows that two families of instability may exist, depending on the relative strength of the vortex layers. The first type for moderate and long waves produces simultaneous growth of disturbances on both layers, while the second for short waves is associated primarily with the weaker layer. Numerical calculations show that the nonlinear growth of the various types of instability leads to asymptotic states of different character. For wake‐like flows with equal but opposite vorticity distributions, the fastest growing eigenmodes lead to the formation of a classic vortex street with an aspect ratio of 0.345. Longer waves lead to the break up of the layer into a number of small vortex regions producing disorganized motion and a general dispersal of the wake vorticity. For compound shear layers with unequal strength, the fastest growing modes show a progression from wake‐like behavior to pure shear‐layer behavior as the strength of the second layer diminishes. In addition, there is a new type of instability associated with short‐wavelength disturbances on the weaker layer. In this case, the shear layer ejects the opposite signed vorticity along with an equal quantity of its own circulation. The ejected vorticity propagates away from the layer at a 45° angle in the form of neutral vortex pairs. The remaining vorticity forms a simpler shear layer of reduced strength.

ISSN:0031-9171    

DOI:10.1063/1.866074

出版商:AIP    

年代:1987

数据来源: AIP

摘要:

The method of multiple scales is used to analyze the nonlinear response of the free surface of a liquid in a cylindrical container to a harmonic vertical oscillation in the presence of a two‐to‐one internal (autoparametric) resonance. Four first‐order ordinary‐differential equations are derived for the modulation of the amplitudes and phases of the two modes involved in the internal resonance with the lower mode is excited by a principal parametric resonance. In the presence of small damping, the long‐time response may be any of (a) a trivial motion, (b) a limit cycle involving both modes, (c) an amplitude‐ and phase‐modulated sinusoid (motion on a two torus), and (d) a chaotically modulated sinusoid.

ISSN:0031-9171    

DOI:10.1063/1.866075

出版商:AIP    

年代:1987

数据来源: AIP