Proc Natl Acad Sci U S A
December 2012
The mathematical modeling of the flow in nanoporous rocks (e.g., shales) becomes an important new branch of subterranean fluid mechanics.
View Article and Find Full Text PDFIt is shown, using the Zeldovich integral relations, that the energy of Tycho's Supernova Remnant is strongly growing with time, approximately as t(1/3). This growth can be attributed to the exothermic reactions going inside the remnant. The use of the assumption of the adiabaticity of the motion inside of the shock front, and no losses or gain of energy at the front, seems therefore unjustified.
View Article and Find Full Text PDFProc Natl Acad Sci U S A
April 2002
According to a model of the turbulent boundary layer that we propose, in the absence of external turbulence the intermediate region between the viscous sublayer and the external flow consists of two sharply separated self-similar structures. The velocity distribution in these structures is described by two different scaling laws. The mean velocity u in the region adjacent to the viscous sublayer is described by the previously obtained Reynolds-number-dependent scaling law Φ = u / u(*) = Aη(α), A = 1/√3 In ReΛ + 5/2, α = 3/2 in ReΛ η = u(*)y/v.
View Article and Find Full Text PDFProc Natl Acad Sci U S A
August 2005
The basic element of Lighthill's "sandwich model" of tropical cyclones is the existence of "ocean spray," a layer intermediate between air and sea made up of a cloud of droplets that can be viewed as a "third fluid." We propose a mathematical model of the flow in the ocean spray based on a semiempirical turbulence theory and demonstrate that the availability of the ocean spray over the waves in the ocean can explain the tremendous acceleration of the wind as a consequence of the reduction of the turbulence intensity by droplets. This explanation complements the thermodynamic arguments proposed by Lighthill.
View Article and Find Full Text PDFProc Natl Acad Sci U S A
June 2005
We demonstrate using the high-quality experimental data that turbulent wall jet flows consist of two self-similar layers: a top layer and a wall layer, separated by a mixing layer where the velocity is close to maximum. The top and wall layers are significantly different from each other, and both exhibit incomplete similarity, i.e.
View Article and Find Full Text PDFWe present a simple physical model of turbulent wall-bounded shear flows that reveals exactly the scaling properties we had previously obtained by similarity considerations. The significance of our results for the understanding of turbulence is pointed out.
View Article and Find Full Text PDFProc Natl Acad Sci U S A
February 2003
We formulate the mass transfer problem for a passive additive in a turbulent boundary layer based on the recently proposed model of the turbulent boundary layer at very large Reynolds numbers. The solutions of three basic problems are obtained. These solutions are self-similar asymptotics describing the mass exchange at its initial stages.
View Article and Find Full Text PDFProc Natl Acad Sci U S A
November 2001
In the boundary layers around the edges of images, basic nonlinear parabolic equations for image intensity used in image processing assume a special degenerate asymptotic form. An asymptotic self-similar solution to this degenerate equation is obtained in an explicit form. The solution reveals a substantially nonlinear effect-the formation of sharp steps at the edges of the images, leading to edge enhancement.
View Article and Find Full Text PDFProc Natl Acad Sci U S A
November 1997
The classical problem of thermal explosion is modified so that the chemically active gas is not at rest but is flowing in a long cylindrical pipe. Up to a certain section the heat-conducting walls of the pipe are held at low temperature so that the reaction rate is small and there is no heat release; at that section the ambient temperature is increased and an exothermic reaction begins. The question is whether a slow reaction regime will be established or a thermal explosion will occur.
View Article and Find Full Text PDFProc Natl Acad Sci U S A
September 1997
A new mathematical model is proposed for the spreading of a liquid film on a solid surface. The model is based on the standard lubrication approximation for gently sloping films (with the no-slip condition for the fluid at the solid surface) in the major part of the film where it is not too thin. In the remaining and relatively small regions near the contact lines it is assumed that the so-called autonomy principle holds-i.
View Article and Find Full Text PDFProc Natl Acad Sci U S A
August 2000
The equation partial differential(t)u = u partial differential(xx)(2)u -(c-1)( partial differential(x)u)(2) is known in literature as a qualitative mathematical model of some biological phenomena. Here this equation is derived as a model of the groundwater flow in a water-absorbing fissurized porous rock; therefore, we refer to this equation as a filtration-absorption equation. A family of self-similar solutions to this equation is constructed.
View Article and Find Full Text PDFProc Natl Acad Sci U S A
April 2000
In a turbulent boundary layer over a smooth flat plate with zero pressure gradient, the intermediate structure between the viscous sublayer and the free stream consists of two layers: one adjacent to the viscous sublayer and one adjacent to the free stream. When the level of turbulence in the free stream is low, the boundary between the two layers is sharp, and both have a self-similar structure described by Reynolds-number-dependent scaling (power) laws. This structure introduces two length scales: one-the wall-region thickness-determined by the sharp boundary between the two intermediate layers and the second determined by the condition that the velocity distribution in the first intermediate layer be the one common to all wall-bounded flows and in particular coincide with the scaling law previously determined for pipe flows.
View Article and Find Full Text PDFProc Natl Acad Sci U S A
February 2000
An asymptotic solution is obtained corresponding to a very intense pulse: a sudden strong increase and fast subsequent decrease of the water level at the boundary of semi-infinite fissurized-porous stratum. This flow is of practical interest: it gives a model of a groundwater flow after a high water period or after a failure of a dam around a collector of liquid waste. It is demonstrated that the fissures have a dramatic influence on the groundwater flow, increasing the penetration depth and speed of fluid penetration into the stratum.
View Article and Find Full Text PDFThe classical problem of the thermal explosion in a long cylindrical vessel is modified so that only a fraction alpha of its wall is ideally thermally conducting while the remaining fraction 1-alpha is thermally isolated. Partial isolation of the wall naturally reduces the critical radius of the vessel. Most interesting is the case when the structure of the boundary is a periodic one, so that the alternating conductive alpha and isolated 1-alpha parts of the boundary occupy together the segments 2pi/N (N is the number of segments) of the boundary.
View Article and Find Full Text PDFProc Natl Acad Sci U S A
July 1997
A processing of recent experimental data by Nagib and Hites [Nagib, H. & Hites, M. (1995) AIAA paper 95-0786, Reno, NV) shows that the flow in a zero-pressure-gradient turbulent boundary layer, outside the viscous sublayer, consists of two self-similar regions, each described by a scaling law.
View Article and Find Full Text PDFProc Natl Acad Sci U S A
February 1997
We compare mean velocity profiles measured in turbulent pipe flows (and also in boundary layer flows) with the predictions of a recently proposed scaling law; in particular, we examine the results of the Princeton "super-pipe" experiment and assess their range of validity.
View Article and Find Full Text PDFThe small viscosity asymptotics of the inertial range of local structure and of the wall region in wallbounded turbulent shear flow are compared. The comparison leads to a sharpening of the dichotomy between Reynolds number dependent scaling (power-type) laws and the universal Reynolds number independent logarithmic law in wall turbulence. It further leads to a quantitative prediction of an essential difference between them, which is confirmed by the results of a recent experimental investigation.
View Article and Find Full Text PDFA similarity principle is formulated according to which the statistical pattern of the pelagic population is identical in all scales sufficiently large in comparison with the molecular one. From this principle, a power law is obtained analytically for the pelagic animal biomass distribution over the animal sizes. A hypothesis is presented according to which, under fixed external conditions, the oxygen exchange intensity of an animal is governed only by its mass and density and by the specific absorbing capacity of the animal's respiratory organ.
View Article and Find Full Text PDFA two-dimensional model of the expansion of a crack in an elastic medium is considered in which friction depends on the slip rate and the modulus of cohesion depends on the speed of expansion of the crack. Elastic waves are neglected (quasi-static model). Under some conditions, the expansion of the crack is realized by the alternation of slow and fast episodes ("shocks") of slip.
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