The first merger wave is documented to have occurred after the depression of 1883, between the years of 1897 and 1907. Whether the shock leads to a wave of mergers, however, depends on whether there is sufficient overall capital liquidity. Global shock wavesfor the supersonic flow past a perturbed. Supersonic flow and shock waves, a manual on the mathematical theory of nonlinear wave motion by courant, richard. The qtheory, as applied to merger waves, claims that this pattern is due to an underlying technological shock that impacts the entire economy causing stock prices and therefore qs to rise, and makes mergers more profitable thereby generating a merger wave. Such behavior arises due to nonlinear dependence of the interphase friction upon the phase composi tion. If the supersonic incoming flow is symmetric near the divergent or convergent part of the nozzle, then, as indicated in section 147 of r. Mcconnell national aeronautics and space administration summary this report shows when and where a shock wave forms in a twodimensional flow field and presents a method for predicting the shape and strength of the shock wave. What is the difference between a shock wave, a compression.
Development of waves series of compression and expansion waves propagating in fluid. The experimental studies were conducted in the 48inch shock tunnel at calspan at a freestream mach number of close to 6. Nasa, public domain v 2 t v 1 t v 1 n v 2 n v 2 v 1. The shock wave boundarylayer interaction swbli occurs in supersonic and hypersonic practical flows such as scramjet inlets, reentry vehicles, nozzles and launch vehicles, and it would result in boundarylayer thickening and can trigger separation and highwall heat flux in the internal and external flow fields, especially in the flowpath of the airbreathing hypersonic. The intersection of the two oblique shock waves on figure 7. Supersonic flow and shock waves applied mathematical sciences v. Oblique shock formation in the discharge from an overexpanded nozzle. Supersonic flow turning for normal shocks, flow is perpendicular to shock no change in flow direction how does supersonic flow change direction, i. Supersonic flow and shock waves, a manual on the mathematical.
The undisturbed boundary layer is characterized by the law of the wall and the law of the wake for compressible flow. Shock dynamics of strong imploding cylindrical and spherical shock waves with nonideal gas effects r k anand wave motion 20. The interaction of shock waves with fluid interfaces sciencedirect. On the theory of hypersonic gas flow with a powerlaw shock. It was also found possible, by a more lengthy derivation, to remove the restriction to weak shock waves. The maximum amplification of the toroidal sw near its symmetry axis is estimated. Knowledge of the point of formation, the strength, and the shape of shock waves are im. Computational analysis of high speed flow over a conical surface. It treats the dynamics of compressible fluids in mathematical form, and attempts to present a systematic theory of nonlinear wave propagation, particularly in relation to.
We shall combine these constraints now and set up a. Experimental study of the shock wave due to a blunt leading edge in the hypersonic merged flow regime by roger m. In the limiting case considered, for high transonic speeds, the sonic line is very close to the wall. What is the difference between a shock wave, a compression wave, and an expansion wave, and when are they produced. Essay shock waves ekta jap 2003 indian institute of science bangalore 560012 india december, 2003 email. Enhanced resolution for the computation of the interaction of shock waves with fluid interfaces is. The analogy between hydraulic jumps in liquids and shock. Winebarger langley research center summary an experimental investigation of lowdensity flow over twodimensional blunt bodies has been conducted in the langley 1foot 0. An introduction to theoretical fluid dynamics nyu courant. Courant institute of mathematical sciences, new york university. Supersonic flow and shock waves richard courant, k.
Precursors and lateral shocks associated with the phenomenon of irregular refraction were identified. Dynamics of shock waves caused by pulsed highcurrent. Pure and applied mathematics, a series of texts and monographs, vol 1. In the case of multiphase filtration the consequence of this equation is the formation of selfsteepening kinematic shock waves 2. Going in the other direction as m 1 decreases, the wave angle increases, and the shock becomes weaker. On the basis of an investigation of the portions of the flow with high entropy adjoining the surface of the body not necessarily for a shock wave of the given form it is shown that the use in the flow problem of the exact solution for the corresponding unsteady self. Buy supersonic flow and shock waves applied mathematical sciences v. Culickt california institute of technology, pasadena, california a finite difference scheme with a shock fitting algorithm has been used to investigate unsteady inviscid now. Shock dynamics of strong imploding cylindrical and. Shock dynamics of strong imploding cylindrical and spherical shock waves with nonideal gas effects r k. Shock wave a thin transition region that propagates at supersonic speed and in which the density, pressure, and speed of the substance involved increase drastically. Supersonic flow and shock waves richard courant springer. If you wish to combine ideas of compressible fluid mechanics and aerodynamics by association and applied mathematics partial.
The interaction of shock waves with gas clouds is a complex and important problem in astrophysical gasdynamics. Existence of supersonic traveling waves for the frenkelkontorova model issa, s. Plane and axisymmetric hypersonic gas flows are considered with shock waves of very great intensity that have a powerlaw form. For a curved shock, if the radius of curvature is much larger than the shock thickness, the flow relations may. Courant s writings include introduction to calculus and analysis 1965, written with john fritz, differential and integral calculus 1965, methods of mathematical physics. Shock waves it is appropriate to begin this section on normal shock waves by revisiting the piston thought experiment begun in section bod in order to construct the events that result from a larger magnitude wave. Normal shock waves a body moving in compressible fluid. When an airplane travels less than the speed of sound, the air ahead of it actually begins to flow out of the way before the plane reaches it. Dirichlets principle, conformal mapping and minimal surfaces 1950, and supersonic flow and shock waves 1948. On the theory of hypersonic gas flow with a powerlaw. Culickt california institute of technology, pasadena, california a finite difference scheme with a shockfitting algorithm has been used to investigate unsteady inviscid now. Instability of one global transonic shock wave for the steady supersonic euler flow past a sharp cone xu, gang and yin, huicheng, nagoya mathematical journal, 2010. Courant and friedrichs classical treatise was first published in 1948 and tthe basic research for it took place during world war ii.
Because the technological shock is supposed to affect the entire economy, it should make. Courant and freidrichs, supersonic flow and shock waves, interscience. It is shown that such an sw is significantly amplified near the torus symmetry axis. We note the following features of the oblique shock solution. Antony jameson courant institute of mathematical sciences new york university summary some recent developments in numerical methods for calcuting solutions to the transonic potential. Supersonic flow and shock waves richard courant, k o. Formation and propagation of a shock wave from a concave boundary by dudley g. To do so it is useful to construct a spacetime diagram an xt diagram for the series of events that result from. Experimental studies of shockwavewalljet interaction in. But as an airplane reaches the speed of sound and catches up to its own pressure waves, the air ahead of it receives no warning of the planes approach. The flow relations across a straight shock which is oblique to the flow may be obtained by superimposing on the normal velocity an additional velocity tangential to the shock which remains unchanged across the shock. The fundamentals of strategic logic and integration for.
For attached shocks with a fixed deflection angle, as the upstream mach number m 1 increases, the wave angle. Thus, an arbitrarily strong shock wave cannot compress a gas by a factor greater than. Shock waves are common in interstellar medium, where they are produced by energetic events, such as stellar winds, supernovae, bipolar flows. Dynamics of convergence and reflection of the toroidal ringshaped shock wave sw in the torus plane and in the plane passing through its symmetry axis is experimentally studied. These oblique shock waves provide the mechanism by which the pressure increases to that downstream of this adjustment process. The airplane plows through the air, creating a shock wave. However, many aspects make the book just as interesting as a text and a reference today. Travlos june 2011 we examine the characteristics of the sixth merger wave that started in 2003 and came to an end approximately in late2007. Shock waves result from, for example, explosions, the motion of bodies at supersonic speeds seesupersonic flow, and intense electrical discharges. Experimental studies have been conducted to examine slot film cooling effectiveness and the interaction between the cooling film and an incident planar shock wave in turbulent hypersonic flow. The pressure waves created by the airplane passing through the air end up being smooth and gradual.
Analysis of unsteady inviscid diffuser flow with a shock wave. Interaction of weak shock waves with cylindrical and. External flow diamond airfoil at zero angle of attack. The basic research for it took place during world war ii, but there are many aspects which still make the book interesting as a text and as a reference. Challenges of the current merger wave atr department. Lee, selfsustained shock oscillations on airfoils at transonic speeds, prog. Numerical computation of transonic flows with shock waves. Shock fronts are an inevitable feature of supersonic flows. Interaction between a normal shock wave and a turbulent.
This rather old book originates from a 1944 report deals with the mathematical intricacies stemming from the mathematical description of compressible flows. Shock waveturbulence boundary layer interaction control. Courant institute of mathematical sciences, new york university collection newyorkuniversity. If you wish to combine ideas of compressible fluid mechanics and. Supersonic flow and shock waves applied mathematical sciences. A brief history of the five merger waves cleverism. The drivers of this wave lie primarily in the availability of abundant liquidity, in line with neoclassical explanations of merger waves. Shock wave article about shock wave by the free dictionary. This macrolevel liquidity component causes industry merger waves to cluster in time even if industry shocks do not. The parameters of a gas in a shock wave may be represented as a function of the mach number m v wave a 0 in the limit, as m. Complex pattern of shock waves formed around a model aircraft in a wind tunnel with.
Supersonic flow and shock waves, a manual on the mathematical theory of. Mergers and merger waves and the factors that give rise to them have been the subject of intense interest for more than a century. Development of compression waves across a compression wave, the flow decelerates and the. Supersonic flow and shock waves applied mathematical. A shock wave compresses air at supersonic speeds the object travels faster than the pressure information, and when the object arrives at a bit of air it compresses suddenly in a shock wave, with corresponding higher temperature. This study finds that economic, regulatory and technological shocks drive industry merger waves. In a related problem, markstein 1957a, b and rudinger 1958 studied the interaction of shock waves with curved flame fronts, and so considered the curved slowfast case. The fundamentals of strategic logic and integration for merger and acquisition projects 10 master thesis marco zappa dmtec, ethz succeed and to discover universally valid performanceenhancing key success factors that do not depend on the specific. For case shown above flow returning to original angle. Shock dynamics of strong imploding cylindrical and spherical. Shock dynamics of strong imploding cylindrical and spherical shock waves with nonideal gas effects r k anand. In physics, a shock wave also spelled shockwave, or shock, is a type of propagating disturbance that moves faster than the local speed of sound in the medium. Instability of one global transonic shock wave for the steady supersonic euler flow past a sharp cone xu, gang and yin, huicheng, nagoya mathematical journal, 2010 existence of supersonic traveling waves for the frenkelkontorova model issa, s.
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