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A direct numerical simulation of shock wave and turbulent boundary layer interaction for a 24 deg compression ramp configuration at Mach 2.9 and Re 2300 is performed. A modified weighted, essentially nonoscillatory scheme is used. The direct numerical simulation results are compared with the experiments of Bookey et al. [Bookey, P. B., Wyckham, C., Smits, A. J., and Martin, M. P., "New Experimental Data of STBLI at DNS/LES Accessible Reynolds Numbers," AIAA Paper No. 2005-309, Jan. 2005 at the same flow conditions. The upstream boundary layer, the mean wall-pressure distribution, the size of the separation bubble, and the velocity profile downstream of the interaction are predicted within the experimental uncertainty. The change of the mean and fluctuating properties throughout the interaction region is studied. The low frequency motion of the shock is inferred from the wallpressure signal and freestream mass-flux measurement. Nomenclature a = speed of sound C f = skin friction coefficient C r k = optimal weight for stencil k f = frequency f s = frequency of shock motion IS k = smoothness measurement of stencil k L sep = separation length M = freestream Mach number p = pressure q k = numerical flux of candidate stencil k Re = Reynolds number based on Re = Reynolds number based on r = number of candidate stencils in WENO S L = dimensionless frequency of shock motion T = temperature u = velocity in the streamwise direction v = velocity in the spanwise direction w = velocity in the wall-normal direction x = coordinate in the streamwise direction y = coordinate in the spanwise direction z = coordinate in the wall-normal direction = 99% thickness of the incoming boundary layer = displacement thickness of the incoming boundary layer = momentum thickness of the incoming boundary layer = density ! k = weight of candidate stencil k Subscripts w = value at the wall 1 = freestream value Superscript = nondimensional value

We consider some of the fundamental statistical mechanics of the electrodifFusion of a long polyelectrolyte, DNA, in a microlithographically constructed 2D rectangular array of cylindrical posts. The DNA polymer is shown to be free draining when not hooked on a post, and the mean time to unhook is explicitly calculated and compared to our measurements.Perhaps the most important application of electrodifFusion of polyelectrolytes in confining environments is the length-dependent fractionation of DNA via gel electrophoresis. This paper will demonstrate that electrophoresis of DNA within microlithographically constructed synthetic lattices can be understood qualitatively and described quantitatively owing to the precisely characterized environment.A polymer can be characterized by its persistence length P, contour length L, and diameter d. In the case of DNA under normal physiological buffer conditions, d is 2.4 nm and P = 0.060 pm [1]. We are concerned here with "long" polymers, where L/p = N » 1. The velocity of the polymer center of mass v, is on the order of pm/sec in water (viscosity rl = 1 x 10 s Pasec at 20'C). Since the Reynolds number 'R = pv, L/r/(p is the mass density of the solvent) is exceedingly small, 10 is [2], the viscous drag forces are much larger than any inertial terms and the velocity of the center of mass is determined by AEL = (v, Here ( is the friction coefficient of the polymer, A is the effective charge/length of the polymer, and E is the applied electric field. A rod of length L at very low R has (~r /L In(~) due to hydrodynamic coupling between rod segments [3]. However, in the case of electrophoresis of polyelectrolytes such as DNA there is a compensating flow of ions on the surface which screens the hydrodynamic coupling on scales longer than the Debye length [4], making ( for the fr"" draining Gaussian coil to a good approximation~3m rlL.The electrophoretic mobility p (p = "z . ) of the polymer free in solution is then independent of L and no lengthdependent electrophoretic fractionation occurs.To circumvent this problem, gels have traditionally been used to separate DNA, for a polyelectrolyte moving in a restricting environment can have a length-dependent electrophoretic mobility p(L). Three separate mechanisms have been identified by which gels fractionate polymers depending on the ratio 8 = Rs/a, the ratio of the radius of gyration Rz of the polymer to the characteristic pore size a of the gel. In three dimensions and when N -L/P »1 R, -P(N)i/2 When 8 ( 1, polymers are fractionated by a sieving process. The mobility is usually described by the Ogston model [5,6]. When 8 & 1, fractionation takes place by the process of reptation if the electric field is weak [7 -9]. A weak field is one in which the dimensionless electric field strength E' (( 1 [10]. If a » p then E' = &&& where kT is the thermal energy. The electrophoretic mobility p, of the polymer in the reptative regime is z& [~+ E'] [11,12]. Note that since ( scales with L, Is becomes independent of the length I of the polymer f...

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Direct numerical simulation data of a Mach 2.9, 24○ compression ramp configuration are used to analyse the shock motion. The motion can be observed from the animated DNS data available with the online version of the paper and from wall-pressure and mass-flux signals measured in the free stream. The characteristic low frequency is in the range of (0.007–0.013) U∞/δ, as found previously. The shock motion also exhibits high-frequency, of O(U∞/δ), small-amplitude spanwise wrinkling, which is mainly caused by the spanwise non-uniformity of turbulent structures in the incoming boundary layer. In studying the low-frequency streamwise oscillation, conditional statistics show that there is no significant difference in the properties of the incoming boundary layer when the shock location is upstream or downstream. The spanwise-mean separation point also undergoes a low-frequency motion and is found to be highly correlated with the shock motion. A small correlation is found between the low-momentum structures in the incoming boundary layer and the separation point. Correlations among the spanwise-mean separation point, reattachment point and the shock location indicate that the low-frequency shock unsteadiness is influenced by the downstream flow. Movies are available with the online version of the paper.