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The interaction between vortical isotropic turbulence (IT) and a normal shock wave is studied using direct numerical simulation (DNS) and linear interaction analysis (LIA). In previous studies, agreement between the simulation results and the LIA predictions has been limited and, thus, the significance of LIA has been underestimated. In this paper, we present high-resolution simulations which accurately solve all flow scales (including the shock-wave structure) and extensively cover the parameter space (the shock Mach number, $\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}M_s$, ranges from 1.1 to 2.2 and the Taylor Reynolds number, ${\mathit{Re}}_{\lambda }$, ranges from 10 to 45). The results show, for the first time, that the turbulence quantities from DNS converge to the LIA solutions as the turbulent Mach number, $M_t$, becomes small, even at low upstream Reynolds numbers. The classical LIA formulae are extended to compute the complete post-shock flow fields using an IT database. The solutions, consistent with the DNS results, show that the shock wave significantly changes the topology of the turbulent structures, with a symmetrization of the third invariant of the velocity gradient tensor and ($M_s$-mediated) of the probability density function (PDF) of the longitudinal velocity derivatives, and an $M_s$-dependent increase in the correlation between strain and rotation.

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Thirty fresh cadaver hands were injected with a silicone rubber compound (Microfil) and dissected to examine the vascular and neural supplies of the thenar area. In 10 specimens, a selective injection technique was used to determine the extent of skin territory nourished by the superficial palmar branch of the radial artery. The purpose of this study was to clarify the anatomic basis for clinical applications of vascularized free- or island-flap transfers from the thenar area. The superficial palmar branch of the radial artery was found in all hands; the average diameter of the branch measured at its bifurcation site was 1.4 mm (0.8 to 3.0 mm). The constant area nourished by the superficial palmar branch was an area approximately 4 x 3 cm located over the proximal parts of the abductor pollicis brevis and opponens pollicis muscles. These results indicate that a fasciocutaneous flap from the radial thenar region can be raised based on the superficial palmar branch and consistently transferred as a free flap. In 63 percent of the hands dissected, the superficial palmar branch was connected to other arteries in the palm, suggesting that the flap can be transferred as a reverse-pedicle island flap in such hands. Innervation of the flap was provided chiefly by a branch of the superficial radial nerve. The radial aspect of the thenar eminence can provide a new and useful donor source for an innervated and vascularized free- or island-flap transfer for reconstruction of various skin defects of the volar side of the fingers.