Reynolds-number effects in the adverse-pressure-gradient (APG) turbulent boundary layer (TBL) developing on the suction side of a NACA4412 wing section are assessed in the present work. To this end, we analyze four cases at Reynolds numbers based on freestream velocity and chord length ranging from Re c = 100, 000 to 1, 000, 000, all of them with 5 • angle of attack. The results of four well-resolved large-eddy simulations (LESs) are used to characterize the effect of Reynolds number on APG TBLs subjected to approximately the same pressure-gradient distribution (defined by the Clauser pressure-gradient parameter β). Comparisons of the wing profiles with zeropressure-gradient (ZPG) data at matched friction Reynolds numbers reveal that, for approximately the same β distribution, the lower-Reynolds-number boundary layers are more sensitive to pressure-gradient effects. This is reflected in the values of the inner-scaled edge velocity U + e , the shape factor H, the components of the Reynolds-stress tensor in the outer region and the outer-region production of turbulent kinetic energy. This conclusion is supported by the larger wall-normal velocities and outer-scaled fluctuations observed in the lower-Re c cases. Thus, our results suggest that two complementing mechanisms contribute to the development of the outer region in TBLs and the formation of large-scale energetic structures: one mechanism associated with the increase in Reynolds number, and another one connected to the APG. Future extensions of the present work will be aimed at studying the differences in the outer-region energizing mechanisms due to APGs and

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A static and spherically symmetric core-envelope massive distribution has been studied with a core in which there is a parabolic variation of density and the variation of density in the envelope is given by an inverse-square distribution. It is shown that in this model the matching of pressure, energy density and the two metric parameters at the core-envelope boundary can be obtained analytically. Some special features of this core-envelope model have been discussed.

High-fidelity wall-resolved large-eddy simulations (LES) are utilized to investigate the flow-physics of small-amplitude pitch oscillations of an airfoil at Re c = 100, 000. The investigation of the unsteady phenomenon is done in the context of natural laminar flow airfoils, which can display sensitive dependence of the aerodynamic forces on the angle of attack in certain "off-design" conditions. The dynamic range of the pitch oscillations is chosen to be in this sensitive region. Large variations of the transition point on the suction-side of the airfoil are observed throughout the pitch cycle resulting in a dynamically rich flow response. Changes in the stability characteristics of a leading-edge laminar separation bubble has a dominating influence on the boundary layer dynamics and causes an abrupt change in the transition location over the airfoil. The LES procedure is based on a relaxation-term which models the dissipation of the smallest unresolved scales. The validation of the procedure is provided for channel flows and for a stationary wing at Re c = 400, 000.

If the causality condition [the speed of sound always remains less than that of light in vacuum, i. e., v ≤ c = 1] is imposed on the spheres of homogeneous energy density, the 'ratio of the specific heats', γ ≤ 2.59457, constraints the compaction parameter, u[≡ (M/a), mass to size ratio in geometrized units] of the dynamically stable configurations ≤ 0.34056 [corresponding to a surface redshift (za) ≤ 0.771]. Apparently, The maximum value of u obtained in this manner belongs to an absolute upper bound, and gives: (i) The maximum value for static neutron star masses as 5.4M ⊙ , if we substitute the density at the surface of the configuration equal to the average nuclear density, E = 2×10 14 g cm −3 [e.g. Nature, 259, 377 (1976)]. (ii) However, if the density of the static configuration is constrained to the value 1.072 × 10 14 g cm −3 , by imposing the empirical result that the minimum rotation period of the fastest rotating pulsar known to date, PSR 1937 + 21, is 1.558 ms, the maximum mass value for static neutron stars exceed upto 7.4M ⊙ . These masses have important implications for the massive compact objects like Cyg X-1, Cyg XR-1, and LMC-X3 etc., which may not, necessarily, represent black holes. (iii) The minimum rotation periods for a static 1.442M ⊙ neutron star to be 0.3041 ms. (iv) A suitable stable model of ultra-compact objects [u > (1/3)] which has important astrophysical significance.