Lagrangian and Eulerian velocity structure functions in hydrodynamic turbulence

The Lagrangian and Eulerian transversal velocity structure functions of fully developed fluid turbulence are found basing on the Navier-Stokes equation. The structure functions are shown to obey the scaling relations inside the inertial range. The scaling exponents are calculated analytically without using dimensional considerations. The obtained values are in a very good agreement with recent numerical and experimental data.Comment: 4 pages, 1 figur

Anisotropic Shock Sensitivity of Cyclotrimethylene Trinitramine (RDX) from Compress-and-Shear Reactive Dynamics

We applied the compress-and-shear reactive dynamics (CS-RD) simulation model to study the anisotropic shock sensitivity of cyclotrimethylene trinitramine (RDX) crystals. We predict that, for mechanical shocks between 3 and 7 GPa, RDX is most sensitive to shocks perpendicular to the (100) and (210) planes, whereas it is insensitive for shocks perpendicular to the (120), (111), and (110) planes. These results are all consistent with available experimental information, further validating the CS-RD model for distinguishing between sensitive and insensitive shock directions. We find that, for sensitive directions, the shock impact triggers a slip system that leads to large shear stresses arising from steric hindrance, causing increased energy inputs that increase the temperature, leading to dramatically increased chemical reactions. Thus, our simulations demonstrate that the molecular origin of anisotropic shock sensitivity results from steric hindrance toward shearing of adjacent slip planes during shear deformation. Thus, strain energy density, temperature rise, and molecule decomposition are effective measures to distinguish anisotropic sensitivities. We should emphasize that CS-RD has been developed as a tool to distinguish rapidly (within a few picoseconds) between sensitive and insensitive shock directions of energetic materials. If the high stresses and rates used here continued much longer and for larger systems, it would ultimately result in detonation for all directions, but we have not demonstrated this