We present direct numerical simulation (DNS) of a stationary turbulent hydraulic jump with inflow Froude number of 2, Weber number of 1820 and density ratio of 831, consistent with ambient water–air systems, all based on the inlet height and inlet velocity. A non-dissipative geometric volume of fluid (VOF) method is used to track the detailed interactions between turbulent flow structures and the nonlinear interface dynamics. Level set equations are also solved concurrent with VOF in order to calculate the interface curvature and surface tension forces. The mesh resolution is set to resolve a wide range of interfacial scales including the Hinze scale. Calculations are compared against experimental data of void fraction and interfacial scales indicating, reasonable agreement despite a Reynolds number mismatch. Multiple calculations are performed confirming weak sensitivity of low-order statistics and void fraction on the Reynolds number. The presented results provide, for the first time, a comprehensive quantitative data for a wide range of phenomena in a turbulent breaking wave using DNS. These include mean velocity fields, Reynolds stresses, turbulence production and dissipation, velocity spectra and air entrainment data. In addition, we present the energy budget as a function of streamwise location by keeping track of various energy exchange processes in the wake of the jump. The kinetic energy is mostly transferred to pressure work, potential energy and dissipation while surface energy plays a less significant role. Our results indicate that the rate associated with various energy exchange processes peak at different streamwise locations, with exchange to pressure work flux peaking first, followed by potential energy flux and then dissipation. The energy exchange process spans a streamwise length of order ${\sim}10$ jump heights. Furthermore, we report statistics associated with bubble transport downstream of the jump. The bubble formation is found to have a periodic nature. Meaning that the bubbles are generated in patches with a specific frequency associated with the roll-up frequency of the roller at the toe of the jump, with its footprint apparent in the velocity energy spectrum. Our study also provides the ensemble-averaged statistics of the flow which we present in this paper. These results are useful for the development and validation of reduced-order models such as dissipation models in wave dynamics simulations, Reynolds-averaged Navier–Stokes models and air entrainment models.

Variable density flows are ubiquitous in a variety of natural and industrial systems. Multi-phase flows in natural and industrial processes, astrophysical flows, and flows involved in combustion processes are such examples. For an ideal gas subject to low-Mach approximation, variations in temperature can lead to a non-uniform density field. In this work, we consider radiatively heated particle-laden turbulent flows. We have developed a parallel C++/MPI-based simulation code for variable-density particle-laden turbulent flows (which can be downloaded from https://

This study addresses the optical performance of a plasma adaptive lens for aero-optical applications by using both axisymmetric and three-dimensional numerical simulations. Plasma adaptive lenses are based on the effects of free electrons on the phase velocity of incident light, which, in theory, can be used as a phase-conjugation mechanism. A closed cylindrical chamber filled with Argon plasma is used as a model lens into which a beam of light is launched. The plasma is sustained by applying a radio-frequency electric current through a coil that envelops the chamber. Four different operating conditions, ranging from low to high powers and induction frequencies, are employed in the simulations. The numerical simulations reveal complex hydrodynamic phenomena related to buoyant and electromagnetic laminar transport, which generate, respectively, large recirculating cells and wall-normal compression stresses in the form of local stagnation-point flows. In the axisymmetric simulations, the plasma motion is coupled with near-wall axial striations in the electrondensity field, some of which propagate in the form of low-frequency traveling disturbances adjacent to vortical quadrupoles that are reminiscent of Taylor-G€ ortler flow structures in centrifugally unstable flows. Although the refractive-index fields obtained from axisymmetric simulations lead to smooth beam wavefronts, they are found to be unstable to azimuthal disturbances in three of the four three-dimensional cases considered. The azimuthal striations are optically detrimental, since they produce high-order angular aberrations that account for most of the beam wavefront error. A fourth case is computed at high input power and high induction frequency, which displays the best optical properties among all the three-dimensional simulations considered. In particular, the increase in induction frequency prevents local thermalization and leads to an axisymmetric distribution of electrons even after introduction of spatial disturbances. The results highlight the importance of accounting for spatial effects in the numerical computations when optical analyses of plasma lenses are pursued in this range of operating conditions. V C 2015 AIP Publishing LLC.

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