Highly resolved three-dimensional and two-dimensional simulations of gravity currents in planar and cylindrical configurations are presented. The volume of release of the heavy fluid is varied and the different phases of spreading, namely acceleration, slumping, inertial and viscous phases, are studied. The incompressible Navier–Stokes equations are solved assuming that the Boussinesq approximation is valid for small density difference. The simulations are performed for three different Reynolds numbers (Re): 895, 3450 and 8950 (this particular choice corresponds to values of Grashof number: 105, 1.5 × 106 and 107, respectively). Following their sudden release, the gravity currents are observed to go through an acceleration phase in which the maximum front velocity is reached. As the interface of the current rolls up, the front velocity slightly decreases from the maximum and levels off to a nearly constant value. At higher Re, three-dimensional disturbances grow rapidly and the currents become strongly turbulent. In contrast, in two-dimensional simulations, the rolled-up vortices remain coherent and very strong. Depending on the initial Re of the flow and on the size of the release, the current may transition from the slumping to the inertial phase, or directly to the viscous phase without an inertial phase. New criteria for the critical Re are introduced for the development of the inertial phase. Once the flow transitions to the inertial or viscous phase, it becomes fully three-dimensional. During these phases of spreading, two-dimensional approximations underpredict the front location and velocity. The enhanced vortex coherence of the two-dimensional simulations leads to strong vortex interaction and results in spurious strong time variations of the front velocity. The structure and dynamics of the three-dimensional currents are in good agreement with previously reported numerical and experimental observations.

[1] Direct numerical simulations (DNS) of planar gravity current in the Boussinesq limit have been conducted with the objective of identifying, visualizing, and describing turbulent structures and their influence on the flow dynamics. The simulations are performed for Reynolds numbers of Re = 8950 and Re = 15,000 with 31-and 131-million grid point resolutions, respectively. This range of Reynolds numbers ensures fully developed turbulent gravity currents, which have never been simulated before using DNS. The flow develops zones with different turbulence characteristics, which eventually interact with each other. The near-wall bottom flow resembles boundary layer flow with several hairpin-like vortices oriented in the direction of the flow and preferential patterns of low-and high-speed streaks. The separation between low-speed streaks at the front scales with the lobe size, which is about 200 wall units for Re = 15,000. Upstream of the front, the separation between low-speed streaks scales with the well-accepted value of 100 wall units for turbulent boundary layers. These patterns have associated regions of low and high bottom shear stresses with implications for sediment erosion and bed load transport. Most of the erosive power of the flow is found in the gravity current front. The interface between heavy and light fluids rolls up by baroclinic generation of KelvinHelmholtz vortices, which undergo sudden breakup and decay to small-scale turbulence. The effect of turbulence and three-dimensionality on the flow dynamics is addressed by comparing two-and three-dimensional simulations. Three-dimensional simulations present active mechanisms that undermine the strong flow coherence, comparing well with experimental observations.

Three-dimensional highly resolved simulations are presented for cylindrical density currents using the Boussinesq approximation for small density difference. Three Reynolds numbers (Re) are investigated (895, 3450 and 8950, which correspond to values of the Grashof number of 105, 1.5 × 106 and 107, respectively) in order to identify differences in the flow structure and dynamics. The simulations are performed using a fully de-aliased pseudospectral code that captures the complete range of time and length scales of the flow. The simulated flows present the main features observed in experiments at large Re. As the current develops, it transitions through different phases of spreading, namely acceleration, slumping, inertial and viscous Soon after release the interface between light and heavy fluids rolls up forming Kelvin–Helmholtz vortices. The formation of the first vortex sets the transition between acceleration and slumping phases. Vortex formation continues only during the slumping phase and the formation of the last Kelvin–Helmholtz vortex signals the departure from the slumping phase. The coherent Kelvin–Helmholtz vortices undergo azimuthal instabilities and eventually break up into small-scale turbulence. In the case of planar currents this turbulent region extends over the entire body of the current, while in the cylindrical case it only extends to the regions of Kelvin–Helmholtz vortex breakup. The flow develops three-dimensionality right from the beginning with incipient lobes and clefts forming at the lower frontal region. These instabilities grow in size and extend to the upper part of the front. Lobes and clefts continuously merge and split and result in a complex pattern that evolves very dynamically. The wavelength of the lobes grows as the flow spreads, while the local Re of the flow decreases. However, the number of lobes is maintained over time. Owing to the high resolution of the simulations, we have been able to link the lobe and cleft structure to local flow patterns and vortical structures. In the near-front region and body of the current several hairpin vortices populate the flow. Laboratory experiments have been performed at the higher Re and compared to the simulation results showing good agreement. Movies are available with the online version of the paper.

The capability of acoustic Doppler velocimeters to resolve flow turbulence is analyzed. Acoustic Doppler velocimeter performance curves ͑APCs͒ are introduced to define optimal flow and sampling conditions for measuring turbulence. To generate the APCs, a conceptual model is developed which simulates different flow conditions as well as the instrument operation. Different scenarios are simulated using the conceptual model to generate synthetic time series of water velocity and the corresponding sampled signals. Main turbulence statistics of the synthetically generated, sampled, and nonsampled time series are plotted in dimensionless form ͑APCs͒. The relative importance of the Doppler noise on the total measured energy is also evaluated for different noise energy levels and flow conditions. The proposed methodology can be used for the design of experimental measurements, as well as for the interpretation of both field and laboratory observations using acoustic Doppler velocimeters.