Open Archive Toulouse Archive Ouverte (oatao) a Numerical Investigation of High-reynolds-number Constant-volume Non-boussinesq Density Currents in Deep Ambient

OATAO is an open access repository that collects the work of Toulouse researchers and makes it freely available over the web where possible. A numerical investigation of high-Reynolds-number constant-volume non-Boussinesq density currents in deep ambient. The time-dependent behaviour of non-Boussinesq high-Reynolds-number density currents, released from a lock of height h 0 and length x 0 into a deep ambient and spreading over horizontal flat boundaries, is considered. We use two-dimensional Navier–Stokes simulations to cover: (i) a wide range of current-to-ambient density ratios, (ii) a range of length-to-height aspect ratios of the initial release within the lock (termed the lock aspect ratio λ = x 0 / h 0) and (iii) the different phases of spreading, from the initial acceleration phase to the self-similar regimes. The Navier–Stokes results are compared with predictions of a one-layer shallow-water model. In particular, we derive novel insights on the influence of the lock aspect ratio (λ) on the shape and motion of the current. It is shown that for lock aspect ratios below a critical value (λ crit), the dynamics of the current is significantly influenced by λ. We conjecture that λ crit depends on two characteristic time scales, namely the time it takes for the receding perturbation created at the lock upon release to reflect back to the front, and the time of formation of the current head. A comparison of the two with space–time diagrams obtained from the Navier–Stokes simulations supports this conjecture. The non-Boussinesq effect is observed to be significant. While the critical lock aspect ratio (λ crit) is of order 1 for Boussinesq currents, its value decreases for heavy currents and increases significantly (up to about 20) for light currents. We present a simple analytical model which captures this trend, as well as the observation that for a light current the speed of propagation is proportional to λ 1/4 when λ < λ crit .