Gravity currents in a linearly stratified ambient fluid created by lock release and influx in semi-circular and rectangular channels

Abstract

We present an experimental investigation, supported by a theoretical model, of the motion of lock-release, constant inflow, and time varying inflow gravity currents (GCs) into a linearly stratified ambient fluid at large Reynolds number. The aim is the experimental validation of a simple model able to predict the slumping phase front speed and the asymptotic self-similar front speed for rectangular and circular cross section channels. The first investigated system is of Boussinesq type with the dense current (salt water dyed with aniline) released in a circular channel of 19 cm diameter and 400 cm long (605 cm in the inflow experiments), half-filled of linearly stratified ambient fluid (salt water with varying salt concentration). The second system has the same components but with a channel of rectangular cross section of 14 cm width, 11 cm ambient fluid depth, and 504 cm length. The density stratification of the ambient fluid was obtained with a computer controlled set of pumps and of mixing tanks. For the experiments with inflow, a multi-pipes drainage system was set at the opposite end with respect to the inflow section, computer controlled to avoid the selective withdrawal. The numerous experiments (28 for circular cross section, lock release; 26 for circular and 14 for rectangular cross section, constant inflow (fluid volume ∝tα, with α = 1); 6 for circular cross section, linearly increasing inflow (α = 2)), with several combination of the stratification parameter (0 < S < 1) confirm the theory within ≈30% (≈40% for a single series of experiments), which is considered a good result in view of the various underlying simplifications and approximations. The results on the front speed of the GCs are discussed in the presence of the internal waves, which have a celerity given by a theoretical and experimentally tested model for the rectangular but not for the circular cross section. The theoretical analysis of internal waves in circular cross sections has been extended and experimentally validated.