École Nationale Supérieure de
Techniques Avancées

Résumé

In this paper the classical lock exchange problem is studied. Inflows on opposite sides of the lock are added to simulate the motion of a river into the sea. An outflow at the top of the domain is added to simulate evaporation. Direct numerical simulations are run to study the problem. The resulting gravity current is characterized by its front length. The initial problem has the density being diffused. A convergence analysis is run to determine the optimum number of gridpoints of the simulations. The influence of the domain length, the Reynolds, the Schmidt and the evaporation speed are studied, characterized and quantified. The domain length, Reynolds and Schmidt do not have a strong impact on the length of the front of the gravity current. However the evaporation speed is directly relation to the front length. An equation between the two is verified. Density is then made bilinearly dependant upon salinity and temperature. These have different diffusivities and different expansion rates for the density, making it possible for double diffusion phenomena to occur. The equations for the fluid are non dimentionalized, and the ensuing dimensionless parameters are used to define the flow. The density ratio is related to the diffusivity ratio and the existing theory on double diffusivity. These parameters are studied to predict the apparition of instabilities in the flow.