טכניון מכון טכנולוגי לישראל
הטכניון מכון טכנולוגי לישראל - בית הספר ללימודי מוסמכים  
M.Sc Thesis
M.Sc StudentGoldman Ron
SubjectGravity Current Generated by Difference in Stratification
DepartmentDepartment of Applied Mathematics
Supervisors Professor Emeritus Marius Ungarish
Professor Irad Yavneh


Abstract

Gravity current is a phenomenon where fluid of one density (the current) flows, in the presence of gravity, into a fluid of different density (the ambient). The driving force of this flow is the horizontal pressure gradient generated by differences in buoyancy. This phenomenon is common in geophysical flows (e.g. flow through straits, river discharge, pyroclastic flows, and spread of pollutions like brine from desalination plants or oil spills). In this work, a high Reynolds number Boussinesq flow field will be considered for a case in which a linearly stratified gravity current is released from a rectangular “reservoir” into an ambient which is also linearly stratified. A one layer shallow water model describing this system exists and relates the motion of the current (velocity and layer height) to three parameters: the ratio between the lock height and the ambient thickness (H); the density range within the ambient (S), and within the current (σ).

The use of the model is computationally cheap compared with direct simulations. However, validation of the model is necessary.  For this purpose, a comparison between the shallow water model and non-hydrostatic Navier Stokes simulations was performed, both in 2D Cartesian geometry and in axisymmetric geometry. We made several modifications to the original code for the simulations: a new tracer has been added to help detect the current; the numerical scheme for tracer convection was changed from MacCormack to FCT in order to avoid unrealistic values; and during the axisymmetric simulations, the performance of the pressure equation solver was improved by replacing the bi-conjugate gradient solver with a multigrid preconditioner.

The qualitative predictions of the model are confirmed: (1) there is an initial “slumping” stage of propagation in which a rarefaction wave emanated from the lock travels in the reservoir and is then reflected towards the front of the current (known as the “nose” of the current). The model predicts that during this stage the nose, in Cartesian geometry, propagates at constant speed and in axisymmetric geometry, decelerates. The front velocity decays in time after the slumping stage is over. (2) For fixed H and S, the increase of σ causes a slower propagation of the current. (3) For some combinations of the parameters H, S, σ the fluid released from the lock lacks initially (or runs out quickly of) buoyancy “driving power” in the horizontal direction, and does not propagate like a gravity current.  A fair quantitative agreement was found between model predictions for Cartesian slumping velocity and the simulated nose velocity.  The discrepancies between model and simulations reveal some non-trivial restrictions of the prediction methods for this flow-field.