טכניון מכון טכנולוגי לישראל
הטכניון מכון טכנולוגי לישראל - בית הספר ללימודי מוסמכים  
Ph.D Thesis
Ph.D StudentZemach Tamar
SubjectSimulations of Non-Homogeneous Flow Fields Subject to
Rotation and Gravity Effects
DepartmentDepartment of Computer Science
Supervisor Professor Emeritus Marius Ungarish
Full Thesis textFull thesis text - English Version


Abstract

The work is concerned with the investigation of gravity currents and intrusions in various circumstances. Gravity currents are formed by fluid flowing primarily horizontally, under the influence of gravity, into another fluid of different density. The gravity current which is released from rest and then propagates horizontally at the neutral buoyancy level in a vertically-stratified ambient fluid is called intrusive gravity current or intrusion. In the present investigation, the density of the intrusion or current is constant; the ambient fluid density change is linear over the full-depth of the container. We present some new results as follows:

1).A closed one-layer shallow-water Boussinesq time-dependent inviscid formulation is presented for the axisymmetric intrusions. In general, the solution of the resulting hyperbolic system is obtained by a finite-differences scheme. However, for the large-time developed motion an analytical similarity solution is derived. It is verified that the initial-value lock-release finite-differences solution approaches the similarity predictions after an initial spread of the outer radius to about 2.5 times the initial radius. To avoid accumulation of numerical errors it was necessary to reformulate the problem in terms of new variables.


2).The behavior of the two-dimensional Boussinesq inviscid steady-state intrusive gravity currents spreading into a stratified ambient fluid is considered. The intrusive and the ambient fluids are assumed to be asymmetric with respect to the horizontal plane passing through the tip of the intrusion. Long's model combined with the flow-force balance over the width of the channel and the pressure balances over a density current are used to obtain the desired results. It is shown that the intrusion velocity decreases with decreasing of system's asymmetry and approaches its minimum for the symmetric configuration.


3).We discus an important extension of the fixed-volume classical intrusions: a flow generated by an external line source with constant volumetric flow rate. Inertia-buoyancy controlled axisymmetric intrusive gravity currents are discussed. The shallow-water theory for this case is presented. The initial-value problem is solved numerically, and long-time similarity solutions are also developed. The results obtained numerically and analytically are compared with previously published experimental data and show good agreement.