Nobuhiro Baba

Computation of advancing gravity currents in ambient flows

The interaction of gravity currents with head and tail ambient flows is investigated by computation using the adaptive grids moving with the head of the current. The incompressible Navier-Stokes equation for a heterogeneous fluid, the continuity equation and the transport equation of the relative variation of density are discretized by the finite volume method. The use of the moving grid system raises the computational efficiency as well as the resolution of the moving head. The ambient flow is incorporated with the implementation of the inflow and outflow boundary conditions. The results indicate that the front speed relative to the ambient flow varies in a nonlinear fashion when the boundary layer develops along the wall. The tail wind makes the head round and thicker, and hence it reduces the speed of the head. On the other hand, the head wind makes the head sharp, thinner, and longer, and then the stable interface suppresses the mixing across the density interface. It is found that the boundary layer along the wall affects the inner structure of the current head according to the ambient flows.

Structure of Head of a Gravity Current (Second Report)

The structure of the head of gravity currents spreading out in all directions is investigated in the experiment and in the computation by extending the method developed in the previous paper for the two-dimensional gravity currents. A finite volume of fluid contained in a rectangular region was released instantaneously in another fluid of slightly different density in a larger region. Box models of fluid dispersion were described to elucidate the mechanisms of energy conversion in different stages of development of spreading gravity currents.Visualization experiments were made with dye to trace the head of the spreading gravity currents. By opening the lock gate equipped obliquely in the corner of a water tank of square section, a finite volume of salt water of slightly different density in the corner of the tank was released instantaneously so as to form the gravity currents spreading over the whole area. The computation was also made in the same conditions as the experiments to study the flow structure of the head of spreading currents. The incompressible Navier-Stokes equation for an inhomogeneous fluid together with the transport equation for solute was solved by the finite volume method.Both the experiment and the computation produce the formation and development of the gravity currents spreading in an axisymmetric manner. The results indicate that there exist different stages of development of this kind of spreading gravity currents. After the released fluid spreads at a constant speed, it slows down in the self-similar stage, and then it decelerates further in the viscous stage. It is found that the structure of the head changes according to the stages of development, which affects the mixing of fluid by spreading gravity current and that the head extending in a circle or a circular arc is subject to the three-dimensional instability to form the mountain-valley structure.