| Abstract: | The purpose of the study is the direct numerical and theoretical modeling of fountain dynamics in a fluid with density stratification
in the form of a pycnocline. The fountain is formed as a vertical jet penetrates through the pycnocline. In numerical simulation
the jet flow is initiated by means of preassigning a boundary condition in the form of an upward-directed laminar flow of
a neutral-buoyancy fluid with an axisymmetric Gaussian velocity profile. The calculations show that at a Froude number Fr
greater than a certain critical value the flow becomes unstable and the fountain executes self-oscillations accompanied by
internal wave generation in the pycnocline. Depending on Fr, two self-oscillation modes can be distinguished. At fairly low
Fr the fountain executes circular motion in the horizontal plane, in the vicinity of the center of jet, its shape remaining
almost invariant. In this case, internal waves in the form of unwinding spirals are radiated. At fairly high Fr another mode
predominates, when the fountain top chaotically “strays” in the vicinity of the center of the jet and, periodically breaking
down, generates wave packets propagating toward the periphery of the computation domain. In both cases, the main peak in the
frequency spectrum of the internal waves coincides with the fountain top oscillation frequency which monotonically decreases
with increase in Fr. In numerical simulation the Fr-dependence of the fountain top oscillation amplitude is in good agreement
with that predicted by the theoretical model of the concurrence of the interacting modes in the soft self-excitation regime. |
