Место издания:Bifurcations and Instabilities in Fluid Dynamics Association Paris
Первая страница:280
Аннотация:We study experimentally the long-term behavior of internal wave attractors. Attractors have been studied theoretically
in [1] and experimentally observed for the first time in [2]. They also mimic some essential features of natural energy
cascade in ocean with periodic forcing as input and with multi-scale internal wave motion and mixing as output. Experi-
ments are here carried out in a trapezoidal test tank filled with linearly stratified fluid. Energy is injected into the system
via the oscillatory motion of a vertical wall described in [3] and internal wave velocity fields are measured with a standard
PIV technique. Hilbert transforms [4] and bispectra [5] are used in the post-processing to analyze the components of the
wave fields.
A previous paper [6] showed that a parametric subharmonic instability (PSI) appears on the most energetic branch of the
attractor with a high growth rate, under typical experimental condition. This induces an energy transfer from the attractor
(the primary wave) to the two waves (secondary waves) created by the triadic instability. The effects of the confinement
on the secondary waves generated by this instability have not been explored in [6] because of a very quick growth of the
instability from a spatially isolated region of the attractor and because the experiment duration was short in comparison
of the typical time scale of secondary waves propagation.
In this present study, we show that the confinement of the fluid domain and the forcing amplitude have a significant impact
onto the scenario of PSI. It is shown that under typical experimental conditions, long-term observations are necessary to
observe and quantify the instability. Secondary waves produced by PSI have a trend toward the formation of standing-wave
patterns, with at least one of the secondary waves corresponding to a global geometric resonance of the trapezoidal tank.
As the forcing amplitude increases, a cascade of triadic interactions is formed which produces internal-wave motion with
a rich multi-peak discrete frequency spectrum imbedded into a continuous spectrum of weaker magnitude. This complex
wave motion is shown to produce significant mixing which is related to the statistics of extreme events. Numerical
simulations using spectral element method show good agreement with experimental results.