  A gradient-wind balanced flow with an elliptic streamline parametrically
excites internal inertia-gravity waves through ageostrophic anticyclonic
instability (AAI). This study numerically investigates the breaking of internal
waves and the following turbulence generation resulting from the AAI. In our
simulation, we periodically distort the calculation domain following the
streamlines of an elliptic vortex and integrate the equations of motion using a
Fourier spectral method. This technique enables us to exclude the overall
structure of the large-scale vortex from the computation and concentrate on
resolving the small-scale waves and turbulence. From a series of experiments,
we identify two different scenarios of wave breaking conditioned on the
magnitude of the instability growth rate scaled by the buoyancy frequency,
$\lambda/N$. First, when $\lambda/N\gtrsim0.008$, the primary wave amplitude
excited by AAI quickly goes far beyond the overturning threshold and directly
breaks. The resulting state is thus strongly nonlinear turbulence. Second, if
$\lambda/N\lesssim0.008$, weak wave-wave interactions begin to redistribute
energy across frequency space before the primary wave reaches a breaking limit.
Then, after a sufficiently long time, the system approaches a Garrett-Munk-like
stationary spectrum, in which wave breaking occurs at finer vertical scales.
Throughout the experimental conditions, the growth and decay time scales of the
primary wave energy are well correlated. However, since the primary wave
amplitude reaches a prescribed limit in one scenario but not in the other, the
energy dissipation rates exhibit two types of scaling properties. This scaling
classification has similarities and differences with D'Asaro and Lien's (2000)
wave-turbulence transition model.
