Periodicity Disruption of a Model Quasibiennial Oscillation of Equatorial Winds

The quasibiennial oscillation (QBO) of equatorial winds on Earth is the clearest example of the spontaneous emergence of a periodic phenomenon in geophysical fluids. In recent years, observations have revealed intriguing disruptions of this regular behavior, and different QBO-like regimes have been reported in a variety of systems. Here, we show that part of the variability in mean-flow reversals can be attributed to the intrinsic dynamics of wave-mean-flow interactions in stratified fluids. Using a constant-in-time monochromatic wave forcing, bifurcation diagrams are mapped for a hierarchy of simplified models of the QBO, ranging from a quasilinear model to fully nonlinear simulations. The existence of new bifurcations associated with faster and shallower flow reversals, as well as a quasiperiodic route to chaos are reported in these models. The possibility for periodicity disruptions is investigated by probing the resilience of regular wind reversals to external perturbations.

Figure 1

Bifurcations in the 1D quasilinear model. (a) Observations of Earth’s atmospheric quasibiennial oscillations. Hovmöller diagram of monthly averaged zonal winds measured by radiosonde in the lower stratosphere above Singapore ($1.4°\mathrm{N}$) [13]. (b) Hovmöller diagram of the mean flow $\overline{u}(z,t)$ in stationary regime for $\alpha =0.6$ and ${\mathrm{Re}}^{-1}=0.06$, using the 1D quasilinear model. (c) Same as (b), but using ${\mathrm{Re}}^{-1}=0.025$. See Supplemental Material [14] for similar time-height plots in other regimes. (d) Bifurcation diagram for $\alpha =0.6$, obtained for each value of ${\mathrm{Re}}^{-1}$ by considering the value of $u$ at two different heights $z_1$ and $z_2$, and then by plotting $u(z_2)$ at times when $u(z_1)$. The dashed red line corresponds to the first bifurcation (from rest to period 1) occurring at ${\mathrm{Re}}_{c1}$. The dashed blue line corresponds to the second bifurcation (from period 1 to quasiperiodic) occurring at ${\mathrm{Re}}_{c2}$. (e) Bifurcation diagram in parameter space $(\alpha ,{\mathrm{Re}}^{-1})$. The colored field is an empirical estimate of the area of the attractor projected in panel (d). Low values (in white) correspond to QBO-like regions (period 1) and frequency-locked regions (rational numbers). The vertical black line at $\alpha =0.6$ corresponds to the bifurcation diagram plotted in panel (c).

Figure 2

Bifurcations in Navier-Stokes simulations. (a) As in Fig. 1, but showing the bifurcation diagram obtained with the nonlinear simulations, using $\alpha =0.6$. Selected values of Re (marked in orange, red, and purple) correspond to panels (b), (c), and (d). The dashed blue line corresponds to the second bifurcation (from period 1 to quasiperiodic) occurring at ${\mathrm{Re}}_{c2}$. (b) Phase space trajectory for ${\mathrm{Re}}^{-1}=0.009$, projected on a 3D space defined by velocities at three different heights: $({\overline{u}}_1,{\overline{u}}_2,{\overline{u}}_3)=[\overline{u}(z=0.5\mathrm{\Lambda },t),\overline{u}(z=1.5\mathrm{\Lambda },t),\overline{u}(z=3\mathrm{\Lambda },t)]$. (c) Same as (b), but using ${\mathrm{Re}}^{-1}=0.0068$. (d) Same as (b), but using ${\mathrm{Re}}^{-1}=0.0058$.

Figure 3

Critical slowing down. (a) Hovmöller diagrams of the mean flow $\overline{u}(z,t)$ in the Navier-Stokes simulations, perturbed by a pulse in wave forcing for $\mathrm{Re}=125$. (b) Same as (a), but using $\mathrm{Re}=50$. (c) Time evolution of the wave-forcing strength $\mathcal{F}(t)$. (d) Characteristic recovery timescale as a function of relative distance to the second bifurcation point, $1-\mathrm{Re}/{\mathrm{Re}}_{c2}$ for different forcing procedures described in Supplemental Material [14]. The star and the cross correspond to the two points associated with the nonlinear computations of panels (a) and (b), respectively. We used ${\mathrm{Re}}_{c2}=24.3$ for the 1D quasilinear model and ${\mathrm{Re}}_{c2}=135$ for the nonlinear 2D model.