The speed of travelling azimuthal waves on Taylor vortices in a circular Couette system (with the inner cylinder rotating and the outer cylinder at rest) has been determined in laboratory experiments conducted as a function of Reynolds number R, radius ratio of the cylinders η, average axial wavelength $\overline{\lambda}$, number of waves m₁ and the aspect ratio Γ (the ratio of the fluid height to the gap between the cylinders). Wave speeds have also been determined numerically for axially periodic flows in infinite-length cylinders by solving the Navier-Stokes equation with a pseudospectral technique where each Taylor-vortex pair is represented with 32 axial modes, 32 azimuthal modes (in an azimuthal angle of 2π/m₁) and 33 radial modes. Above the onset of wavy-vortex flow the wave speed for a given η decreases with increasing R until it reaches a plateau that persists for some range in R. In the radius-ratio range examined in our experiments we find that the wave speed in the plateau region increases monotonically from 0.14Ω at η = 0.630 to 0.45Ω at η = 0.950 (where the wave speed is expressed in terms of the rotation frequency Ω of the inner cylinder). There is a much weaker dependence of the wave speed on $\overline{\lambda}$, m₁ and Γ. For three sets of parameter values (R, $\overline{\lambda}$, η and m₁) the wave speeds have been measured, extrapolated to infinite aspect ratio, and compared with the numerically computed values. For each of these three cases the agreement is within 0.1 %.

The Kuroshio Extension region is well known for its strong eddy activity. In this paper, using satellite altimetry‐measured sea surface height anomaly data from 1993 to 2012 in an extended Kuroshio Extension region (140–180°E, 25–45°N), we analyze eddy characteristics: eddy size, polarity, lifetime, intensity, trajectory, and spatial and temporal distributions. Using temperature and salinity vertical profiles measured by Argo floats, we examine the eddy impact on vertical stratification. During the 20‐year period, 7,574 eddies are identified (based on following complete eddy trajectories) with a lifetime equal to or longer than 4 weeks. The numbers of cyclonic and anticyclonic eddies are found to be approximately the same. The distribution of eddy sizes peaks at a radius of about 40 km. The radius at the peak is at the same order as the first baroclinic deformation radius or the horizontal shear scale of the Kuroshio flow. The normalized eddy statistical characteristics show that eddies have different characteristics at different stages of their lifetimes. Among eddies with lifetimes longer than 50 weeks, more anticyclonic (cyclonic) eddies are found north (south) of 35°N. In contrast, among eddies with lifetimes shorter than 20 weeks, more cyclonic (anticyclonic) eddies are found north (south) of 35°N. The asymmetric distribution of eddies suggests two different eddy generation mechanisms: (1) the development of meanders in the Kuroshio path leading to the pinch off of eddies with longer lifetime (larger size) and (2) horizontal shear instability (barotropic instability) leading to eddies of shorter life (smaller size). We further apply an eddy‐resolved numerical product to quantitatively investigate the eddy generation mechanisms.

We describe a simple and intuitive model that relates the catastrophe theory unfolding of a double-well potential with the unfolding of a bimodal map characterizing the dynamics of an autonomous chaotic van der Pol–Duffing oscillator. The construction of the model was facilitated by developing an analogy with the stochastic dynamics of a particle in a double-well potential. Experimental evidence supporting the model is given.