Transition to defect-mediated turbulence in the ribbon patterns observed in a viscoelastic Taylor-Couette flow is investigated when the rotation rate of the inner cylinder is increased while the outer cylinder is fixed. In four polymer solutions with different values of the elasticity number, the defects appear just above the onset of the ribbon pattern and trigger the appearance of disordered oscillations when the rotation rate is increased. The flow structure around the defects is determined and the statistical properties of these defects are analyzed in the framework of the complex Ginzburg-Landau equation.

Extreme waves play a crucial role in marine inundation hazards and coastal erosion. Prediction of non-linear wave–wave interactions is crucial in assessing the propagation of shallow water extreme waves in coastal regions. In this article, we experimentally study non-linear wave–wave interactions of large-amplitude focused wave groups propagating in a two-dimensional wave flume over a mild slope ($\mathit{\beta }=\mathrm{1}:\mathrm{25}$ ). The influence of the frequency spectrum and the steepness on the non-linear interactions of focused waves are examined. The generated wave trains correspond to Pierson–Moskowitz and JONSWAP (γ=3.3 or γ=7) spectra. Subsequently, we experimentally approach this problem by the use of a bispectral analysis applied on short time series, via the wavelet-based bicoherence parameter, which identifies and quantifies the phase coupling resulting from non-resonant or bound triad interactions with the peak frequency. The bispectral analysis shows that the phase coupling increases gradually and approaches 1 just prior to breaking, accordingly with the spectrum broadening and the energy increase in high-frequency components. Downstream breaking, the values of phase coupling between the peak frequency and its higher harmonics decrease drastically, and the bicoherence spectrum becomes less structured.

Nonlinear wave run-up on the beach caused by a harmonic wave maker located at some distance from the shore line is studied experimentally. It is revealed that under certain wave excitation frequencies, a significant increase in run-up amplification is observed. It is found that this amplification is due to the excitation of resonant mode in the region between the shoreline and wave maker. Frequency and magnitude of the maximum amplification are in good correlation with the numerical calculation results represented in the paper (Stefanakis et al., 2011). These effects are very important for understanding the nature of rogue waves in the coastal zone.

Formation of freak waves resulting from the wave packets propagating in finite water depth on the background of a current is studied experimentally and numerically. In the experiment, the freak waves appear as a result of dispersion focusing of wave train excited by wave maker with modulated frequency. The space evolution of the frequency modulated train is studied in numerical simulations. We showed that in the water of finite depth, a distance of focusing increases and amplitude in the focal point decreases in comparison with infinite water depth. Experimental results are in good agreement with numerical simulations if wave breaking of surface waves does not occur.