nan Andonowati

Extreme wave phenomena in down-stream running modulated waves

Modulational, Benjamin-Feir, instability is studied for the down-stream evolution of surface gravity waves. An explicit solution, the soliton on finite background, of the NLS equation in physical space is used to study various phenomena in detail. It is shown that for sufficiently long modulation lengths, at a unique position where the largest waves appear, phase singularities are present in the time signal. These singularities are related to wave dislocations and lead to a discrimination between successive ‘extreme’ waves and much smaller intermittent waves. Energy flow in opposite directions through successive dislocations at which waves merge and split, causes the large amplitude difference. The envelope of the time signal at that point is shown to have a simple phase plane representation, and will be described by a symmetry breaking unfolding of the steady state solutions of NLS. The results are used together with the maximal temporal amplitude MTA, to design a strategy for the generation of extreme (freak, rogue) waves in hydrodynamic laboratories.

Displaced phase-amplitude variables for waves on finite background

Wave amplification in nonlinear dispersive wave equations may be caused by nonlinear focussing of waves from a certain background. In the model of nonlinear Schrodinger equation we will introduce a transformation to displaced phase-amplitude variables with respect to a background of monochromatic waves. The potential energy in the Hamiltonian then depends essentially on the phase. Looking as a special case to phases that are time independent, the oscillator equation for the signal at each position becomes autonomous, with the change of phase with position as only driving force for a spatial evolution towards extreme waves. This is observed to be the governing process of wave amplification in classes of already known solutions of NLS, namely the Akhmediev-, Ma- and Peregrine-solitons. We investigate the case of the soliton on finite background in detail in this Letter as the solution that descibes the complete spatial evolution of modulational instability from background to extreme waves.

Direct characterization of states and modes in defect grating structures

For one-dimensional optical structures consisting of gratings surrounding a defect region, optical field solutions inside the bandgap are investigated that are steady states or fully transmitted modes. The observation that a mode is a suitable combination of two states, and that each state is a resonant phenomenon, implies that an accidental degeneracy condition has to be satisfied in order that two states occur at the same frequency. Finding the conditions, and thereby the required design-parameters of the structure, makes it possible to characterize the modes without the necessity to scan the whole bandgap for transmission properties. The mathematical formulation is based on the optical transfer map and leads to a non-standard, not well-studied, eigenvalue problem on the defect region with effective boundary conditions that simulate the surrounding gratings.

Wave run-up of a possible Anak-Krakatau tsunami on planned and optimized Jakarta Sea Dike

The infrastructural plans in the Jakarta Bay to reduce risks of flooding in Jakarta city comprise a large Sea Dike that encloses a retention lake. Part of the planned dike has the shape of the iconic Garuda bird. This paper shows that if in the future an explosion of Anak Krakatau will occur with strength 1/4th of the original Karkatau 1883 explosion, wave crests of 11m and troughs of 6m may collide against the bird’s head. As an alternative example, a more optimized design of the dike is constructed that reduces the maximal wave effects considerably.