A water bell forms when a fluid jet impacts upon a target and separates into a two-dimensional sheet. Depending on the angle of separation from the target, the sheet can curve into a variety of different geometries. We show analytically that harmonic perturbations of water bells have linear wave solutions with geometry-dependent growth. We test the predictions of this model experimentally with a custom target system, and observe growth in agreement with the model below a critical forcing amplitude. Once the critical forcing amplitude is exceeded, a nonlinear transcritical bifurcation occurs; the response amplitude increases linearly with increasing forcing amplitude, albeit with a fundamentally different spatial form, and distinct nodes appear in the amplitude envelope.

We experimentally investigate how disorder comes about in parametrically excited waves on a fluid surface (Faraday waves). We find that the transition from an ordered pattern to disorder corresponding to "defect-mediated turbulence" is mediated by a spatially incoherent oscillatory phase. This phase consists of highly damped waves that propagate through the effectively elastic lattice defined by the pattern. They have a well-defined frequency, velocity, and transverse polarization. As these waves decay within a few lattice spaces, they are spatially and temporally uncorrelated at larger scales.

We study the spatial and temporal structure of nonlinear states formed by parametrically excited waves on a fluid surface (Faraday instability), in a highly dissipative regime. Short-time dynamics reveal that 3-wave interactions between different spatial modes are only observed when the modes' peak values occur simultaneously. The temporal structure of each mode is functionally described by the Hill's equation and is unaffected by which nonlinear interaction is dominant.

The excitation of large amplitude nonlinear waves is achieved via parametric autoresonance of Faraday waves. We experimentally demonstrate that phase locking to low amplitude driving can generate persistent high-amplitude growth of nonlinear waves in a dissipative system. The experiments presented are in excellent agreement with theory.

Interacting surface waves, parametrically excited by two commensurate frequencies (Faraday waves), yield a rich family of nonlinear states, which result from a variety of three-wave resonant interactions. By perturbing the system with a third frequency, we selectively favor different nonlinear wave interactions. Where quadratic nonlinearities are dominant, the only observed patterns correspond to "grid" states. Grid states are superlattices in which two corotated sets of critical wave vectors are spanned by a sublattice whose basis states are linearly stable modes. Specific driving phase combinations govern the selection of different grid states.

The nonlinear interactions of parametrically excited surface waves have been shown to yield a rich family of nonlinear states. When the system Is driven by two commensurate frequencies, a variety of interesting auperlattice type states are generated via a number of different 3-wave resonant interactions, These states occur either as symmetry-breaking bifurcations of hexagonal patterns composed of a single unstable mode or via nonlinear interactions between the two different unstable modes generated by the two forcing frequencies. Near the system's bicritical point, a well-defined region of phase space exists in which a highly disordered state, both in space and time, is observed. We first show that this state results from the competition between two distinct nonlinear super-lattice states, each with different characteristic temporal and spatial symmetries. After characterizing the type of spatio-temporal disorder that is embodied in this disordered state, we will demonstrate that it can be controlled, Control to either of its neighboring nonlinear states is achieved by the application of a small-amplitude excitation at a third frequency, where the spatial symmetry of the selected pattern is determined by the temporal symmetry of the third frequency used. This technique can also excite rapid switching between different nonlinear states.

The parametrically excited surface waves were investigated to study the control of spatiotemporal disorder. The study described nonlinear waves on the 2D surface of a fluid, and the uncontrolled system was driven by a spatially uniform, temporally periodic vibration of the fluid layer. By imposing a small-amplitude control frequency, both the control of the state and force rapid transitions between different, stabilized, nonlinear states was achieved. It was observed that the mechanism driving the spatiotemporal disorder in the system is the continual competition between a number of specific nonlinear states.

We present an experimental investigation of superlattice patterns generated on the surface of a fluid via parametric forcing with two commensurate frequencies. The spatiotemporal behavior of four qualitatively different types of superlattice patterns is described in detail. These states are generated via a number of different three-wave resonant interactions. They occur either as symmetry-breaking bifurcations of hexagonal patterns composed of a single unstable mode or via nonlinear interactions between the two primary unstable modes generated by the two forcing frequencies. A coherent picture of these states together with the phase space in which they appear is presented. In addition, we describe a number of new superlattice states generated by four-wave interactions that arise when symmetry constraints rule out three-wave resonances.

Two-mode rhomboid patterns are generated experimentally via two-frequency parametric forcing of surface waves. These patterns are formed by the simple nonlinear resonance: k→'1 - k→2 = k→1 where k1 and k2(=k'2) are concurrently excited eigenmodes. The state possesses a direction-dependent time dependence described by a superposition of the two modes, and a dimensionless scaling delineating the state’s region of existence is presented. We also show that 2n-fold quasipatterns naturally arise from these states when the coupling angle between k→2 and k→'1 is 2π/n.

We present an experimental characterization of the effects of turbulence and breaking gravity waves on air-water gas exchange in standing waves. We identify two regimes that govern aeration rates: turbulent transport when no wave breaking occurs and bubble dominated transport when wave breaking occurs. In both regimes, we correlate the qualitative changes in the aeration rate with corresponding changes in the wave dynamics. In the latter regime, the strongly enhanced aeration rate is correlated with measured acoustic emissions, indicating that bubble creation and dynamics dominate air-water exchange.

The basic mechanism for the formation of highly localized states, appearing in a Newtonian fluid, is described. It is demonstrated that oscillon states whose time dependence is temporally harmonic with the forcing frequency exist in such fluids.

Finite-time singularities-local divergences in the amplitude or gradient of a physical observable at a particular time-occur in a diverse range of physical systems. Examples include singularities capable of damaging optical fibres and lasers in nonlinear optical systems, and gravitational singularities associated with black holes. In fluid systems, the formation of finite-time singularities cause spray and air-bubble entrainment, processes which influence air-sea interaction on a global scale. Singularities driven by surface tension have been studied in the break-up of pendant drops and liquid sheets. Here we report a theoretical and experimental study of the generation of a singularity by inertial focusing, in which no break-up of the fluid surface occurs. Inertial forces cause a collapse of the surface that leads to jet formation; our analysis, which includes surface tension effects, predicts that the surface profiles should be describable by a single universal exponent. These theoretical predictions correlate closely with our experimental measurements of a collapsing surface singularity. The solution can be generalized to apply to a broad class of singular phenomena.

The observation of localized stationary structures, coined oscillons, in granular media has evoked much interest. By parametric excitation of clay suspensions, we demonstrate a hysteretic transition to oscillon-type states in a nongranular medium. When the symmetry of up-down reflection + time translation is lost, these states undergo a transition to propagating localized states previously seen in Newtonian fluids. These observations are in accord with recent theoretical predictions of sufficient conditions for oscillon formation. In addition, a novel measurement technique for the effective suspension viscosity demonstrates their shear-thinning properties. 1999

Highly localized solitary states, driven by means of the spatially uniform, vertical acceleration of a thin fluid layer, are observed to propagate along the 2D surface of a fluid in a highly dissipative regime. Unlike classical solitons, these states propagate at a single constant velocity for given fluid parameters and their existence is dependent on the highly dissipative character of the system. The properties of these states are discussed and examples of bound states and two-state interactions are presented.