Excitation of Initial Waves by Wind: A Theoretical Model and Its Experimental Verification.

We present a theory of evolution of wind waves in time and space under abruptly applied wind forcing that is experimentally validated in a laboratory wind-wave tank. The model describes qualitatively and quantitatively the complex wave field development from the initial smooth surface to the finite state. The stochastic nature of wind waves is treated by considering an ensemble of coexisting unstable harmonics that grow due to shear flow instability. Breaking limits the wave growth initially; the process is then controlled by fetch-limited growth duration.

Periodic Wave Trains in Nonlinear Media: Talbot Revivals, Akhmediev Breathers, and Asymmetry Breaking.

We study theoretically and observe experimentally the evolution of periodic wave trains by utilizing surface gravity water wave packets. Our experimental system enables us to observe both the amplitude and the phase of these wave packets. For low steepness waves, the propagation dynamics is in the linear regime, and these waves unfold a Talbot carpet. By increasing the steepness of the waves and the corresponding nonlinear response, the waves follow the Akhmediev breather solution, where the higher frequency periodic patterns at the fractional Talbot distance disappear. Further increase in the wave steepness leads to deviations from the Akhmediev breather solution and to asymmetric breaking of the wave function. Unlike the periodic revival that occurs in the linear regime, here the wave crests exhibit self acceleration, followed by self deceleration at half the Talbot distance, thus completing a smooth transition of the periodic pulse train by half a period. Such phenomena can be theoretically modeled by using the Dysthe equation.

Diffractive Guiding of Waves by a Periodic Array of Slits.

We show that in order to guide waves, it is sufficient to periodically truncate their edges. The modes supported by this type of wave guide propagate freely between the slits, and the propagation pattern repeats itself. We experimentally demonstrate this general wave phenomenon for two types of waves: (i) plasmonic waves propagating on a metal-air interface that are periodically blocked by nanometric metallic walls, and (ii) surface gravity water waves whose evolution is recorded, the packet is truncated, and generated again to show repeated patterns. This guiding concept is applicable for a wide variety of waves.

Amplitude and Phase of Wave Packets in a Linear Potential.

We theoretically study and successfully observe the evolution of Gaussian and Airy surface gravity water wave packets propagating in an effective linear potential. This potential results from a homogeneous and time-dependent flow created by a computer-controlled water pump. For both wave packets we measure the amplitudes and the cubic phases appearing due to the linear potential. Furthermore, we demonstrate that the self-acceleration of the Airy surface gravity water wave packets can be completely canceled by a linear potential.

Dispersion Management of Propagating Waveguide Modes on the Water Surface.

We report on the theoretical and experimental study of the generation of propagating waveguide modes on the water surface. These propagating modes are modulated in the transverse direction in a manner that satisfies boundary conditions on the walls of the water tank. It is shown that the propagating modes possess both anomalous and normal dispersion regimes, in contrast to the extensively studied zero mode that, in the case of deep water, only has normal dispersion with a fixed frequency independent dispersion coefficient. Importantly, by using a carrier frequency at which the group velocity dispersion crosses zero, a linear nonspreading and shape-preserving wave packet is observed. By increasing the wave steepness, nonlinear effects become pronounced, thereby enabling the first observation of linearly chirped parabolic water wave pulses in the anomalous dispersion regime. This parabolic wave maintains its linear frequency chirp and does not experience wave breaking during propagation.

Diffractive Focusing of Waves in Time and in Space.

We study the general wave phenomenon of diffractive focusing from a single slit for two types of waves and demonstrate several properties of this effect. Whereas in the first situation, the envelope of a surface gravity water wave is modulated in time by a rectangular function, leading to temporal focusing, in the second example, surface plasmon polariton waves are focused in space by a thin metal slit to a transverse width narrower than the slit itself. The observed evolution of the phase carrier of the water waves is measured for the first time and reveals a nearly flat phase as well as an 80% increase in the intensity at the focal point. We then utilize this flat phase with plasmonic beams in the spatial domain, and study the case of two successive slits, creating a tighter focusing of the waves by putting the second slit at the focal point of the first slit.

Propagation Dynamics of Nonspreading Cosine-Gauss Water-Wave Pulses.

Linear gravity water waves are highly dispersive; therefore, the spreading of initially short wave trains characterizes water surface waves, and is a universal property of a dispersive medium. Only if there is sufficient nonlinearity does this envelope admit solitary solutions which do not spread and remain in fixed forms. Here, in contrast to the nonlinear localized wave packets, we present both theoretically and experimentally a new type of linearly nondispersive water wave, having a cosine-Gauss envelope, as well as its higher-order Hermite cosine-Gauss variations. We show that these waves preserve their width despite the inherent dispersion while propagating in an 18-m wave tank, accompanied by a slowly varying carrier-envelope phase. These wave packets exhibit self-healing; i.e., they are restored after bypassing an obstacle. We further demonstrate that these nondispersive waves are robust to weakly nonlinear perturbations. In the strong nonlinear regime, symmetry breaking of these waves is observed, but their cosine-Gauss shapes are still approximately preserved during propagation.

Propagation Dynamics of Airy Water-Wave Pulses.

We observe the propagation dynamics of surface gravity water waves, having an Airy function envelope, in both the linear and the nonlinear regimes. In the linear regime, the shape of the envelope is preserved while propagating in an 18-m water tank, despite the inherent dispersion of the wave packet. The Airy wave function can propagate at a velocity that is slower (or faster if the Airy envelope is inverted) than the group velocity. Furthermore, the introduction of the Airy wave packet as surface water waves enables the observation of its position-dependent chirp and cubic-phase offset, predicted more than 35 years ago, for the first time. When increasing the envelope of the input Airy pulse, nonlinear effects become dominant, and are manifested by the generation of water-wave solitons.

Observation of accelerating solitary wavepackets.

We study theoretically and observe experimentally the evolution of solitary surface gravity water wavepackets propagating in homogeneous and time-dependent flow created by a computer-controlled water pump, resulting in an effective linear potential. Unlike a potential free soliton, in this case the wavepacket envelope accelerates, while its phase is proportional to the cubic power of the position in the water tank. For increased wave steepness, we observe the emergence of asymmetry in the envelope, and hence it no longer retains its soliton shape. Furthermore, we study a case of ballistic dynamics of solitary surface gravity water wavepackets with initial nonzero momentum and demonstrate that their trajectory is similar to that of a projectile pulled by gravity. Nevertheless, their envelope shape is preserved during propagation, and the envelope phase is identical to that measured without an initial momentum.

Measurements of Waves in a Wind-wave Tank Under Steady and Time-varying Wind Forcing.

This manuscript describes an experimental procedure that allows obtaining diverse quantitative information on temporal and spatial evolution of water waves excited by time-dependent and steady wind forcing. Capacitance-type wave gauge and Laser Slope Gauge (LSG) are used to measure instantaneous water surface elevation and two components of the instantaneous surface slope at a number of locations along the test section of a wind-wave facility. The computer-controlled blower provides airflow over the water in the tank whose rate can vary in time. In the present experiments, the wind speed in the test section initially increases quickly from rest to the set value. It is then kept constant for the prescribed duration; finally, the airflow is shut down. At the beginning of each experimental run, the water surface is calm and there is no wind. Operation of the blower is initiated simultaneously with the acquisition of data provided by all sensors by a computer; data acquisition continues until the waves in the tank fully decay. Multiple independent runs performed under identical forcing conditions allow determining statistically reliable ensemble-averaged characteristic parameters that quantitatively describe wind-waves' variation in time for the initial development stage as a function of fetch. The procedure also allows characterizing the spatial evolution of the wave field under steady wind forcing, as well as decay of waves in time, once the wind is shut down, as a function of fetch.

Measurements of Local Instantaneous Convective Heat Transfer in a Pipe - Single and Two-phase Flow.

This manuscript provides step by step description of the manufacturing process of a test section designed to measure the local instantaneous heat transfer coefficient as a function of the liquid flow rate in a transparent pipe. With certain amendments, the approach is extended to gas-liquid flows, with a particular emphasis on the effect of a single elongated (Taylor) air bubble on heat transfer enhancement. A non-invasive thermography technique is applied to measure the instantaneous temperature of a thin metal foil heated electrically. The foil is glued to cover a narrow slot cut in the pipe. The thermal inertia of the foil is small enough to detect the variation in the instantaneous foil temperature. The test section can be moved along the pipe and is long enough to cover a considerable part of the growing thermal boundary layer. At the beginning of each experimental run, a steady state with a constant water flow rate and heat flux to the foil is attained and serves as the reference. The Taylor bubble is then injected into the pipe. The heat transfer coefficient variations due to the passage of a Taylor bubble propagating in a vertical pipe is measured as function of the distance of the measuring point from the bottom of the moving Taylor bubble. Thus, the results represent the local heat transfer coefficients. Multiple independent runs preformed under identical conditions allow accumulating sufficient data to calculate reliable ensemble-averaged results on the transient convective heat transfer. In order to perform this in a frame of reference moving with the bubble, the location of the bubble along the pipe has to be known at all times. Detailed description of measurements of the length and of the translational velocity of the Taylor bubbles by optical probes is presented.

Self-similar propagation of Hermite-Gauss water-wave pulses.

We demonstrate both theoretically and experimentally propagation dynamics of surface gravity water-wave pulses, having Hermite-Gauss envelopes. We show that these waves propagate self-similarly along an 18-m wave tank, preserving their general Hermite-Gauss envelopes in both the linear and the nonlinear regimes. The measured surface elevation wave groups enable observing the envelope phase evolution of both nonchirped and linearly frequency chirped Hermite-Gauss pulses, hence allowing us to measure Gouy phase shifts of high-order Hermite-Gauss pulses for the first time. Finally, when increasing pulse amplitude, nonlinearity becomes essential and the second harmonic of Hermite-Gauss waves was observed. We further show that these generated second harmonic bound waves still exhibit self-similar Hermite-Gauss shapes along the tank.