A theoretical model is developed for wave heights and set-up in a surf zone. In the time averaged equations of energy and momentum the energy flux, radiation stress and energy dissipation are determined by simple approximations which include the surface roller in the breaker. Comparison with measurements shows good agreement. Also the transitions immediately after breaking are analysed and shown to be in accordance with the above mentioned ideas and results.

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Wave Heights and Set-up in a Surf Zone

The functionalities of the untethered miniature swimming robots significantly decrease as the robot size becomes smaller, due to limitations of feasible miniaturized on-board components. Here we propose an untethered jellyfish-inspired soft millirobot that could realize multiple functionalities in moderate Reynolds number by producing diverse controlled fluidic flows around its body using its magnetic composite elastomer lappets, which are actuated by an external oscillating magnetic field. We particularly investigate the interaction between the robot's soft body and incurred fluidic flows due to the robot's body motion, and utilize such physical interaction to achieve different predation-inspired object manipulation tasks. The proposed lappet kinematics can inspire other existing jellyfish-like robots to achieve similar functionalities at the same length and time scale. Moreover, the robotic platform could be used to study the impacts of the morphology and kinematics changing in ephyra jellyfish.

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Multi-functional soft-bodied jellyfish-like swimming

Air entrainment in liquids is a complex phenomenon that has important applications in industry and the environment. This article addresses recent research on how air is entrained during the impact of a liquid stream on a pool of the same material in a variety of scenarios. At the fundamental level, these scenarios include the prototype flows of impacting stationary laminar and turbulent steady jets, the transient impact of isolated masses of liquid, the impact of jets with organized disturbances, and translating steady and transient jets. Although significant advances have been made recently, the complexity of this multiphase, three-dimensional, and frequently turbulent flow phenomenon leaves many unanswered questions. To help elucidate the problems still to be addressed in future research, the final section of the article examines air entrainment in the more complex application of plunging breaking waves and points out the many parts of this process that are poorly understood.

Air-Entrainment Mechanisms in Plunging Jets and Breaking Waves

Beach response to a sequence of extreme storms

We investigate air entrainment and bubble statistics in three-dimensional breaking waves through novel direct numerical simulations of the two-phase air-water flow, resolving the length scales relevant for the bubble formation problem, the capillary length and the Hinze scale. The dissipation due to breaking is found to be in good agreement with previous experimental observations and inertial-scaling arguments. The air-entrainment properties and bubble-size statistics are investigated for various initial characteristic wave slopes. For radii larger than the Hinze scale, the bubble size distribution, can be described by N (r, t) = B(V 0 /2π)(e(t − ∆τ)/W g)r −10/3 r −2/3 m during the active breaking stages, where e(t − ∆τ) is the time dependent turbulent dissipation rate, with ∆τ the collapse time of the initial air pocket entrained by the breaking wave, W a weighted vertical velocity of the bubble plume, r m the maximum bubble radius, g gravity , V 0 the initial volume of air entrained, r the bubble radius and B a dimensionless constant. The active breaking time-averaged bubble size distribution is described by ¯ N (r) = B(1/2π)(l L c /W gρ)r −10/3 r −2/3 m , where l is the wave dissipation rate per unit length of breaking crest, ρ the water density and L c the length of breaking crest. Finally, the averaged total volume of entrained air, ¯ V , per breaking event can be simply related to l by ¯ V = B(l L c /W gρ), which leads to a relationship to a characteristic slope, S, of ¯ V ∝ S 5/2. We propose a phenomenological turbulent bubble break-up model, based on earlier models and the balance between mechanical dissipation and work done against buoyancy forces. The model is consistent with the numerical results and existing experimental results.

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Air entrainment and bubble statistics in breaking waves

This paper describes detailed measurements and analysis of the time-varying distribution of void fractions in three different breaking waves under laboratory conditions. The measurements were made with highly sensitive optical fibre phase detection probes and document the rapid spatial and temporal evolutions of both the bubble plume generated beneath the free surface and the splashes above. Integral properties of the measured void fraction fields reveal a remarkable degree of similarity between characteristics of the two-phase flow in different breaker types as they evolve with time. Depending on the breaker type, the energy expended in entraining air and generating splash accounts for a minimum of between 6.5 and 14% of the total energy dissipated during wave breaking.

Chris Blenkinsopp

Papers

Void fraction measurements in breaking waves

Measurements of the time-varying free-surface profile across the swash zone obtained using an industrial LIDAR

Net sediment transport and morphological change in the swash zone of a high-energy sandy beach from swash event to tidal cycle time scales

Swash zone sediment transport, step dynamics and morphological response on a gravel beach

Swash zone sediment fluxes: Field observations