Flow structure beneath rotational water waves with stagnation points

The purpose of this work is to explore in detail the structure of the interior flow generated by periodic surface waves on a fluid with constant vorticity. The problem is mapped conformally to a strip and solved numerically using spectral methods. Once the solution is known, the streamlines, pressure and particle paths can be found and mapped back to the physical domain. We find that the flow beneath the waves contains zero, one, two or three stagnation points in a frame moving with the wave speed, and describe the bifurcations between these flows. When the vorticity is sufficiently strong, the pressure in the flow and on the bottom boundary also has very different features from the usual irrotational wave case.

The time evolution of the maximal horizontal surface fluid velocity for an irrotational wave approaching breaking

We derive an equation that relates the evolution in time of the maximum of the horizontal fluid velocity at the surface of an irrotational deep-water plunging or spilling breaker to the first component of the pressure gradient at the surface. The approach applies to overhanging wave profiles, up to breaking time.

Analysis of Road Capacity Based on Traffic Volatility Models

Establishing traffic fluctuation model considering different factors: learning from fluid mechanics, in the initial state on the basis of the length of the team, apply irrotational wave that characterize the condition of vehicle’s congestion and ease to characterize the dynamic changes of vehicle queue lengths and to build volatility traffic model. From the perspective of factors that the effect wave propagation velocity, research the model into two conditions: whether the new vehicles and the originals can meet at the upstream of the cross section of the accident or not. In the meantime, in each situation, interception intersection’s signal cycle as calculation period to simulate cycle data towards time.

WHEN DO WAVES BECOME TURBULENT?

Babanin and Haus (2009) recently presented evidence of high levels of turbulence induced by steep non-breaking waves. They proposed a Reynolds-like threshold wave parameter (a2ω/ν=3000, a wave amplitude, ω wave angular frequency, ν water viscosity) for the spontaneous occurrence of turbulence beneath surface waves. This contradicts the common assumed basis of existing irrotational wave theories and their classical experimental validation. Many laboratory wave experiments were carried out in the early 1960’s (e.g. Wiegel, 1964). In those experiments no evidence of turbulence was reported and steep waves behaved as predicted by the high order irrotational wave theories within the accuracy of the theories and experimental techniques at the time. The spontaneous generation of turbulence under waves can have serious consequences for wave modelling, where the irrotational flow assumption has secured its place in engineering design. This contribution describes unique flow visualisation experiments for large scale steep non-breaking waves using conventional dye techniques in the wave boundary layer extending above the wave trough level. The measurements showed no evidence of turbulent mixing for waves up to a2ω/ν=7000. There is presently no evidence that water waves become spontaneously turbulent (up a2ω/ν=7000) except within the bed boundary layers, under wind forcing or at breaking. Excellent agreement was found with higher order irrotational theories. Orbital velocities, Stokes drift and Stokes coefficients were measured and compared with theoretical values, suggesting that conventional theories underestimate unforced monochromatic wave non-linearity, although the corrections remain small.

Crest instabilities of gravity waves. Part 2. Matching and asymptotic analysis

In a previous study (Longuet-Higgins & Cleaver 1994) we calculated the stability of the flow near the crest of a steep, irrotational wave, the ‘almost-highest’ wave, considered as an isolated wave crest. In the present paper we consider the modification of this inner flow when it is matched to the flow in the rest of the wave, and obtain the normal-mode perturbations of the modified inner flow. It is found that there is just one exponentially growing mode. Its rate of growth β is a decreasing function of the matching parameter ε and hence a decreasing function of the wave steepness ak. When compared numerically to the rates of growth of the lowest superharmonic instability in a deep-water wave as calculated by Tanaka (1983) it is found that the present theory provides a satisfactory asymptote to the previously calculated values of the growth rate. This suggests that the instability of the lowest superharmonic is essentially due to the flow near the crest of the wave.

THE METHOD OF GENERALIZED REFLECTION AND TRANSMISSION COEFFICIENTS

The objective of this work is to provide a method for predicting the surface response of a stratified half space to the radiation from a localized source when neither the assumptions of the plane wave theory nor the assumptions of the normal mode theory are valid. The earth model consists of a finite number of perfectly elastic, homogeneous, isotropic layers separated by interfaces which are plane and parallel to one another. The method leads to an infinite series for the Laplace transform of the response function (displacement, velocity, stress, etc.) in a multi‐interface system. Each term in the series describes all the energy which traverses a particular generalized ray path between the source and the receiver. The specification of the mode of propagation across each stratum (either as an irrotational wave or as an equivoluminal wave) and of the sequence in which the strata are traversed serve to define a generalized ray path. A prescription is given for constructing the integral representation for the disturbance which has traversed such a path directly from the integral representation for the source radiation. The method therefore obviates the necessity for solving a tedious boundary value problem. The time function associated with each term can be obtained by using Cagniard’s method.