ALBERT

Description: 〈div data-abstract-type="normal"〉〈p〉Parametrically forced gravity waves can give rise to high-velocity surface jets via the wave-depression cavity implosion. The present results have been obtained in circular cylindrical containers of 10 and 15 cm in diameter (Bond number of order 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190304144947658-0960:S0022112019000867:S0022112019000867_inline1.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉) in the large fluid depth limit. First, the phase diagrams of instability threshold and wave breaking conditions are determined for the working fluid used, here water with 1 % detergent added. The collapse of the wave-depression cavity is found to be self-similar. The exponent 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190304144947658-0960:S0022112019000867:S0022112019000867_inline2.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉 of the variation of the cavity radius 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190304144947658-0960:S0022112019000867:S0022112019000867_inline3.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉 with time 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190304144947658-0960:S0022112019000867:S0022112019000867_inline4.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉, in the form 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190304144947658-0960:S0022112019000867:S0022112019000867_inline5.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉, is close to 0.5, indicative of inertial collapse, followed by a viscous cut-off of 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190304144947658-0960:S0022112019000867:S0022112019000867_inline6.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉. This supports a Froude number scaling of the surface jet velocity caused by cavity collapse. The dimensionless jet velocity scales with the cavity depth that is shown to be proportional to the last stable wave amplitude. It can be expressed by a power law or in terms of finite time singularity related to a singular wave amplitude that sets the transition from a non-pinching to pinch-off cavity collapse scenario. In terms of forcing amplitude, cavity collapse and jetting are found to occur in bands of events of non-pinching and pinching of a bubble at the cavity base. At large forcing amplitudes, incomplete cavity collapse and splashing can occur and, at even larger forcing amplitudes, wave growth is again stable up to the singular wave amplitude. When the cavity is formed, an impulse model shows the importance of the singular cavity diameter that determines the strength of the impulse.〈/p〉〈/div〉

Description: In this paper we present results on parametrically forced gravity waves in a circular cylinder in the limit of large fluid-depth approximation. The phase diagram that shows the stability-forcing-amplitude threshold and the wave-breaking threshold has been determined in the frequency range of existence of the lowest axisymmetric wave mode. The instability is shown to be supercritical for forcing frequencies at and above the natural frequency and subcritical below in a frequency range where the instability and breaking thresholds do not coincide. Above the instability threshold, the growth in wave amplitude is exponential, but with an initial time delay. The wave-amplitude response curve of stationary wave motions exhibits steady-state wave motion, amplitude modulations and bifurcations to other wave modes at frequencies where the parametric instability boundary of the axisymmetric mode overlaps with the neighbouring modes. The amplitude modulations are either on a slow time scale or exhibit period tripling and intermittent period tripling, without wave breaking. In the wave-breaking regime, a finite-time singularity may occur with intense jet formation, a phenomenon demonstrated by others in fluids of high viscosity and large surface tension. Here, this singular behaviour with jet formation is demonstrated for a low viscosity and low kinematic surface tension liquid. The results indicate that the jet is driven by inertial collapse of the cavity created at the wave trough. Therefore, the jet velocity is determined by the wave fluid velocity but depends, in addition, on kinematic surface tension and viscosity as these affect the last stable wave crest shape and the cavity size. © 2008 Cambridge University Press.

Description: We present new local groundwater-level rise data from two Late Glacial aeolian dunes, located near Barendrecht and Oud-Alblas in the western Rhine-Meuse delta. These data are based on AMS radiocarbon dating of terrestrial macrofossils, collected from the base of peat formed on the slopes of these dunes. This method avoids contamination of bulk peat samples by old soil carbon or younger rootlets and rhizomes, as well as the hardwater effect. The new data are used to assess the reliability of previously published groundwater-level index data based on conventional radiocarbon dating of bulk basal peat samples from the slopes of the Late Glacial aeolian dunes at Barendrecht, Hillegersberg, Bolnes and Wijngaarden, all located in the western Rhine-Meuse delta.Comparison of the new and published groundwater-level data shows no significant systematic difference between conventionally dated bulk peat samples and AMS-dated samples of terrestrial macrofossils. The new data from the dune at Barendrecht confirm the reliability of the younger than 6600 cal yr BP age-depth data from the dunes at Hillegersberg and near Bolnes. This result supports the validity of this part of the mean sea-level (MSL) curve for the western Netherlands. Consequently, the position of the groundwater-level curve for Flevoland (central Netherlands) below this MSL curve can most likely be attributed to differential land-level movement.The available data show that the groundwater-gradient effect in the western Rhine-Meuse delta became less than 5 cm/km after 6600 cal yr BP. Finally, temporal correlation between temporary increases in local groundwater-level rise with known shifts of river courses in the delta plain suggests, that avulsions can explain sudden local deviations from the trend in groundwater-level rise. A general conclusion of this study is that a complex relationship exists between sea level and local delta-plain water levels.

Description: Parametrically forced gravity waves can give rise to high-velocity surface jets via the wave-depression cavity implosion. The present results have been obtained in circular cylindrical containers of 10 and 15 cm in diameter (Bond number of order 103) in the large fluid depth limit. First, the phase diagrams of instability threshold and wave breaking conditions are determined for the working fluid used, here water with 1% detergent added. The collapse of the wave-depression cavity is found to be self-similar. The exponent α of the variation of the cavity radius rm with time τ, in the form rm=R/α τ α, is close to 0.5, indicative of inertial collapse, followed by a viscous cut-off of α ∼ 1. This supports a Froude number scaling of the surface jet velocity caused by cavity collapse. The dimensionless jet velocity scales with the cavity depth that is shown to be proportional to the last stable wave amplitude. It can be expressed by a power law or in terms of finite time singularity related to a singular wave amplitude that sets the transition from a non-pinching to pinch-off cavity collapse scenario. In terms of forcing amplitude, cavity collapse and jetting are found to occur in bands of events of non-pinching and pinching of a bubble at the cavity base. At large forcing amplitudes, incomplete cavity collapse and splashing can occur and, at even larger forcing amplitudes, wave growth is again stable up to the singular wave amplitude. When the cavity is formed, an impulse model shows the importance of the singular cavity diameter that determines the strength of the impulse. © 2019 Cambridge University Press.

Description: Flexural-gravity wave characteristics are analysed, in the presence of a compressive force and a two-layer fluid, under the assumption of linearized water wave theory and small amplitude structural response. The occurrence of blocking for flexural-gravity waves is demonstrated in both the surface and internal modes. Within the threshold of the blocking and the buckling limit, the dispersion relation possesses four positive roots (for fixed wavenumber). It is shown that, under certain conditions, the phase and group velocities coalesce. Moreover, a wavenumber range for certain critical values of compression and depth is provided within which the internal wave energy moves faster than that of the surface wave. It is also demonstrated that, for shallow water, the wave frequencies in the surface and internal modes will never coalesce. It is established that the phase speed in the surface and internal modes attains a minimum and maximum, respectively, when the interface is located approximately in the middle of the water depth. An analogue of the dead water phenomenon, the occurrence of a high amplitude internal wave with a low amplitude at the surface, is established, irrespective of water depth, when the densities of the two fluids are close to each other. When the interface becomes close to the seabed, the dead water effect ceases to exist. The theory developed in the frequency domain is extended to the time domain and examples of negative energy waves and blocking are presented. © 2018 Cambridge University Press.

Description: The equilibrium shape of liquid drops on elastic substrates is determined by minimizing elastic and capillary free energies, focusing on thick incompressible substrates. The problem is governed by three length scales: the size of the drop R, the molecular size a and the ratio of surface tension to elastic modulus γ/E. We show that the contact angles undergo two transitions upon changing the substrate from rigid to soft. The microscopic wetting angles deviate from Young's law when γ/(Ea) 1, while the apparent macroscopic angle only changes in the very soft limit γ/(ER) 1. The elastic deformations are worked out for the simplifying case where the solid surface energy is assumed to be constant. The total free energy turns out to be lower on softer substrates, consistent with recent experiments. © 2014 Cambridge University Press.