A millimetric droplet bouncing on the surface of a vibrating fluid bath can self-propel by virtue of a resonant interaction with its own wave field (Couder et al. 2005a;Protière et al. 2006). This system represents the first known example of a pilot-wave system of the form envisaged by Louis de Broglie in his double-solution pilot-wave theory (de Broglie 1930(de Broglie , 1956(de Broglie , 1987. We here develop a numerical model of pilot-wave hydrodynamics by coupling recent models of the droplet's bouncing dynamics (Moláček & Bush 2013a,b) with a more realistic model of weakly viscous wave generation and evolution. (Lamb 1932;Dias et al. 2008). The resulting model is the first to capture a number of features reported in experiment, including the rapid transient wave generated during impact, the Doppler effect, and walker-walker interactions.

296As interest in the aquatic cycle of organic carbon (OC) has increased, the deployment of in situ optical sensors to measure CDOM fluorescence (chromophoric dissolved organic matter) as a proxy for OC concentration has become more common (e.g., Downing et al. 2009;Sandford et al. 2010). CDOM sensors typically use UV light (~350 nm) to excite the emission of blue light (~450 nm) from certain organic fluorophores, allowing investigators to distinguish CDOM from more commonly measured phytoplankton pigments. Given that CDOM may be more labile than previously thought and given that rates of OC mineralization may vary with fluctuating environmental factors, such as temperature and light, these inexpensive sensors could afford a substantial advantage over traditional wet chemistry methods-provided that the artifactual effects of environmental factors on fluorescence efficiency are well constrained (Graneli et al. 1996;Bertilsson and Tranvik 2000;Bastviken et al. 2004;Hanson et al. 2003;Vahatalo 2009).Here, we quantify the effect of temperature on the fluorescence of CDOM from two dystrophic Wisconsin lakes and an aquatic NOM reference material. Based on laboratory experiments over a wide range of OC concentrations, we derive a function that can be used to standardize CDOM measurements to any reference temperature (and, thereby, remove the effect of temperature variation on CDOM fluorescence). Using a reference temperature of 20°C, we then apply the function to field data and show how temperature compensation affects temporal changes in CDOM fluorescence under natural conditions. Methods and proceduresTwo commercial CDOM fluorometers were used: 1) the C3 Submersible Fluorometer from TurnerDesigns, Inc.; and 2) the ), and the subscripts r and m stand for the reference and measured values. (We note that an analogous function is used widely to calculate temperature-specific conductance from the measured conductivity of natural waters.) For the two sensors we tested, the temperature-specific fluorescence coefficients (r) were -0.015 ± 0.001 and -0.008 ± 0.0008 for Wisconsin bog waters at 20°C. When applied to field data, temperature compensation removed the effect of multi-day trends in water temperature, and it also damped the diel CDOM cycle. We conclude that temperature compensation is a necessary and important aspect of CDOM monitoring using in situ fluorescence sensors.

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.

In this paper, the unsteady evolution of two-dimensional fully nonlinear free-surface gravity–capillary solitary waves is computed numerically in infinite depth. Gravity–capillary wavepacket-type solitary waves were found previously for the full Euler equations, bifurcating from the minimum of the linear dispersion relation. Small and moderate amplitude elevation solitary waves, which were known to be linearly unstable, are shown to evolve into stable depression solitary waves, together with a radiated wave field. Depression waves and certain large amplitude elevation waves were found to be robust to numerical perturbations. Two kinds of collisions are computed: head-on collisions whereby the waves are almost unchanged, and overtaking collisions which are either almost elastic if the wave amplitudes are both large or destroy the smaller wave in the case of a small amplitude wave overtaking a large one.

A droplet may ‘walk’ across the surface of a vertically vibrating bath of the same fluid, due to the propulsive interaction with its wave field. This hydrodynamic pilot-wave system exhibits many dynamics previously believed to exist only in the quantum realm. Starting from first principles, we derive a discrete-time fluid model, whereby the bath–droplet interactions are modelled as instantaneous. By analysing the stability of the fixed points of the system, we explain the dynamics of a walking droplet and capture the quantisations for multiple-droplet interactions. Circular orbits in a harmonic potential are studied, and a double quantisation of chaotic trajectories is obtained through systematic statistical analysis.