It is generally accepted that the evolution of the deep-water surface gravity wave spectrum is governed by quartet resonant and quasi-resonant interactions. However, it has also been reported in both experimental and computational studies that non-resonant triad interactions can play a role, e.g. generation of bound waves. In this study, we investigate the effects of triad and quartet interactions on the spectral evolution, by numerically tracking the contributions from quadratic and cubic terms in the dynamical equation. In a finite time interval, we find that the contribution from triad interactions follows the trend of that from quartet resonances (with comparable magnitude) for most wavenumbers, except that it peaks at low wavenumbers with very low initial energy. This result reveals two effects of triad interactions. (1) The non-resonant triad interactions can be connected to form quartet resonant interactions (hence exhibiting the comparable trend), which is a reflection of the normal form transformation applied in wave turbulence theory of surface gravity waves. (2) The triad interactions can fill energy into the low-energy portion of the spectrum (low wavenumber part in this case) on a very fast time scale, with energy distributed in both bound and free modes at the same wavenumber. We further analyse the latter mechanism using a simple model with two initially active modes in the wavenumber domain. Analytical formulae describing the distribution of energy in free and bound modes are provided, along with numerical validations.

Thermal Marangoni effects play important roles in bubble dynamics such as bubbles generated by water electrolysis or boiling. As macroscopic bubbles often originate from nucleated nanobubbles, it is crucial to understand how thermocapillarity operates at the nanoscale. In this study, the motion of transient bulk gas nanobubbles in water driven by a vertical temperature gradient between two solid plates is investigated using molecular dynamics simulations and analytical theory. The simulation results show that due to the thermal Marangoni force, nanobubbles move towards the hot plate at a constant velocity, similar to the behaviour of macroscale gas bubbles. However, unlike macroscale gas bubbles whose thermal conductivity and viscosity are negligible compared to those of water, the thermal conductivity and viscosity of nanoscale gas bubbles are significantly increased due to their large gas density. The thermal resistance and the slip length are also found to matter at the liquid–gas interface, though they decrease with increasing gas densities. The previous thermocapillary theory for macroscale bubbles is extended by considering all these nanoscopic effects. Expressions of the Marangoni force and the drag force are derived. By balancing the Marangoni force and the drag force, the theoretical velocity of the nanobubble migration in a thermal gradient is obtained. When using the measured transport properties of liquid, gas, and their interfaces, the theoretically obtained velocity is consistent with the result of the molecular simulations. We find that the slip length is too small to have considerable effects on nanobubble motions in the current liquid–gas system.

An important feature of the dynamics of double-diffusive fluids is the spontaneous formation of thermohaline staircases, where wide regions of well-mixed fluid are separated by sharp density interfaces. Recent developments have produced a number of one-dimensional reduced models to describe the evolution of such staircases in the salt fingering regime relevant to mid-latitude oceans; however, there has been significantly less work done on layer formation in the diffusive convection regime. We aim to fill this gap by presenting a new model for staircases in diffusive convection based on a regularisation of the $\gamma$-instability (Radko 2003 J. Fluid Mech. vol. 805, 147–170), with a range of parameter values relevant to both polar oceans and astrophysical contexts. We use the results of numerical simulations to inform turbulence-closure parametrisations as a function of the horizontally averaged kinetic energy $e$, and ratio of the haline to thermal gradients $R_0^*$. These parametrisations result in a one-dimensional model that reproduces the critical value of $R_0^*$ for the layering instability, and the spatial scale of layers, for a wide range of parameter values, although there is a mismatch between the range of $R_0^*$ for layer formation in the model and observational values from polar oceans. Staircases form in the one-dimensional model, evolving gradually through layer merger events that closely resemble simulations.

Surface gravity waves induce a drift on objects floating on the water’s surface. This study presents laboratory experiments investigating the drift of large two-dimensional floating objects on deep-water, unidirectional, regular waves, with wave steepness ranging from 0.04 to 0.31 (0.04 $\lt k{a_w}\lt$ 0.31, where $k$ is the wavenumber and $a_w$ the wave amplitude). The objects were carefully designed to have a rectangular cross-section with a constant aspect ratio; their size varied from 2.6 $\%$ to 27 $\%$ of the incident wavelength. We observed Lagrangian behaviour for small objects. Small and large objects exhibited fundamentally different drift behaviour at high compared with low wave steepness, with a regime shift observed at a certain size and wave steepness. The scaling of object drift with steepness depends on the relative size of the object. For small objects, drift scales with steepness squared, whereas drift becomes a linear function of steepness as the object size increases. For objects that are relatively large but smaller than 13–16% of a wavelength (low to high steepness), we provide experimental evidence supporting the mechanisms of drift enhancement recently identified by Xiao et al. (J. Fluid Mech., vol. 980, 2024, p. A27) and termed the ‘diffraction-modified Stokes drift’. This enhanced drift behaviour, compared with the theoretical Stokes drift for infinitely small fluid parcels, is attributed to changes in the objects’ oscillatory motion and local wave amplitude distribution (standing wave pattern) due to the presence of the object. In the case of larger objects, similar to Harms (J. Waterw. Port Coast. Ocean Eng., vol. 113(6), 1987, pp. 606–622), we relate the critical size at which drift is maximised to their vertical bobbing motion. We determine the domain of validity for both Stokes drift and the diffraction-modified Stokes drift model of Xiao et al. (J. Fluid Mech., vol. 980, 2024, A27) in terms of relative size and wave steepness and propose an empirical parametrisation based on our experimental data.