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.