The modulation of short gravity waves by long waves or currents

Modulation of subtropical stratospheric gravity waves by equatorial rainfall

Internal gravity waves influence a variety of phenomena in Earth’s stratosphere and upper troposphere, including aviation weather turbulence and circulations that set high-altitude distributions of ozone and greenhouse gases. Here coupling between the dominant mode of subseasonal variability of the equatorial atmosphere—the Madden-Julian oscillation (MJO)—and subtropical stratospheric gravity w...

The suppression of short waves by a train of long waves

The Rigorous Approximation of Long-Wavelength Capillary-Gravity Waves

In a previous paper we proved that long-wavelength solutions of the waterwave problem in the case of zero surface tension split up into two wave packets, one moving to the right and one to the left, where each of these wave packets evolves independently as a solution of a Korteweg-de Vries (KdV) equation. In this paper we examine the effect of surface tension on this scenario. We find that we o...

Bending of Light by Gravity Waves

We describe the statistical properties of light rays propagating though a random sea of gravity waves and compare with the case for scalar metric perturbations from density inhomogeneities. For scalar fluctuations the deflection angle grows as the square-root of the path length D in the manner of a random walk, and the rms displacement of a ray from the unperturbed trajectory grows as D. For gr...

Waves on unsteady currents

Models for surface gravity wave propagation in the presence of currents often assume the current field to be quasi-stationary, which implies that the absolute wave frequency is time invariant. However, in the presence of unsteady currents or time-varying water depth, linear wave theory predicts a time variation of the absolute wave frequency and wavenumber . Herein, observations of wave frequen...