Numerical Simulations of Internal Wave Generation by Convection in Water

TL;DR

This study uses numerical simulations to analyze how internal gravity waves are generated by convection in water near its density maximum, confirming that bulk excitation by Reynolds stresses accurately models wave generation.

Contribution

The paper introduces a novel spectral code simulation approach to distinguish physical mechanisms of internal wave excitation, validating bulk excitation as a key process.

Findings

Bulk excitation by Reynolds stresses matches full simulation results.

Interface forcing overestimates high-frequency wave generation.

Physical excitation occurs via plume sweeping, not impulsive penetration.

Abstract

Water's density maximum at 4C makes it well suited to study internal gravity wave excitation by convection: an increasing temperature profile is unstable to convection below 4C, but stably stratified above 4C. We present numerical simulations of a water-like fluid near its density maximum in a two dimensional domain. We successfully model the damping of waves in the simulations using linear theory, provided we do not take the weak damping limit typically used in the literature. In order to isolate the physical mechanism exciting internal waves, we use the novel spectral code Dedalus to run several simplified model simulations of our more detailed simulation. We use data from the full simulation as source terms in two simplified models of internal wave excitation by convection: bulk excitation by convective Reynolds stresses, and interface forcing via the mechanical oscillator effect. We find excellent agreement between the waves generated in the full simulation and the simplified simulation implementing the bulk excitation mechanism. The interface forcing simulations over excite high frequency waves because they assume the excitation is by the "impulsive" penetration of plumes, which spreads energy to high frequencies. However, we find the real excitation is instead by the "sweeping" motion of plumes parallel to the interface. Our results imply that the bulk excitation mechanism is a very accurate heuristic for internal wave generation by convection.