Simulations of Convective Excitation of Internal Waves in Water

Abstract:

Convection adjacent to stable stratification can excite internal waves. These convectively excited internal waves can transport energy, momentum, and other quantities in a variety of geophysical and atmospherical contexts, including in the Earth's stratosphere, and the radiative zones of stars. To better understand the excitation mechanism, we perform simplified 2D simulations of a recent experiment by Perrard et al. (2013). The simulations are run using the new, very flexible, pseudo-spectral code Dedalus. The experiment and simulations exploit water's density maximum at 4C: a linear temperature profile includes both convectively unstable and stably stratified regions. The simulations and experiment show qualitatively similar excitation spectra. We then test two heuristic models of internal wave excitation by convection, the interface forcing mechanism and the deep excitation mechanism. To test these, we run linear simulations of the simulation. In one case, we solve the linear wave equation, with a boundary condition mimicking the motions of the interface from the simulations. This successfully reproduces the low frequency waves, but overestimates the excitation of high frequency waves. This is because high frequency convective motions are nonlinear, but the interface forcing simulation treats them as linear. Next, we test the deep excitation mechanism by solving the linear wave equation with a source term related to the Reynolds stress in the convective region. This successfully reproduces all waves, and the correlation between the linear model and the full simulation is about 0.95. This suggests that the deep excitation mechanism most accurately explains the wave generation in this system.