Abstract
Inertial gravity wave radiation from an unsteady rotational flow (spontaneous radiation) is investigated numerically in an f-plane shallow water system for a wide range of Rossby numbers, 1 ≤ Ro ≤ 1000, and Froude numbers, 0.1 ≤ Fr ≤ 0.8. A barotropically unstable jet flow is initially balanced and maintained by forcing so that spontaneous gravity wave radiation is generated continuously. The amount of gravity wave flux is proportional to Fr for large Ro(≥30), which is consistent with the power law of the aeroacoustic sound wave radiation theory (the Lighthill theory). In contrast, for small Ro(≤10) this power law does not hold because of the vortex stabilization due to the small deformation radius. In the case of fixed Fr, gravity wave flux is almost constant for larger Ro(>30) and decreases rapidly for smaller Ro(<5). There is a local maximum value between these Ro(∼10). Spectral frequency analysis of the gravity wave source shows that for Ro = 10, while the source term related to the earth’s rotation is larger than that related to unsteady rotational flow, the inertial cutoff frequency is still lower than the peak frequency of the dominant source. The results suggest that the effect of the earth’s rotation may intensify spontaneous gravity wave radiation for Ro ∼ 10.
Time Integration of Shallow Water Equations in the Gravity Wave Regime
