On the interaction between Kelvin waves at different phase speeds and the background flow

Abstract

AbstractKelvin waves have been theorized to be absorbed near the critical layer, where the phase speed matches the speed of the background flow. Nevertheless, it is not clear through observations how the structure of the Kelvin waves evolves near the critical layer or in response to vertical wind shear with or without a critical layer. A novel varying‐coefficient regression technique that has been used to study evolving relationships across the seasonal cycle is used to capture how the wavelet‐filtered waves with a specific phase speed appear in different background winds or vertical shear regimes or a combination of both. Results show a relaxation of the in‐phase relationship between the zonal wind and geopotential height anomalies at slower Doppler‐shifted speeds, followed by the appearance of the Gill pattern at further reduction of the Doppler‐shifted speed, demonstrating a lack of dominant Kelvin wave signals in those conditions. We define the “observed critical layer” as the layer where the signals consistent with Kelvin waves fade away irrespective of the value of the Doppler‐shifted speed, which reduces to zero at the “theoretical critical layer.” Results show that wave structures consistent with Kelvin waves are not present at the top of layer with westerly vertical shear of the zonal wind, yet they exist during the easterly vertical shear of the zonal wind. The second part of the paper presents the dispersion equation of the Kelvin wave under vertical wind shear. The phase speed of the Kelvin wave proportionally increases with the Richardson number (and hence proportionally decreases with the vertical wind shear). The Richardson number varies with the vertical resolution of the data used, adding uncertainty to the calculated phase speed of the wave in the presence of vertical wind shear.