Upward and downward atmospheric Kelvin waves over the Indian Ocean

Abstract

Stratospheric Kelvin waves are often understood as plane gravity waves, yet tropospheric Kelvin waves have been interpreted as a superposition between the baroclinic modes. Fourier filtering is used to decompose the ECMWF‐Interim reanalysis dynamical fields into upward and downward propagating components. Then wavelet regression is used to isolate the propagating Kelvin waves over the Indian Ocean across different speeds at zonal wavenumber 4. Results for fast waves show dry upward‐phase signal in the troposphere, while downward‐phase Kelvin waves occupy most of the stratosphere. The presence of upward‐phase tilted waves in the troposphere suggests that the tropospheric Kelvin wave is not a superposition of the upward and downward components, as one might expect in a normal mode. We found that propagating Kelvin waves in the troposphere obey gravity wave dynamics with geopotential height in phase with the zonal wind, the vertical velocity out of phase with the zonal wind, and the temperature in quadrature with the zonal wind. Both dry and moist tropospheric Kelvin waves show a westward vertical tilt, suggesting that tilt probably cannot be a superposition between baroclinic modes coupled to convective and stratiform heating. In the context of radiating gravity waves, results suggest that faster tropospheric Kelvin waves appear to be associated with higher Brunt–Väisälä frequencies, and waves maintain similar vertical tilt across a wide range of phase speeds.

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

“…Contrary to the common technique of filtering Kevin waves between two distinct equivalent depths, frequencies, and wave numbers using the Fourier transform (Wheeler and Kiladis, 1999; Wheeler et al ., 2000), data are filtered at a specific phase speed and wave number using wavelet filtering to study the interaction of the wave signal at a particular phase speed with a predetermined speed or vertical shear of the background flow, as we discuss in Section 3.2. The wavelet kernel is designed following Paul (2017b) and Ahmed and Roundy (2021) as a two‐dimensional array – see Equation () – where the rows and the columns represent the time $$$ t $$$ and longitude $$$ x $$$: $$$$ {\displaystyle \begin{array}{cc}\psi \left(x,t\right)& =\frac{1}{\sqrt{a\uppi}}\frac{1}{\sqrt{b\uppi}}\cos \left[2\uppi \left({f}_xx-{f}_tt\right)\right]\\ {}& \kern1em \times \exp \left(-\frac{x^2}{b}\right)\exp \left(-\frac{t^2}{a}\right)\end{array}} $$$$ …”

“…Contrary to the common technique of filtering Kevin waves between two distinct equivalent depths, frequencies, and wave numbers using the Fourier transform (Wheeler and Kiladis, 1999;Wheeler et al, 2000), data are filtered at a specific phase speed and wave number using wavelet filtering to study the interaction of the wave signal at a particular phase speed with a predetermined speed or vertical shear of the background flow, as we discuss in Section 3.2. The wavelet kernel is designed following Paul (2017b) and Ahmed and Roundy (2021) as a two-dimensional array -see Equation ( 1) -where the rows and the columns represent the time t and longitude x:…”

“…$$ For stratospheric (upward energy) Kelvin waves, $$$ \omega /k=-N/m $$$, where $$$ m<0 $$$. For tropospheric (downward energy) Kelvin waves, $$$ \omega, k=N/m $$$, where $$$ m>0 $$$, under the assumption that the tropopause is not a rigid lid (Ahmed and Roundy, 2021).…”