Thermoacoustic internal gravity wave turbulence in the Earth's lower atmosphere

We propose, for the first time, a two-dimensional model for the nonlinear coupling of internal gravity and thermal waves in the presence of temperature-dependent density inhomogeneity due to thermal expansion and thermal feedback in stratified fluids of the Earth's lower atmosphere ($0-50$ km). Such a coupling gives rise to the evolution of thermoacoustic internal gravity waves (IGWs), which are distinctive from the known IGWs in the literature. We perform numerical simulations to study the nonlinear interactions of velocity and density perturbations associated with the IGWs and thermal fluctuations corresponding to the thermal mode. We show that solitary vortices of IGWs coupled to the thermal wave can lead to thermoacoustic turbulence. We observe the formation of large-scale velocity potential flows and small-scale structures in the density and temperature profiles. Interestingly, while the wave energy spectra exhibit power laws: $k_x^{-1.67}$ and $k_z^{-2.89}$, respectively, for horizontal and vertical wave numbers, in the troposphere ($0-15$ km) with negative temperature gradient, the same in the stratosphere ($15-50$ km) with positive temperature gradient tend to relax toward $k_x^{-1.83}$-horizontal and $k_z^{-1.03}$-vertical spectra. We find that while the energy spectra in the tropospheric turbulence are consistent with the observed phenomena without temperature gradients, those in the stratosphere differ.