Tropical background and wave spectra: contribution of wave-wave interactions in a moderately nonlinear turbulent flow

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  • 1 The Fredy and Nadine Herrmann Institute of Earth Sciences, Hebrew University of Jerusalem, Jerusalem, Israel
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Abstract

Variability in the tropical atmosphere is concentrated at wavenumber-frequency combinations where linear theory indicates wave-modes can freely propagate, but with substantial power in between. This study demonstrates that such a power spectrum can arise from small scale convection triggering large scale waves via wave-wave interactions in a moderately turbulent fluid. Two key pieces of evidence are provided for this interpretation of tropical dynamics using a nonlinear rotating shallow water model: a parameter sweep experiment in which the amplitude of an external forcing is gradually ramped up, and also an external forcing in which only symmetric or only anti-symmetric modes are forced. These experiments do not support a commonly accepted mechanism involving the forcing projecting directly onto the wave-modes with a strong response, yet still simulate a power spectrum resembling that observed, though the linear projection mechanism could still complement the mechanism proposed here in observations. Interpreting the observed tropical power spectrum using turbulence offers a simple explanation as to why power should be concentrated at the theoretical wave-modes, and also provides a solid footing for the common assumption that the back-ground spectrum is red, even as it clarifies why there is no expectation for a turbulent cascade with a specific, theoretically derived slope such as -5/3. However it does explain why the cascade should be towards lower wavenumbers, that is an inverse energy cascade, similar to the midlatitudes even as compressible wave-modes are important for tropical dynamics.

Corresponding author address: Fredy and Nadine Herrmann Institute of Earth Sciences, Hebrew University of Jerusalem, Edmond J. Safra Campus, Givat Ram, Jerusalem, 91904 Israel. E-mail: nathan.paldor@mail.huji.ac.il

Abstract

Variability in the tropical atmosphere is concentrated at wavenumber-frequency combinations where linear theory indicates wave-modes can freely propagate, but with substantial power in between. This study demonstrates that such a power spectrum can arise from small scale convection triggering large scale waves via wave-wave interactions in a moderately turbulent fluid. Two key pieces of evidence are provided for this interpretation of tropical dynamics using a nonlinear rotating shallow water model: a parameter sweep experiment in which the amplitude of an external forcing is gradually ramped up, and also an external forcing in which only symmetric or only anti-symmetric modes are forced. These experiments do not support a commonly accepted mechanism involving the forcing projecting directly onto the wave-modes with a strong response, yet still simulate a power spectrum resembling that observed, though the linear projection mechanism could still complement the mechanism proposed here in observations. Interpreting the observed tropical power spectrum using turbulence offers a simple explanation as to why power should be concentrated at the theoretical wave-modes, and also provides a solid footing for the common assumption that the back-ground spectrum is red, even as it clarifies why there is no expectation for a turbulent cascade with a specific, theoretically derived slope such as -5/3. However it does explain why the cascade should be towards lower wavenumbers, that is an inverse energy cascade, similar to the midlatitudes even as compressible wave-modes are important for tropical dynamics.

Corresponding author address: Fredy and Nadine Herrmann Institute of Earth Sciences, Hebrew University of Jerusalem, Edmond J. Safra Campus, Givat Ram, Jerusalem, 91904 Israel. E-mail: nathan.paldor@mail.huji.ac.il
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