Status: this preprint is open for discussion and under review for Nonlinear Processes in Geophysics (NPG).
Stationary Solutions and Oscillatory Dynamics in a Mathematical Model of a Saturated Moist Atmosphere
Dalila Remaoun Bourega
Abstract. This paper investigates the mathematical properties of a simplified atmospheric system describing vertical air flows with water condensation. We provide a rigorous proof for the existence and uniqueness of the stationary solution under specific technical conditions. Numerical simulations reveal damped oscillations in the air flow intensity and liquid water content, interpreted as a self-regulating physical cycle driven by latent heat and droplet accumulation. By establishing a qualitative analogy with a Volterra integro-differential equation, we demonstrate that these oscillations are governed by memory effects. The convergence of the evolutionary variables toward the stationary values provides a robust validation of the model's consistency.
Received: 08 May 2026 – Discussion started: 22 May 2026
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This work studies a mathematical model of atmospheric convection with water condensation. We prove existence and uniqueness of a stationary solution for a nonlinear differential system governing vertical air flow. Numerical simulations reveal damped oscillations in flow intensity and liquid water content, driven by latent heat and droplet accumulation. A qualitative analogy with a Volterra integro-differential equation explains the memory-driven oscillatory dynamics underlying storm formation.
This work studies a mathematical model of atmospheric convection with water condensation. We...
