This paper presents a dynamical model to explain the stratospheric sudden warming phenomenon, focusing on the interaction between vertically propagating planetary waves and zonal winds. The model suggests that global-scale disturbances in the troposphere propagate into the stratosphere, where they decelerate the polar night jet, leading to the breakdown of the polar vortex. If the disturbance is intense and persistent, it can eventually lead to the disappearance of the westerly jet and the formation of an easterly wind, resulting in "critical layer interaction." This interaction further intensifies the easterly wind and causes rapid warming of the polar air. The model is validated through numerical integrations of the adiabatic-geostrophic potential vorticity equation, showing results similar to observed sudden warming phenomena. The introduction reviews previous studies on the sudden warming, highlighting the role of planetary-scale disturbances and the importance of wave propagation and interaction with zonal winds. The mechanism of the model is discussed, including the propagation of planetary waves and their interaction with zonal winds, with specific attention to the Charney-Drazin theorem and the acceleration of zonal winds by planetary waves. The basic equations used in the model are derived, and the initial conditions, boundary conditions, and forcing function are specified. Numerical integrations are performed under various conditions to test the model's validity. The results show that the model captures key features of the sudden warming event, such as the weakening and breakdown of the polar vortex, the appearance of circumpolar easterly winds, and the rapid warming of the polar air. Finally, the model's results are compared with observations from the 1963 sudden warming event, showing similarities in the evolution of the event but also discrepancies in the temperature distributions and the timing of certain phenomena. The paper concludes by discussing the limitations of the model and suggesting areas for further research, particularly on wave-wave interactions.This paper presents a dynamical model to explain the stratospheric sudden warming phenomenon, focusing on the interaction between vertically propagating planetary waves and zonal winds. The model suggests that global-scale disturbances in the troposphere propagate into the stratosphere, where they decelerate the polar night jet, leading to the breakdown of the polar vortex. If the disturbance is intense and persistent, it can eventually lead to the disappearance of the westerly jet and the formation of an easterly wind, resulting in "critical layer interaction." This interaction further intensifies the easterly wind and causes rapid warming of the polar air. The model is validated through numerical integrations of the adiabatic-geostrophic potential vorticity equation, showing results similar to observed sudden warming phenomena. The introduction reviews previous studies on the sudden warming, highlighting the role of planetary-scale disturbances and the importance of wave propagation and interaction with zonal winds. The mechanism of the model is discussed, including the propagation of planetary waves and their interaction with zonal winds, with specific attention to the Charney-Drazin theorem and the acceleration of zonal winds by planetary waves. The basic equations used in the model are derived, and the initial conditions, boundary conditions, and forcing function are specified. Numerical integrations are performed under various conditions to test the model's validity. The results show that the model captures key features of the sudden warming event, such as the weakening and breakdown of the polar vortex, the appearance of circumpolar easterly winds, and the rapid warming of the polar air. Finally, the model's results are compared with observations from the 1963 sudden warming event, showing similarities in the evolution of the event but also discrepancies in the temperature distributions and the timing of certain phenomena. The paper concludes by discussing the limitations of the model and suggesting areas for further research, particularly on wave-wave interactions.