Exploring the Role of Differential Equations in Climate Modeling

Dear Colleagues,

Ordinary and partial differential equations play a central role in all areas of science and engineering where the fundamental laws of physics are used, and climate modeling is one of them. This Special Issue focuses on new developments in analysis, modeling, and computational techniques using differential equations in climate and weather phenomena. Climate and weather dynamics involve a hierarchy of scales, ranging from processes of associated phase changes that occur on the scales of micro-meters and milliseconds to planetary and inter-annual as well as decadal climatic fluctuations, such as the El Niño–Southern oscillation and the Pacific Decadal oscillation. The sheer existence of climate and weather variations stems from the persistence of a large variety of external drivers, such as gravitational, Coriolis, and centrifugal forces due to celestial motions, and the incidence of solar light, which is modulated by the diurnal and seasonal cycles. When combined with the extraordinary nature of fluids and fluid-likes that cover the Earth’s surface, i.e., air, water, and ice, that continuously deform under the induced shear stresses as well as the thermodynamic properties of their chemical constituents, there result a menagerie of dynamical phenomena, such as turbulent eddies of different sizes and shapes, wave disturbances of all kinds and scales, clouds of different forms, winds, currents, and ice flows of various sorts. The understanding of these phenomena and the role they play in the climate–Earth system, as well as the way it is rapidly changing, passes through the careful study of the underlying differential equations. Contributions to the study of the mathematical and physical aspects of process-oriented models for wave dynamics, ice flows, turbulence, phase chance, and energy balance are particularly encouraged.

Prof. Dr. Boualem Khouider
Guest Editor

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• weather
• climate
• waves
• moisture
• sea ice
• convection
• numerical methods
• differential equations
• stability
• PDE analysis
• turbulence
• ice flows
• clouds