This book introduces the fascinating subject of hydrodynamics and critical convection in a rotating layer—a model that helps us understand the behavior of the Earth’s fluid core and similar regions deep inside many planets and their large moons. It explores how heat and mass are transferred within the simplest possible model of a planet’s fluid core, with special attention to asymptotic methods that reveal the underlying physical mechanisms.

 
All chapters include exercises designed for self-study and for testing the reader’s understanding of the material. These have also been used as part of classroom instruction and independent assessments. The book is well-suited for graduate-level researchers and advanced students working in planetary, solar, or stellar physics, as well as computational fluid dynamics and applied mathematics.

 
The authors have contributed original research to the topics discussed in this book. The first author, Prof. Sergey Starchenko, has taught related lecture courses at the Rybinsk State Aviation Technological University (RGATU, Russia) between 2000 and 2005. He has also conducted short-term advanced courses—lasting from ten to thirty days—supported by the University of Bratislava (February 2007) and through India’s GiAN and SPARC programs (September 2022, February 2025, and September–October 2025).

Prof. Sergey Starchenko is a leading authority in fluid dynamics. His research related to the proposed book is focusing on rotating convection, asymptotic, low-dimensional and critical models, planetary and astrophysical systems. He has contributed to academic literature through the authorship of textbooks and chapters in scientific books. His research work has also been published widely in peer-reviewed scientific journals related to geophysical and astrophysical fluid dynamics.

Prof. Hari Ponnamma Rani is expert in Computational Fluid dynamic related studies. Her research interest includes non-linear dynamics, dynamical systems, hydrodynamic stability, rotating and double-diffusive convection. Her research contributions include publications in international peer-reviewed journals as well as contributions to academic books.

Prof. Maria Kotelinova is an expert in mathematical and asymptotic modeling of rotating fluids and critical convection. Her work addresses instability mechanisms and reduced models relevant to planetary hydrodynamics. She has contributed to authoritative books and high-impact journal publications in geophysical and planetary fluid dynamics.