Abstract 

Waves in fluids are fascinating phenomena that significantly impact various aspects of life. At small length scales, interfacial waves, which occur under electric or magnetic fields, are widely used in cooling systems, coating processes, and microfluidic devices. At intermediate scales, nonlinear ocean waves greatly influence the extent of pack ice and the fragmentation of ice floes in the Marginal Ice Zone, playing a crucial role in climate change. At larger lengths, ocean surface waves and internal waves affect shipping, coastal morphology, and near-shore navigation. 

From a mathematical viewpoint, the Navier-Stokes and Euler equations pose severe challenges for rigorous analysis, modeling, and numerical simulation. The governing equations for waves in fluids are a widely accepted model and have been the subject of much research. However, the free boundary nature and strongly nonlinear boundary conditions add complexity and preclude many of the tools used in other wave problems. The level of difficulty is so great that both theory and much fundamental understanding have only scratched the surface of the subject. The numerical investigation of waves in fluids presents a complex set of challenges that sit at the intersection of mathematical rigor, computational efficiency, and physical accuracy. Key issues include ensuring numerical accuracy and stability, managing multi physics coupling and multiscale phenomena, dealing with complex geometries and free-boundary conditions, and addressing demands on computational resources, among others. Advances in numerical algorithms along with high-performance computing architectures and interdisciplinary collaboration, are crucial for overcoming these obstacles. 

By addressing these challenges, we not only enhance our understanding of fluid dynamics but also promote innovations in fields such as climate modeling, marine engineering, and renewable energy systems. 

This conference will bring together global experts in pure, applied, and computational mathematics, as well as fluid dynamics, to discuss the latest research on wave phenomena in fluid systems. The event focuses on connecting theoretical insights with computational innovations, aiming to advance methods for modeling, analyzing, and simulating waves in various fluid environments, including oceanic and atmospheric flows, as well as industrial applications. 

Main Themes include (but are not limited to): 

1. Mathematical Foundations:

• Rigorous analysis of free boundary problems;

• Nonlinear wave theory, modeling, stability analysis, and asymptotic methods;

• Hamiltonian and variational frameworks for fluid wave dynamics.

2. Computational Advancements:

• High-performance algorithms for waves in fluids (e.g., spectral methods, adaptive meshing, high-order finite difference/element/volume methods); • Machine learning-enhanced simulations and data-driven modeling.

3. Interdisciplinary Applications:

• Geophysical fluid dynamics (tsunamis, internal waves, storm surges, wave-ice interactions);

• Industrial and engineering applications, renewable energy systems, flow control.

Description of the aim 

The proposed international conference on "Waves in Fluids: Mathematical Theory and Scientific Computing" is of great significance for the scientific community, industry, and society as a whole. The main objectives of the conference are to advance research across these themes, facilitate the transfer of knowledge from experienced researchers to those in the early stages of their careers, and foster collaboration between pure and applied mathematics, particularly in the realms of rigorous analysis and scientific computing. Here are the key reasons why this conference is both timely and impactful.  

1. Advancing Fundamental Knowledge

Waves in fluids are a fundamental phenomenon observed in nature and engineering systems, from ocean waves and atmospheric dynamics to aerodynamics and industrial fluid flows. This conference will provide a platform for researchers to share the latest advancements in mathematical modeling, theoretical analysis, and computational methods, thereby deepening our understanding of these complex systems. 

2. Bridging Disciplines

The study of waves in fluids inherently requires interdisciplinary collaboration between mathematicians, physicists, engineers, and computational scientists. 

By bringing together experts from these diverse fields, the conference will foster cross-disciplinary dialogue, leading to innovative solutions and new research directions. 

3. Addressing Real-World Challenges

Wave phenomena in fluids have profound implications for real-world applications, including climate and environmental science, engineering applications, and geophysical exploration. This conference will highlight how cutting-edge research can address these pressing global challenges. 

4. Promoting Scientific Computation

The development of advanced numerical methods and high-performance computing tools has revolutionized the study of waves in fluids. This conference will showcase state-of-the-art computational techniques, including machine learning and data-driven approaches, which are transforming the field. 

5. Encouraging Early-Career Researchers

The conference will provide a unique opportunity for young scientists, graduate students, and postdoctoral researchers to present their work, receive feedback from leading experts, and build professional networks. This will help cultivate the next generation of researchers in fluid dynamics and related fields. 

6. Strengthening International Collaboration

By gathering participants from around the world, the conference will facilitate the exchange of ideas, foster international partnerships, and promote collaborative research projects. This global perspective is essential for tackling complex problems that transcend borders.