What is the connection between mathematical equations and waves? A study published by Călin Iulian Martin presents research results on wave breaking for azimuthally varying water flow rates in cylindrical coordinates. It concerns the analysis of nonlinear partial differential equations.
These deal with the particular type of singularity that we are witnessing with wave breaking, which is defined as the situation in which the wave remains intact until the maximum time of existence at which its slope becomes infinite. The focus is on the problem of geophysical waves written in cylindrical coordinates, which are fixed at a point on the rotating Earth, together with the free surface and rigid boundary conditions below. The simplest type of singularity is considered to be the situation where the solution becomes unbounded in finite time.
How it works
More concretely, according to the study published by Călin Iulian Martin, a wave-breaking singularity occurs when the function representing the surface wave remains bounded, but its slope becomes infinite in finite time. Breaking waves transfer horizontal momentum to surface currents, contribute to mixing of the upper layers of the ocean, transport sediments in shallow water, and enhance gas exchange in the sea.
Efforts to create a mathematical model to explain this natural phenomenon are not new. The first physically relevant equation for modeling the behavior of long waves was developed in 1895 and has been refined several times. Beyond the interest in developing fundamental science and theoretical understanding of nature, there is a practical interest. In addition to the study published by the researcher from Cluj, the scientific world is intensely concerned by the subject.
Researchers believe that ocean waves act as a buffer for exchanges between the ocean and the atmosphere. They contribute to exchanges between the ocean and the atmosphere and create favorable environmental conditions for marine biodiversity.
But there are also economic implications. Some researchers say ocean and sea waves have the potential to generate enough energy to power the entire planet, but the technology needed to convert wave energy into electricity is at an early stage of development.
Researchers consider waves to be energy-efficient if they have an electricity-generating capacity of 30 kW per linear meter, and globally there are about 800,000 kilometers of coastline where waves frequently occur. According to the United Nations’ Intergovernmental Panel on Climate Change, globally, waves can generate a theoretical 32,000 TWh of electricity per year, compared with the world’s total annual electricity production of 28,000 TWh.
Engineers at the International Renewable Energy Agency have worked out a plausible scenario: if mankind used just 2% of the 800,000 kilometers of coastline suitable for wave power technology, and energy conversion was 40% efficient, then mankind could produce 500 GW. Romania currently has 6 GW of hydropower capacity.
Who is Călin Iulian Martin?
Călin Iulian Martin, from the Faculty of Mathematics and Computer Science at the Babeș-Bolyai University, is considered one of the best mathematicians. He is ranked among the world’s top 2% of scientists, according to a ranking published by the University of Cluj. Călin Iulian Martin has also taught at the University of Vienna, and in recent years has been trying to create differential equations to explain phenomena such as breaking waves. These scientific endeavors could influence energy production worldwide.
