Editors’ Vox is a blog from AGU’s Publications Department.
Helicities are known to play essential roles in several geophysical, astrophysical, and space plasma phenomena and are thus studied by means of diverse methods from various disciplinary viewpoints. A book recently published in AGU’s Geophysical Monograph Series, Helicities in Geophysics, Astrophysics, and Beyond, discusses the importance of helicities to an array of scientific disciplines and explores how they relate to real world issues. We asked the book’s editors to explain helicities, their significance and applications, and the features of their book.
How would you describe helicities in very simple terms to a non-specialist?
Helicity quantifies the alignment between a vector field and its curl and indicates how twisted and tangled the original vector field is.
For any vector field in mathematics or physics, one can define its rotation, or curl. Helicity, in general, quantifies the alignment between the vector field and its curl and indicates how twisted and tangled the original vector field is.
There is magnetic helicity (vector potential and curl-generated magnetic field), current helicity (magnetic field vector and curl-generated electric current density), kinetic helicity (velocity field and curl-generated vorticity) and other kinds of helicity. Magnetic helicity, in particular, is crucial from geophysics all the way to cosmology due to its fundamental conservation property under certain conditions.
Helicity of any kind can be easily visualized as left- or right-handed depending on the dominant direction of tangling, like a left- or a right-handed screw. The helical shape above and featured on the book’s cover, for example, is achieved by a right-handed turn applied to the original, untwisted lamina.
Why are helicities significant?
Helicities as quantities neatly summarize vector field complexity because they are scalar values. More importantly, helicities are conserved quantities at the limit of vanishing viscosity and resistivity, namely, when the original vector field is ideal.
In several physical systems, including the basic physical equations describing the universe, forms of helicity are as important as forms of energy. Nonzero helicities (i.e., not perfect canceling between left- and right-handed contributions) globally in a physical system reflect a broken symmetry in the system. Helicities affect the statistical and dynamical properties of the system under study. For instance, the presence of helicities in turbulence leads to formation and suppression of individual structures, as energy aims to homogenize the system through enhanced transport. Think of the oppositely helical wingtip vortices in airplane wake, for example. In brief, helicities can be viewed as complementary, but equally fundamental, to the relevant forms of energy.
Which scientific disciplines are engaged in the study of different aspects of helicities and helicity-related phenomena?
Various scientific disciplines are engaged including:
- mathematics, e.g., topology and geometry of the fields
- astrophysics and geophysics through dynamo processes, e.g., magnetic-field generation and sustainment mechanisms, and vorticity generation
- fundamental physics, e.g., left-right skewness of neutrino, vortex entanglement in quantum superfluid, spontaneous structure formation in a rotating system, zonal flow generation in fusion plasmas
- biology, e.g., double helical structure of DNA, ventral nodal flow in the formation of the left-right asymmetry in human body
- engineering, e.g., swirling flow in the combustion chamber
How did you structure this book to cover such a broad topic with many different perspectives?
The volume is structured in three parts. Part I “Helicity Essentials: Basic and Fundamental Concepts” looks at mathematical and field theoretical treatment of helicities. Part II “Helicity Manifestations in Nature and their Observations” presents observations of helicities in solar physics, space physics, and atmospheric science, and helical properties from biophysics to solar physics.
We hope that [the book] will provide the interested reader with valuable information, meaningful clues, and further references for the continuation of their study.
Part III “Theoretical and Numerical Helicity Modeling” explores helicity in particle physics and dynamos, stability and relaxation analysis involving helicity, theory and numerical simulations of structure and sunspot formation with helicity, as well as helicity transport and spatiotemporal evolution of helicity.
Our book is by no means an exhaustive treatise on helicity, but we hope that it will provide the interested reader with valuable information, meaningful clues, and further references for the continuation of their study.
What have been some of the most interesting advances in helicity studies over recent years?
Recently not only volume-integrated helicity but also several theoretical helicity frameworks have been investigated, with special emphasis on spatiotemporal evolution in global and local scales (i.e., local density of helicities). In addition, high-resolution, data-driven numerical simulations of helicities in the Sun have been extensively and intensively performed.
In recent years, the discipline of space weather, with Sun-induced space weather agents such as solar flares and coronal mass ejections, seems to have a crucial relevance to magnetic, current, and kinetic helicity. To understand solar eruptions, several results imply magnetic helicity and its fundamental conservation principle as key aspects. There are several theoretical and numerical challenges in fully revealing the impact of helicities, but diverse communities attest to their central importance.
What do you imagine will be the latest developments in helicity studies reported in another book 10 years from now?
More work will be done to advance recent developments in theoretical, numerical, and observational investigations of magnetic helicity. Other helicity forms, such as current helicity and cross helicity (i.e., magnetic field and electric current density correlation), as well as generalized helicity in Hall magnetohydrodynamics, will be more extensively investigated too.
Helicity is about complexity and broken symmetries, and the countless forms of complexity have led to fascinating and formidable topics of study in the last few centuries, not just decades. Finding meaningful ways to deal with complexity, involving helicity, may well lead to developments that are hard to predict as we speak, even within the next 10 or 20 years.
Is this book accessible to someone new to helicity studies or for advanced readers only?
There is something for everyone in the book: the newcomer fascinated by helicity should focus more on Part I of the book before delving into the next parts. With the fundamental knowledge one can then look into key examples and manifestations of helicity in Part II.
Part III is for more advanced readers who wish to ponder on potential future directions and some existing applications that might enable, or even spearhead, future developments.
We aimed toward a mixed and healthy balance, in full understanding that helicity studies cannot be exhausted by any single volume.
Helicities in Geophysics, Astrophysics, and Beyond, 2023. ISBN: 978-1-119-84168-5. List price: $195 (hardcover), $156 (ebook).
Chapter 1 is freely available. Visit the book’s page on Wiley.com and click on “Read an Excerpt” below the cover image.
—Kirill Kuzanyan ([email protected]; 
0000-0003-1677-4417), IZMIRAN/Russian Academy of Sciences, Russia; Nobumitsu Yokoi (0000-0002-5242-7634), University of Tokyo, Japan; Manolis K. Georgoulis (0000-0001-6913-1330), Academy of Athens, Greece; and Rodion Stepanov (0000-0001-8098-0720), Perm Federal Research Center, Russia
Editor’s Note: It is the policy of AGU Publications to invite the authors or editors of newly published books to write a summary for Eos Editors’ Vox.
