ArticleslgStudy

mathematics

Vilhelm Bjerknes

Vilhelm Bjerknes is a mathematics topic covered in the lgStudy science library. This page brings together a partial reference excerpt, illustrations, worked examples, real-world applications and a short study plan, so you can understand Vilhelm Bjerknes rather than just read about it. In short: Vilhelm Friman Koren Bjerknes ( BYURK-niss, Norwegian: [ˈʋɪlˌhɛlm ˈbjæɾknɛs]; 14 March 1862 – 9 April 1951) was a Norwegian geophysicist and meteorologist with essential contributions to the foundation of the modern practice of weather forecasting. He formulated the primitive equations that are still in use in numerical weather prediction and climate modeling.

Vilhelm Bjerknes — main illustration
Vilhelm Bjerknes — illustration

Key takeaways

  • Vilhelm Bjerknes belongs to mathematics; place it in that map before memorising details.
  • Learn the definition first, then one example that makes the definition concrete.
  • Connect Vilhelm Bjerknes to a quantity you can measure, compute or draw — that is where exam questions come from.
  • Reproduce the core statement of Vilhelm Bjerknes from memory before moving on to harder problems.

Reference excerpt

Vilhelm Friman Koren Bjerknes ( BYURK-niss, Norwegian: [ˈʋɪlˌhɛlm ˈbjæɾknɛs]; 14 March 1862 – 9 April 1951) was a Norwegian geophysicist and meteorologist with essential contributions to the foundation of the modern practice of weather forecasting. He formulated the primitive equations that are still in use in numerical weather prediction and climate modeling. He is the founder of the Bergen School of Meteorology, which was successful in advancing weather prediction and meteorology in the early 20th century.

Life and career

Born in Christiania (later renamed Oslo), Bjerknes enjoyed an early exposure to fluid dynamics, as assistant to his father, Carl Anton Bjerknes, who had discovered by mathematical analysis the apparent actions at a distance between pulsating and oscillating bodies in a fluid, and their analogy with the electric and magnetic actions at a distance. Apparently no attempt had been made to demonstrate experimentally the theories arrived at by the older professor until Vilhelm Bjerknes, then about 17 or 18 years of age, turned his mathematical knowledge and mechanical abilities to the devising of a series of instruments by which all the well-known phenomena of electricity and magnetism were illustrated and reproduced by spheres and discs and membranes set into rhythmic vibration in a bath containing a viscous fluid such as syrup. These demonstrations formed the most important exhibit in the department of physics at the Exposition Internationale d'Électricité held in Paris in 1881, and aroused greatest interest in the scientific world. Vilhelm Bjerknes became assistant to Heinrich Hertz in Bonn 1890–1891 and made substantial contributions to Hertz' work on electromagnetic resonance. He succeeded in giving the explanation of the phenomenon called "multiple resonance," discovered by Sarasin and De la Rive. Continuing his experiments at the University of Christiania (1891–1892), he proved experimentally the influence which the conductivity and the magnetic properties of the metallic conductors exert upon the electric oscillations, and measured the depth to which the electric oscillations penetrate in metals of different conductivity and magnetic permeability (the "skin effect"). Finally, in 1895 he furnished a complete theory of the phenomenon of electric resonance, involving a method of utilizing resonance experiments for the determination of the wavelengths, and especially of the damping (the logarithmic decrement) of the oscillations in the transmitter and the receiver of the electric oscillations. These methods contributed much to the development of wireless telegraphy. His papers on electric oscillations were published in Annalen der Physik (1891–1895). In 1895, he became professor of applied mechanics and mathematical physics at the Stockholm University where he had been lecturer since 1893. There he elucidated the fundamental interaction between fluid dynamics and thermodynamics. His major contribution was the primitive equations which are used in climate models. It was this work that inspired both V. Walfrid Ekman and Carl-Gustav Arvid Rossby to apply it to large-scale motions in the oceans and atmosphere and to make modern weather forecasting feasible. Bjerknes himself had foreseen the possible applications as early as 1904. This attack upon the meteorological problems from a hydrodynamical point of view was after 1906 supported by the Carnegie Institution of Washington, D.C., of which he became a research associate. Two introductory volumes, Statics and Kinematics, of a greater work, Dynamic Meteorology and Hydrography, were published in 1913 under the auspices of the Institution. In his 1906 work Fields of force, Bjerknes was the first to describe and mathematically derive translational forces on bubbles in an acoustic field, now known as Bjerknes forces. In his Vorlesungen über Hydrodynamische Fernkräfte nach C. A. Bjerknes Theorie (1900–1902) he gave the first complete mathematical and experimental exposition of the discoveries of his father, whose age and excessive self-criticism had prevented him from finishing his work himself. In a later book, Die Kraftfelder (1909), he stated the same theory in a very much generalized form according to methods of his own.

In 1907, Bjerknes returned to the Royal Frederick University in Oslo before becoming professor of geophysics at the University of Leipzig in 1912. In 1916, he started the publication Synoptische Darstellung atmosphärischer Zustände über Europa. In 1917, he founded the Geophysical Institute, University of Bergen where he wrote his book On the Dynamics of the Circular Vortex with Applications to the Atmosphere and to Atmospheric Vortex and Wave Motion (1921), and laid the foundation for the Bergen School of Meteorology, which was not a literal school but a school of thought on how the practice of weather forecasting and meteorology should be undertaken. He was the originator of an improved and more scientific weather service, afterwards controlled by his son and collaborator, the meteorologist Jacob Bjerknes (1897–1975). From 1926 to his retirement in 1932, he held a position at the University of Oslo. He was elected a member of the Royal Swedish Academy of Sciences in 1905 and of the Pontifical Academy of Sciences in 1936 and a Fellow of the Royal Society. He was awarded the 1932 Symons Gold Medal of the Royal Meteorological Society. He died of heart problems in Oslo. In 1893, Bjerknes had married Honoria Bonnevie, who in earlier years assisted him much in his scientific work. Their son Jacob Aall Bonnevie Bjerknes also became a meteorologist. The craters Bjerknes on the Moon and Bjerknes on Mars are named in his honor. The European Geosciences Union awards the Vilhelm Bjerknes Medal annually to recognize "distinguished research in atmospheric sciences".

References

Further reading M.R. Friedman (1989) "Appropriating the weather: Vilhelm Bjerknes and the construction of a modern meteorology". Cornell University Press. Pihl, Mogens (1970–1980). "Bjerknes, Vilhelm Frimann Koren". Dictionary of Scientific Biography. Vol. 2. New York: Charles Scribner's Sons. pp. 167–169. ISBN 978-0-684-10114-9.

External links Family genealogy

Illustrations

Vilhelm Bjerknes illustration
Vilhelm Bjerknes: Vilhelm Bjerknes with his wife Honoria and his first two children, Karl Anton and Jacob Bjerknes, circa 1898
Vilhelm Bjerknes with his wife Honoria and his first two children, Karl Anton and Jacob Bjerknes, circa 1898
Vilhelm Bjerknes: Vilhelm Bjerknes with his brother Ernst Wilhelm Bjerknes (left) and his sister-in-law, Norway's first female professor, Kristine Bonnevie at her cabin Snefugl at Mysuseter  circa 1946
Vilhelm Bjerknes with his brother Ernst Wilhelm Bjerknes (left) and his sister-in-law, Norway's first female professor, Kristine Bonnevie at her cabin Snefugl at Mysuseter circa 1946

Worked examples

Example 1 — a first encounter with Vilhelm Bjerknes

Start with the simplest possible case. Write down what Vilhelm Bjerknes claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In mathematics, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to Vilhelm Bjerknes before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about Vilhelm Bjerknes ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of Vilhelm Bjerknes

In research
Vilhelm Bjerknes appears in mathematics research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry
Engineering practice reuses Vilhelm Bjerknes in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom
Vilhelm Bjerknes is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1862 births, 1951 deaths, Academic staff of Stockholm University, so understanding it makes those chapters shorter.
In everyday life
Look for Vilhelm Bjerknes outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.
Ask Teacher Smith questions about this articleOpens your AI tutor with a question about “Vilhelm Bjerknes” →

Affiliate

Preply — study more efficiently by working with a personal tutor. 50% off.

How to study Vilhelm Bjerknes in 20 minutes

  1. Read the reference excerpt below once, without taking notes.
  2. Close the page and write down what Vilhelm Bjerknes means in your own words.
  3. Compare your version with the excerpt and mark what you missed.
  4. Work through the three examples above with pen and paper.
  5. Explain Vilhelm Bjerknes out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Vilhelm Bjerknes in simple terms?

Vilhelm Friman Koren Bjerknes ( BYURK-niss, Norwegian: [ˈʋɪlˌhɛlm ˈbjæɾknɛs]; 14 March 1862 – 9 April 1951) was a Norwegian geophysicist and meteorologist with essential contributions to the foundation of the modern practice of weather forecasting. He formulated the primitive equations that are sti…

Why does Vilhelm Bjerknes matter?

Because it connects several mathematics ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study Vilhelm Bjerknes?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on Vilhelm Bjerknes.

Tags

  • 1862 births
  • 1951 deaths
  • Academic staff of Stockholm University
  • Bjerknes family
  • Burials at the Cemetery of Our Saviour
  • Foreign members of the Royal Society
  • International members of the National Academy of Sciences
  • Members of the Royal Society of Sciences in Uppsala
  • Members of the Royal Swedish Academy of Sciences
  • Norwegian climatologists
  • Norwegian fellows of the Royal Society
  • Norwegian mathematicians

Keep exploring