Taylor–von Neumann–Sedov blast wave

Key takeaways

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Reference excerpt

Taylor–von Neumann–Sedov blast wave (or sometimes referred to as Sedov–von Neumann–Taylor blast wave) refers to a blast wave induced by a strong explosion. The blast wave was described by a self-similar solution independently by G. I. Taylor, John von Neumann and Leonid Sedov during World War II.

History G. I. Taylor was told by the British Ministry of Home Security that it might be possible to produce a bomb in which a very large amount of energy would be released by nuclear fission and asked to report the effect of such weapons. Taylor presented his results on June 27, 1941. Exactly at the same time, in the United States, John von Neumann was working on the same problem and he presented his results on June 30, 1941. It was said that Leonid Sedov was also working on the problem around the same time in the USSR, although Sedov never confirmed any exact dates. The complete solution was published first by Sedov in 1946. von Neumann published his results in August 1947 in the Los Alamos scientific laboratory report on "Blast wave" (PDF). Archived (PDF) from the original on June 1, 2022., although that report was distributed only in 1958. Taylor got clearance to publish his results in 1949 and he published his works in two papers in 1950. In the second paper, Taylor calculated the energy of the atomic bomb used in the Trinity (nuclear test) using the similarity, just by looking at the series of blast wave photographs that had a length scale and time stamps, published by Julian E Mack in 1947. This calculation of energy caused, in Taylor's own words, 'much embarrassment' (according to Grigory Barenblatt) in US government circles since the number was then still classified although the photographs published by Mack were not. Taylor's biographer George Batchelor writes This estimate of the yield of the first atom bomb explosion caused quite a stir... G.I. was mildly admonished by the US Army for publishing his deductions from their (unclassified) photographs.

Mathematical description Consider a strong explosion (such as nuclear bombs) that releases a large amount of energy E {\displaystyle E} in a small volume during a short time interval. This will create a strong spherical shock wave propagating outwards from the explosion center. The self-similar solution tries to describe the flow when the shock wave has moved through a distance that is extremely large when compared to the size of the explosive. At these large distances, the information about the size and duration of the explosion will be forgotten; only the energy released E {\displaystyle E} will have influence on how the shock wave evolves. To a very high degree of accuracy, then it can be assumed that the explosion occurred at a point (say the origin r = 0 {\displaystyle r=0} ) instantaneously at time t = 0 {\displaystyle t=0} . The shock wave in the self-similar region is assumed to be still very strong such that the pressure behind the shock wave p 1 {\displaystyle p_{1}} is very large in comparison with the pressure (atmospheric pressure) in front of the shock wave p 0 {\displaystyle p_{0}} , which can be neglected from the analysis. Although the pressure of the undisturbed gas is negligible, the density of the undisturbed gas ρ 0 {\displaystyle \rho _{0}} cannot be neglected since the density jump across strong shock waves is finite as a direct consequence of Rankine–Hugoniot conditions. This approximation is equivalent to setting p 0 = 0 {\displaystyle p_{0}=0} and the corresponding sound speed c 0 = 0 {\displaystyle c_{0}=0} , but keeping its density non zero, i.e., ρ 0 ≠ 0 {\displaystyle \rho _{0}\neq 0} . The only parameters available at our disposal are the energy E {\displaystyle E} and the undisturbed gas density ρ 0 {\displaystyle \rho _{0}} . The properties behind the shock wave such as p 1 , ρ 1 {\displaystyle p_{1},\,\rho _{1}} are derivable from those in front of the shock wave. The only non-dimensional combination available from r , t , ρ 0 {\displaystyle r,\,t,\,\rho _{0}} and E {\displaystyle E} is

r ( ρ 0 E t 2 ) 1 / 5 . {\displaystyle r\left({\frac {\rho _{0}}{Et^{2}}}\right)^{1/5}.}

… excerpt ends here. Continue reading the full article.

Worked examples

Example 1 — a first encounter with Taylor–von Neumann–Sedov blast wave

Start with the simplest possible case. Write down what Taylor–von Neumann–Sedov blast wave 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 Taylor–von Neumann–Sedov blast wave 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 Taylor–von Neumann–Sedov blast wave 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 Taylor–von Neumann–Sedov blast wave

In research: Taylor–von Neumann–Sedov blast wave 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 Taylor–von Neumann–Sedov blast wave 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: Taylor–von Neumann–Sedov blast wave is common in secondary-school and first-year university syllabi. It links to neighbouring topics Equations of fluid dynamics, Fluid dynamics, so understanding it makes those chapters shorter.
In everyday life: Look for Taylor–von Neumann–Sedov blast wave 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.

How to study Taylor–von Neumann–Sedov blast wave in 20 minutes

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Frequently asked questions

What is Taylor–von Neumann–Sedov blast wave in simple terms?

Taylor–von Neumann–Sedov blast wave (or sometimes referred to as Sedov–von Neumann–Taylor blast wave) refers to a blast wave induced by a strong explosion. The blast wave was described by a self-similar solution independently by G.

Why does Taylor–von Neumann–Sedov blast wave 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 Taylor–von Neumann–Sedov blast wave?

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 Taylor–von Neumann–Sedov blast wave.