mathematics

Kaufmann vortex

Kaufmann vortex 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 Kaufmann vortex rather than just read about it. In short: The Kaufmann vortex, also known as the Scully model, is a mathematical model for a vortex taking account of viscosity. It uses an algebraic velocity profile.

Key takeaways

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

Reference excerpt

The Kaufmann vortex, also known as the Scully model, is a mathematical model for a vortex taking account of viscosity. It uses an algebraic velocity profile. This vortex is not a solution of the Navier–Stokes equations. Kaufmann and Scully's model for the velocity in the Θ direction is:

V Θ ( r ) = Γ 2 π r r c 2 + r 2 {\displaystyle V_{\Theta }\ (r)={\frac {\Gamma }{2\pi }}{\frac {r}{r_{c}^{2}+r^{2}}}}

The model was suggested by W. Kaufmann in 1962, and later by Scully and Sullivan in 1972 at the Massachusetts Institute of Technology.

See also Rankine vortex – a simpler, but more crude, approximation for a vortex. Lamb–Oseen vortex – the exact solution for a free vortex decaying due to viscosity.

References

Worked examples

Example 1 — a first encounter with Kaufmann vortex

Start with the simplest possible case. Write down what Kaufmann vortex 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 Kaufmann vortex 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 Kaufmann vortex 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 Kaufmann vortex

In research: Kaufmann vortex 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 Kaufmann vortex 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: Kaufmann vortex is common in secondary-school and first-year university syllabi. It links to neighbouring topics Equations of fluid dynamics, Fluid dynamics stubs, Vortices, so understanding it makes those chapters shorter.
In everyday life: Look for Kaufmann vortex 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.

Affiliate

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

How to study Kaufmann vortex in 20 minutes

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

Frequently asked questions

What is Kaufmann vortex in simple terms?

The Kaufmann vortex, also known as the Scully model, is a mathematical model for a vortex taking account of viscosity. It uses an algebraic velocity profile.

Why does Kaufmann vortex 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 Kaufmann vortex?

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 Kaufmann vortex.