science

Monin–Obukhov similarity theory

Monin–Obukhov similarity theory is a science 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 Monin–Obukhov similarity theory rather than just read about it. In short: Monin–Obukhov (M–O) similarity theory describes the non-dimensionalized mean flow and mean temperature in the surface layer under non-neutral conditions as a function of the dimensionless height parameter, named after Russian scientists A. S.

Key takeaways

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

Reference excerpt

Monin–Obukhov (M–O) similarity theory describes the non-dimensionalized mean flow and mean temperature in the surface layer under non-neutral conditions as a function of the dimensionless height parameter, named after Russian scientists A. S. Monin and A. M. Obukhov. Similarity theory is an empirical method that describes universal relationships between non-dimensionalized variables of fluids based on the Buckingham π theorem. Similarity theory is extensively used in boundary layer meteorology since relations in turbulent processes are not always resolvable from first principles. An idealized vertical profile of the mean flow for a neutral boundary layer is the logarithmic wind profile derived from Prandtl's mixing length theory, which states that the horizontal component of mean flow is proportional to the logarithm of height. M–O similarity theory further generalizes the mixing length theory in non-neutral conditions by using so-called "universal functions" of dimensionless height to characterize vertical distributions of mean flow and temperature. The Obukhov length ( L {\displaystyle L} ), a characteristic length scale of surface layer turbulence derived by Obukhov in 1946, is used for non-dimensional scaling of the actual height. M–O similarity theory marked a significant landmark of modern micrometeorology, providing a theoretical basis for micrometeorological experiments and measurement techniques.

The Obukhov length The Obukhov length L {\displaystyle L} is a length parameter for the surface layer in the boundary layer, which characterizes the relative contributions to turbulent kinetic energy from buoyant production and shear production. The Obukhov length was formulated using Richardson's criterion for dynamic stability. It was derived as,

L = − u ∗ 3 κ g T Q ρ c p {\displaystyle L=-{\dfrac {u_{*}^{3}}{\kappa {\dfrac {g}{T}}{\dfrac {Q}{\rho c_{p}}}}}}

where κ ≈ 0.40 {\displaystyle \kappa \approx 0.40} is the von Kármán constant, u ∗ {\displaystyle u_{*}} friction velocity, Q {\displaystyle Q} turbulent heat flux, and c p {\displaystyle c_{p}} heat capacity. Virtual potential temperature θ v {\displaystyle \theta _{v}} is often used instead of temperature T {\displaystyle T} to correct for the effects of pressure and water vapor. Q {\displaystyle Q} can be written as vertical eddy flux,

Q = ρ c p w ′ θ v ′ ¯ {\displaystyle Q=\rho c_{p}{\overline {w'\theta _{v}'}}}

with w ′ {\displaystyle w'} and θ v ′ {\displaystyle \theta _{v}'} perturbations of vertical velocity and virtual potential temperature, respectively. Therefore, the Obukhov length can also be defined as,

L = − u ∗ 3 κ g θ v ¯ w ′ θ v ′ ¯ {\displaystyle L=-{\dfrac {u_{*}^{3}}{\kappa {\dfrac {g}{\overline {\theta _{v}}}}{\overline {w'\theta _{v}'}}}}}

… excerpt ends here. Continue reading the full article.

Illustrations

Worked examples

Example 1 — a first encounter with Monin–Obukhov similarity theory

Start with the simplest possible case. Write down what Monin–Obukhov similarity theory claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In science, 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 Monin–Obukhov similarity theory 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 Monin–Obukhov similarity theory 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 Monin–Obukhov similarity theory

In research: Monin–Obukhov similarity theory appears in science 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 Monin–Obukhov similarity theory 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: Monin–Obukhov similarity theory is common in secondary-school and first-year university syllabi. It links to neighbouring topics Dimensional analysis, Microscale meteorology, so understanding it makes those chapters shorter.
In everyday life: Look for Monin–Obukhov similarity theory 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.

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How to study Monin–Obukhov similarity theory in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what Monin–Obukhov similarity theory 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.
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Frequently asked questions

What is Monin–Obukhov similarity theory in simple terms?

Why does Monin–Obukhov similarity theory matter?

Because it connects several science 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 Monin–Obukhov similarity theory?

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 Monin–Obukhov similarity theory.