Alfvén’s theorem in magnetohydrodynamics
E679641
Alfvén’s theorem in magnetohydrodynamics is a fundamental result stating that in a perfectly conducting fluid, magnetic field lines are “frozen” into the plasma and move with it, preserving their topology over time.
All labels observed (1)
| Label | Occurrences |
|---|---|
| Alfvén’s theorem in magnetohydrodynamics canonical | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T7651053 — resolving that mention is where its identity was fixed. The disambiguator weighed these candidate entities and picked the highlighted one (or “None”, minting a new entity). This is how homonymy is resolved: the same surface form can point to different entities.
Target entity: Alfvén’s theorem in magnetohydrodynamics Context triple: [Hannes Alfvén, knownFor, Alfvén’s theorem in magnetohydrodynamics]
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A.
Kruskal–Shafranov instability criterion
The Kruskal–Shafranov instability criterion is a fundamental condition in plasma physics that predicts when a magnetically confined plasma column becomes unstable to kink-like distortions.
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B.
Parker spiral model of the interplanetary magnetic field
The Parker spiral model of the interplanetary magnetic field describes how the Sun’s rotating, magnetized solar wind stretches the solar magnetic field into an Archimedean spiral shape throughout the heliosphere.
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C.
Kolmogorov spectrum of turbulence
The Kolmogorov spectrum of turbulence is a fundamental theory in fluid dynamics that predicts how kinetic energy is distributed across different scales in fully developed turbulent flow, most famously yielding the −5/3 power law for the inertial subrange.
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D.
Taylor–Proudman theorem
The Taylor–Proudman theorem is a fundamental result in geophysical fluid dynamics stating that in a rapidly rotating, inviscid, incompressible fluid, steady flows tend to be uniform along the axis of rotation, leading to columnar motion.
-
E.
Jeans instability
Jeans instability is a gravitational phenomenon in astrophysics where regions within a gas cloud become unstable and collapse under their own gravity, leading to the formation of structures like stars and galaxies.
- F. None of above. chosen
- G. Unsure - the case is ambiguous/there is not enough information to decide.
Target entity: Alfvén’s theorem in magnetohydrodynamics Target entity description: Alfvén’s theorem in magnetohydrodynamics is a fundamental result stating that in a perfectly conducting fluid, magnetic field lines are “frozen” into the plasma and move with it, preserving their topology over time.
-
A.
Kruskal–Shafranov instability criterion
The Kruskal–Shafranov instability criterion is a fundamental condition in plasma physics that predicts when a magnetically confined plasma column becomes unstable to kink-like distortions.
-
B.
Parker spiral model of the interplanetary magnetic field
The Parker spiral model of the interplanetary magnetic field describes how the Sun’s rotating, magnetized solar wind stretches the solar magnetic field into an Archimedean spiral shape throughout the heliosphere.
-
C.
Kolmogorov spectrum of turbulence
The Kolmogorov spectrum of turbulence is a fundamental theory in fluid dynamics that predicts how kinetic energy is distributed across different scales in fully developed turbulent flow, most famously yielding the −5/3 power law for the inertial subrange.
-
D.
Taylor–Proudman theorem
The Taylor–Proudman theorem is a fundamental result in geophysical fluid dynamics stating that in a rapidly rotating, inviscid, incompressible fluid, steady flows tend to be uniform along the axis of rotation, leading to columnar motion.
-
E.
Jeans instability
Jeans instability is a gravitational phenomenon in astrophysics where regions within a gas cloud become unstable and collapse under their own gravity, leading to the formation of structures like stars and galaxies.
- F. None of above. chosen
Statements (47)
| Predicate | Object |
|---|---|
| instanceOf |
physical theorem
ⓘ
result in magnetohydrodynamics ⓘ |
| alsoKnownAs |
Alfvén’s frozen-in flux theorem
NERFINISHED
ⓘ
frozen-in field theorem NERFINISHED ⓘ |
| appliesTo |
ideal magnetohydrodynamics
ⓘ
perfectly conducting fluid ⓘ plasma ⓘ |
| assumes |
infinite electrical conductivity
ⓘ
negligible resistivity ⓘ non-relativistic MHD in its standard form ⓘ single-fluid MHD description ⓘ validity of ideal Ohm’s law ⓘ |
| basedOn | ideal induction equation of MHD ⓘ |
| consequence |
magnetic field lines are advected with the fluid flow
ⓘ
topological invariants of magnetic field lines are conserved in ideal MHD ⓘ |
| contrastsWith | magnetic reconnection in resistive MHD ⓘ |
| describes | frozen-in behavior of magnetic field lines in a conducting fluid ⓘ |
| domain |
classical plasma physics
ⓘ
continuum electrodynamics ⓘ |
| field | magnetohydrodynamics ⓘ |
| historicalContext | introduced in the development of magnetohydrodynamics in the 20th century ⓘ |
| holdsWhen | magnetic Reynolds number is very large ⓘ |
| implies |
magnetic flux through any material surface comoving with the fluid is conserved
ⓘ
no reconnection of magnetic field lines in ideal MHD ⓘ |
| mathematicallyExpressedAs |
dΦ_B/dt = 0 for a surface moving with the fluid
ⓘ
∂B/∂t = ∇ × (v × B) in ideal MHD ⓘ |
| namedAfter | Hannes Alfvén NERFINISHED ⓘ |
| relatedConcept |
ideal Ohm’s law E + v × B = 0
ⓘ
magnetic flux freezing ⓘ magnetic helicity conservation in ideal MHD ⓘ |
| relatedTo | Alfvén waves NERFINISHED ⓘ |
| relates |
fluid velocity field
ⓘ
magnetic field lines ⓘ magnetic flux conservation ⓘ |
| requires |
Maxwell–Faraday equation
NERFINISHED
ⓘ
magnetostatic approximation for displacement current in MHD ⓘ |
| statesThat |
magnetic field line topology is preserved in time in ideal MHD
ⓘ
magnetic field lines are frozen into the plasma in ideal MHD ⓘ magnetic field lines move with the fluid in a perfectly conducting plasma ⓘ |
| usedIn |
astrophysical plasma physics
ⓘ
fusion plasma confinement theory ⓘ solar physics ⓘ space plasma physics ⓘ theory of magnetic field line topology ⓘ theory of magnetic flux tubes ⓘ |
| violatedWhen |
finite resistivity is present
ⓘ
non-ideal MHD effects are important ⓘ |
How these facts were elicited
The pipeline generated the facts above by prompting gpt-5.1 with this entity's name + description and the instruction below.
You are a knowledge base construction expert. Given a subject entity and a description of it, return factual statements that you know for the subject as a JSON list of dictionaries(triples), where keys must be "subject", "predicate" and "object". The number of facts may be very high, between 25 to 50 or more, for very popular subjects. For less popular subjects, the number of facts can be very low, like 5 or 10. # Requirements - If you don't know the subject at all, return an empty list. - If the subject is not a named entity, return an empty list. - Include at least one triple where predicate is "instanceOf". - Do not get too wordy. - Separate several objects into multiple triples with one object.
Subject: Alfvén’s theorem in magnetohydrodynamics Description of subject: Alfvén’s theorem in magnetohydrodynamics is a fundamental result stating that in a perfectly conducting fluid, magnetic field lines are “frozen” into the plasma and move with it, preserving their topology over time.
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.