Ertel potential vorticity theorem
E521730
The Ertel potential vorticity theorem is a fundamental result in geophysical fluid dynamics that states potential vorticity is materially conserved for an inviscid, adiabatic flow, making it a key tool for understanding large-scale atmospheric and oceanic motions.
Statements (46)
| Predicate | Object |
|---|---|
| instanceOf |
physical law
ⓘ
theorem in geophysical fluid dynamics ⓘ |
| appliesTo |
adiabatic flow
ⓘ
inviscid flow ⓘ rotating stratified fluids ⓘ |
| associatedConcept |
Lagrangian conservation law
ⓘ
absolute vorticity ⓘ conservative tracer ⓘ material derivative ⓘ potential temperature ⓘ |
| assumes |
no diabatic heating
ⓘ
no friction ⓘ |
| classification | conservation law in fluid dynamics ⓘ |
| concernsQuantity | Ertel potential vorticity NERFINISHED ⓘ |
| dependsOn |
absolute vorticity vector
ⓘ
fluid density or potential temperature ⓘ gradient of a materially conserved scalar ⓘ |
| describes | evolution of potential vorticity in a rotating stratified fluid ⓘ |
| era | 20th century ⓘ |
| field |
atmospheric dynamics
ⓘ
geophysical fluid dynamics ⓘ ocean dynamics ⓘ |
| generalizes | potential vorticity conservation in shallow-water equations ⓘ |
| holdsWhen |
external torques are negligible
ⓘ
source and sink terms of the conserved scalar vanish ⓘ |
| implies | potential vorticity is conserved following fluid parcels in inviscid adiabatic flow ⓘ |
| importance | fundamental constraint on large-scale geophysical flows ⓘ |
| isToolFor |
analysis of jet streams
ⓘ
analysis of ocean fronts ⓘ diagnosis of tropopause structure ⓘ isentropic analysis of the atmosphere ⓘ primitive equation modeling ⓘ quasi-geostrophic theory ⓘ |
| mathematicalForm | Dq/Dt = 0 for inviscid adiabatic flow ⓘ |
| namedAfter | Hans Ertel NERFINISHED ⓘ |
| relates |
fluid parcel motion
ⓘ
stratification ⓘ vorticity ⓘ |
| states | potential vorticity is materially conserved for inviscid adiabatic flow ⓘ |
| usedFor |
diagnosing balanced flows
ⓘ
potential vorticity inversion ⓘ studying Rossby waves ⓘ studying baroclinic instability ⓘ understanding large-scale atmospheric motions ⓘ understanding large-scale oceanic motions ⓘ |
| validUnder | hydrostatic approximation in large-scale flows ⓘ |
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.
Bjerknes circulation theorem (applications in meteorology)
→
relatedTo
→
Ertel potential vorticity theorem
ⓘ
subject surface form:
Bjerknes circulation theorem