-5/3 law
E1041767
The -5/3 law is a fundamental scaling rule in turbulence theory stating that, in the inertial subrange, the energy spectrum of turbulent flows decays proportionally to the wavenumber raised to the power of -5/3.
Statements (45)
| Predicate | Object |
|---|---|
| instanceOf |
physical law
ⓘ
scaling law ⓘ turbulence theory concept ⓘ |
| appliesTo |
homogeneous isotropic turbulence
ⓘ
incompressible turbulence ⓘ turbulent flows ⓘ |
| approximationType | phenomenological law ⓘ |
| associatedWith | Kolmogorov 1941 theory NERFINISHED ⓘ |
| assumes |
high Reynolds number turbulence
ⓘ
local isotropy ⓘ scale separation between energy injection and dissipation ⓘ statistical stationarity ⓘ |
| basedOn | Kolmogorov similarity hypotheses NERFINISHED ⓘ |
| contrastWith |
exponential decay in dissipation range
ⓘ
k^(-3) spectrum in 2D enstrophy cascade ⓘ |
| describes |
energy spectrum of turbulence
ⓘ
inertial subrange scaling ⓘ |
| domain | wavenumber space ⓘ |
| field |
fluid dynamics
ⓘ
statistical physics ⓘ turbulence theory ⓘ |
| hasExponent | -5/3 ⓘ |
| historicalPeriod | 20th century turbulence research ⓘ |
| holdsApproximately | over intermediate wavenumbers between forcing and dissipation scales ⓘ |
| involves |
constant energy flux across scales
ⓘ
energy cascade from large to small scales ⓘ |
| mathematicalForm | E(k) ∝ ε^(2/3) k^(-5/3) ⓘ |
| parameter | energy dissipation rate ε ⓘ |
| predicts |
power-law decay of energy spectrum
ⓘ
self-similar cascade of kinetic energy ⓘ |
| relatedTo |
Kolmogorov microscale
NERFINISHED
ⓘ
dissipation range ⓘ energy-containing range ⓘ |
| relatesQuantity |
energy spectrum
ⓘ
wavenumber ⓘ |
| scaleInvariance | self-similar over inertial subrange ⓘ |
| statesThat | the energy spectrum E(k) scales as k^(-5/3) in the inertial subrange ⓘ |
| testedBy |
atmospheric boundary layer measurements
ⓘ
direct numerical simulations of turbulence ⓘ laboratory experiments ⓘ |
| usedIn |
astrophysical turbulence analysis
ⓘ
atmospheric turbulence modeling ⓘ engineering turbulence models ⓘ oceanic turbulence studies ⓘ |
| validIn | inertial subrange ⓘ |
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.