Table A1.

Mathematical symbology

SymbolMeaningDimension
dDistanceL
tTimeT
uαVelocity vectorLT1 or dimensionless
gαβMetric tensorL2 or dimensionless
PαβProjection tensorL2
uα;βVelocity gradients tensorT1
θExpansion (cubic dilation)T1 (=u;αα=u)
σαβShearing tensor (strain rate)T1
ωαβRotation two-form (vorticity)T1
ρMass densityML3
CSpecific heat capacityL2T2K1
kThermal conductivityMLT3K1
ϑAbsolute temperatureK
ηDynamic viscosityML1T1
β1First normal-stress coefficientML1
β2Second normal-stress coefficientML1
TαβStress-energy tensorML−αT−β (α + β = 3)
qαHeat flux vectorMT3
ταβStress tensorML1T2
κThermal diffusivityL2T1 (=κ/ρC)
νKinematic viscosityL2T1 (=η/ρ)
χMechanical diffusivityL2T1 (=ηd2/β1)