Fluid Mechanics
Definition of symbols
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Appendix B

Definition of symbols

Definition of symbols, in alphabetical order (mathematical symbols first, greek alphabet second, latin alphabet last).
SymbolMeaningUnitsFirst used
∇\nablaDel (nabla) operatorm−1^{-1}2.18
∇T\nabla TGradient of scalar TTK m−1^{-1}2.19
∇⋅u\nabla\cdot\mathbf{u}Divergence of velocitys−1^{-1}2.20
∇×u\nabla\times\mathbf{u}Curl (vorticity) of velocitys−1^{-1}2.21
∇2\nabla^2Laplacian operatorm−2^{-2}2.22
β\betaMeridional gradient of the Coriolis parameters−1^{-1} m−1^{-1}5.22
βT\beta_TThermal expansion coefficientK−1^{-1}4.52
βS\beta_SHaline contraction coefficientPSU−1^{-1}4.52
βp\beta_pCompressibility coefficientPa−1^{-1}4.52
ηk\eta_kKolmogorov length scalem8.51
μ\muDynamic viscositykg m−1^{-1} s−1^{-1}4.35
ν\nuKinematic viscositym2^{2} s−1^{-1}4.36
νη\nu_\etaKolmogorov time scales8.52
ρ\rhoDensitykg m−3^{-3}3.13
τ\boldsymbol{\tau}Stress tensorPa, N m−2^{-2}2.3
a⋅b\mathbf{a}\cdot\mathbf{b}Dot (scalar) product of vectors—2.7
a×b\mathbf{a}\times\mathbf{b}Cross (vector) product of vectors—2.9
det(⋅)det(\cdot)Determinant of a matrix—2.9
I\mathbf{I}Identity tensor—2.4
i,j,k\mathbf{i},\mathbf{j},\mathbf{k}Cartesian unit vectors—2.5
LLCharacteristic length scalem4.57
ppPressurePa—
ReReReynolds number—4.60
RoRoRossby number—5.29
TTTemperatureK—
UUCharacteristic velocity scalem s−1^{-1}4.56
u\mathbf{u}Velocity vectorm s−1^{-1}2.1
u‾\overline{\mathbf{u}}Mean flowm s−1^{-1}8.1
u′\mathbf{u'}Fluctuating velocitym s−1^{-1}8.1
uηu_\etaKolmogorov velocity scalem s−1^{-1}8.53
u′u′‾\overline{\mathbf{u'}\mathbf{u'}}Reynolds stress tensorm2^2 s−2^{-2}8.19