Nomenclature

Frame of reference

• Define frame of reference, and notation. Use u,v,w and x,y, and z?
• Decomposition of total, mean, turbulent and waves.

Turbulence Spectrum

Taylor's Frozen Turbulence for converting temporal to spatial measurements [math]\displaystyle{ \left(\bar{u}_1\frac{\partial }{\partial{x}} = \frac{\partial}{\partial{t}}\right) }[/math]

• Missing the y-axis.

Symbol	Description	Eqn	Units
[math]\displaystyle{ f }[/math]	Frequency	[math]\displaystyle{ \frac{\omega}{2\pi} }[/math]	Hz
[math]\displaystyle{ f_n }[/math]	Nyquist frequency	[math]\displaystyle{ f_n=0.5f_s }[/math]	Hz
[math]\displaystyle{ f_s }[/math]	Sampling frequency	[math]\displaystyle{ \frac{1}{\Delta t} }[/math]	Hz
[math]\displaystyle{ k }[/math]	Wavenumbers (angular)	[math]\displaystyle{ k=\frac{f}{\bar{u}}=2\pi\hat{k} }[/math]	rad/m
[math]\displaystyle{ \hat{k} }[/math]	Wavenumbers	[math]\displaystyle{ \frac{k}{2\pi} }[/math]	cpm
[math]\displaystyle{ \hat{k}_\Delta }[/math]	Nyquist wavenumber, based on sampling volume's size [math]\displaystyle{ \Delta l }[/math]	[math]\displaystyle{ \hat{k}_\Delta=\frac{0.5}{\Delta l} }[/math]	cpm
[math]\displaystyle{ \hat{k}_n }[/math]	Nyquist wavenumber, via Taylor's hypothesis (temporal measurements)	[math]\displaystyle{ \hat{k}_n=\frac{f_n}{u} }[/math]	cpm
[math]\displaystyle{ \Delta t }[/math]	Sampling interval	[math]\displaystyle{ \frac{1}{f_s} }[/math]	s
[math]\displaystyle{ \omega }[/math]	Angular frequency	[math]\displaystyle{ 2\pi f }[/math]	rad/s

Theoretical Length and Time Scales

Symbol	Description	Eqn	Units
[math]\displaystyle{ \epsilon }[/math]	Turbulent kinetic energy dissipation		W/kg
[math]\displaystyle{ \eta }[/math]	Kolmogorov length scale (smallest overturns)	[math]\displaystyle{ \eta=\left(\frac{\nu^3}{\epsilon}\right)^{1/4}=\frac{1}{2\pi\hat{k}_K} }[/math]	m