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>\left(\bar{u}_1\frac{\partial }{\partial{x}} = \frac{\partial}{\partial{t}}\right)</math>

• Missing the y-axis.

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

Theoretical Length and Time Scales

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