Nomenclature

Frame of reference

• Define frame of reference, and notation. Use u,v,w and x,y, and z?
• Dumping a sketch would be useful

Reynold's Decomposition

• Variable names for Decomposition of total, mean, turbulent and waves.

Turbulence properties

Symbol	Description	Eqn	Units
<math>\epsilon</math>	Turbulent kinetic energy dissipation		W/kg
<math>\nu</math>	Viscosity of water for seawater at 35psu and 20 oC	<math> 1\times 10^{-6}</math>	m2/s
<math>N</math>	Buoyancy frequency	<math> N = \sqrt{\frac{-g}{\bar{\rho}} \frac{\partial\bar{\rho}}{\partial z}}</math>	rad/s

Theoretical Length and Time Scales

Symbol	Description	Eqn	Units
<math>\tau_N</math>	Buoyancy timescale	<math> \tau_N = \frac{2\pi}{N}</math>	s
<math>L_E</math>	Ellison length scale (limit of vertical displacement without irreversible mixing)	<math>L_E=\frac {\langle \rho'^2\rangle^{1/2}}{\partial \overbar{\rho}/\partial z}</math>	m
<math>L_\rho/math>	density length scale	<math> L_\rho </math>	m
<math>L_s/math>	Corssin shear length scale (turbulence draws energy from uniform background shear)	<math> L_C = \sqrt{\epsilon/S^3} </math>	m
<math>\tau_N</math>	Buoyancy timescale	<math> \tau_N = \frac{2\pi}{N}</math>	s
<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 [per rad?]
<math>L_o</math>	Ozmidov length scale, measure of largest overturns in a stratified fluid	<math>L_o=\left(\frac{\epsilon}{N^3}\right)^{1/2}</math>	m [per rad?]

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-axi variable. CEB proposes:
  • <math>\Psi_{variable}</math> for model/theoretical spectrum of variable e.g., du/dx or u
  • <math>\Phi_{variable}</math> for observed spectrum of variable e.g., du/dx or u
• Lowest frequency and wavenumber resolvable

Symbol	Description	Eqn	Units
<math>\Delta t</math>	Sampling interval	<math> \frac{1}{f_s} </math>	s
<math>\Delta s</math>	Sampling volume dimension		m
<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>f_s=\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>\hat{k}=\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>\omega</math>	Angular frequency	<math>2\pi f</math>	rad/s