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.

Background (total) velocity

Parameter name	Symbol	Description	Standard long name	Units
EAST_VEL	<math> u </math>	zonal velocity	eastward_velocity	<math>\mathrm{m\, s^{-1}}</math>
NORTH_VEL	<math> v </math>	meridional velocity	northward_velocity	<math>\mathrm{m\, s^{-1}}</math>
UP_VEL	<math> W </math>	vertical velocity	upward_velocity	<math>\mathrm{m\, s^{-1}}</math>
ERROR_VEL	<math> u_e </math>	error velocity	error_velocity	<math>\mathrm{m\, s^{-1}}</math>
U_VEL	<math> U </math>	velocity parellel to mean flow	meanflow_velocity	<math>\mathrm{m\, s^{-1}}</math>
V_VEL	<math> V </math>	velocity perpendicular to mean flow	crossflow_velocity	<math>\mathrm{m\, s^{-1}}</math>
Drop_Speed	<math> W_d </math>	Profiler fall speed	mean_drop_speed	<math>\mathrm{m\, s^{-1}}</math>
FlowPast_Speed	<math> U_P </math>	Flow speed past sensor	mean_velocity_past_turbulence_sensor	<math>\mathrm{m\, s^{-1}}</math>
AlongBeam_Velocity	<math> b </math>	Along-beam velocity from acoustic Doppler sensor	observed_velocity_along_an_acoustic_beam	<math>\mathrm{m\, s^{-1}}</math>
AlongBeam_Residual_Velocity	<math> b^{\prime} </math>	Along-beam velocity from acoustic Doppler sensor with background flow deducted	residual_velocity_along_an_acoustic_beam	<math>\mathrm{m\, s^{-1}}</math>
Vertical_Bin_Size	<math> \delta{z} </math>	Vertical size of measurement bin for acoustic Doppler sensor	vertical_bin_size	<math>\mathrm{m}</math>
AlongBeam_Distance	<math> r </math>	Along-beam distance from acoustic Doppler sensor	distance_along_an_acoustic_beam	<math>\mathrm{m}</math>
AlongBeam_Bin_Size	<math> \delta{r} </math>	Along-beam bin size for acoustic Doppler sensor	bin_size_along_an_acoustic_beam	<math>\mathrm{m}</math>
Beam_Angle	<math> \theta </math>	Beam transmit and receive angle relative to instrument axis for acoustic Doppler sensor	acoustic_beam_angle	<math> ^{\circ} </math>

Turbulence properties

Parameter name	Symbol	Description	Standard long name	Eqn	Units
EPSI	<math>\varepsilon</math>	Turbulent kinetic energy dissipation rate	tke_dissipation		<math> \mathrm{W\, kg^{-1}} </math>
RI	<math>Ri</math>	Richardson number	richardson_number	<math> Ri = \frac{N^2}{S^2}</math>
RI_F	<math>Ri_f</math>	Flux gradient Richardson number	flux_grad_richardson_number	<math> \frac{B}{P} </math> or Ivey & Immerger? Karan et cie
Krho	<math>\kappa_\rho</math>	Turbulent diffusivity	turbulent_diffusivity	<math> \kappa = \Gamma \varepsilon N^{-2} </math>	<math>\mathrm{m^2\, s^{-1}}</math>
DLL	<math>D_{LL}</math>	Second-order longitudinal structure function	second_order_longitudinal_structure_function	<math> D_{LL} = \big\langle[b^{\prime}(r) - b^{\prime}(r+n\delta{r})]^2\big\rangle </math>	<math>\mathrm{m^2\, s^{-2}}</math>

Fluid properties and background gradients for turbulence calculations

Parameter Name	Symbol	Description	Standard long name	Eqn	Units
Z	<math>z</math>	vertical coordinate -- positive upwards	vertical_coordinate		<math>\mathrm{m} </math>
G	<math>g</math>	acceleration of gravity	acceleration_of_gravity	<math> \sim 9.81 </math>	<math>\mathrm{m\, s^{-2}} </math>
SALINITY	<math>S_a</math>	Salinity	Salinity	<math> \sim 35 </math>
TEMP	<math>T</math>	Temperature	Temperature	<math> \sim -2 \rightarrow 40 </math>	<math> \mathrm{^{\circ}C } </math>
PRES	<math>P</math>	Pressure	Pressure	<math> 0\ \rightarrow\ \sim 1\times10^4 </math>	<math> \mathrm{dbar} </math>
DENSITY	<math>\rho</math>	Density of water	Density	<math> \rho = \rho\left(T,S_a,P \right) </math>	<math> \mathrm{kg\, m^{-3}} </math>
ALPHA	<math>\alpha</math>	Temperature coefficient of expansion	Temperature_coefficient_of_expansion	<math> \alpha = \frac{1}{\rho} \frac{\partial\rho}{\partial T} </math>	<math> \mathrm{K^{-1}} </math>
BETA	<math>\beta</math>	Saline coefficient of contraction	Saline_coefficient_of_contraction	<math> \beta = \frac{1}{\rho} \frac{\partial\rho}{\partial S_a} </math>	<math> </math>
S	<math>S</math>	Background velocity shear	background_velocity_shear	<math> S = \left( \left( \frac{\partial U}{\partial z}\right)^2 + \left( \frac{\partial V}{\partial z}\right)^2 \right)^{1/2}</math>	s<math>^{-1}</math>
KVISC35	<math>\nu_{35}</math>	Temperature dependent kinematic viscosity of seawater at a salinity of 35	seawater_kinematic_viscosity_at_35psu	<math> \sim 1\times 10^{-6}</math>	<math> \mathrm{m^2\, s^{-1} } </math>
KVISC00	<math>\nu_{00}</math>	Temperature dependent kinematic viscosity of freshwater	freshwater_kinematic_viscosity	<math> \sim 1\times 10^{-6}</math>	<math> \mathrm{m^2\, s^{-1} } </math>
GAMMA_A	<math>\Gamma</math>	Adiabatic temperature gradient -- salinity, temperature and pressure dependent	Rate of change of temperature due to pressure	<math> \sim 1\times 10^{-4} </math>	<math> \mathrm{K\, dbar^{-1} } </math>
N	<math>N</math>	Background stratification, i.e buoyancy frequency	background_buoyancy_frequency	<math> N^2 = g\left[ \alpha\left(\Gamma + \frac{\partial T}{\partial z} \right) - \beta \frac{\partial S_a}{\partial z} \right] </math>	<math> \mathrm{rad\, s^{-1} } </math>

Theoretical Length and Time Scales

Parameter	Symbol	Description	Standard long name	Eqn	Units
T_N	<math>\tau_N</math>	Buoyancy timescale	buoyancy_time_scale	<math> \tau_N = \frac{2\pi}{N}</math>	s
L_E	<math>L_E</math>	Ellison length scale (limit of vertical displacement without irreversible mixing)	Eliison_lenght_scale	<math>L_E=\frac {\langle \rho'^2\rangle^{1/2}}{\partial \overline{\rho}/\partial z}</math>	m
L_RHO	<math> L_\rho</math>	Density length scale	density_length_scale	<math> L_\rho </math>	m
L_S	<math>L_S</math>	Corssin length scale	Corssin_shear_length_scale	<math> L_S = \sqrt{\varepsilon/S^3} </math>	m
L_K	<math>\eta</math>	Kolmogorov length scale (smallest overturns)	Kolmogorov_length_scale	<math>\eta=\left(\frac{\nu^3}{\varepsilon}\right)^{1/4}=\frac{1}{2\pi\hat{k}_K}</math>	m
L_O	<math>L_o</math>	Ozmidov length scale, measure of largest overturns in a stratified fluid	Ozmidov_stratification_length_scale	<math>L_o=\left(\frac{\varepsilon}{N^3}\right)^{1/2}</math>	m
L_T	<math>L_T</math>	Thorp length scale	Thorpe_stratification_length_scale	<math>L_T</math>	m

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>	<math> \mathrm{s} </math>
<math>f_s</math>	Sampling rate	<math>f_s=\frac{1}{\Delta t} </math>	<math> \mathrm{s^{-1}} </math>
<math>\Delta s</math>	Sampling volume dimension	<math> \Delta s = U_P \Delta t </math>	<math> \mathrm{m} </math>
<math>f</math>	Cyclic frequency	<math>f=\frac{\omega}{2\pi}</math>	<math> \mathrm{Hz} </math>
<math>\omega</math>	Angular frequency	<math>\omega = 2\pi f</math>	<math> \mathrm{rad\, s^{-1}} </math>
<math>f_N</math>	Nyquist frequency	<math>f_N=0.5f_s</math>	<math> \mathrm{Hz} </math>
<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

Supplementary Data required for computing Turbulence

Channel	Shear Probes	ADCP	ADVs
Ax	x	x	x
Ay	x	x	x
Az	x	x	x