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

Turbulence properties

Parameter name	Symbol	Description	Standard long name	Eqn	Units
EPSI	[math]\displaystyle{ \varepsilon }[/math]	Turbulent kinetic energy dissipation rate	tke_dissipation		[math]\displaystyle{ \mathrm{W\, kg^{-1}} }[/math]
RI	[math]\displaystyle{ Ri }[/math]	Richardson number	richardson_number	[math]\displaystyle{ Ri = \frac{N^2}{S^2} }[/math]
RI_F	[math]\displaystyle{ Ri_f }[/math]	Flux gradient Richardson number	flux_grad_richardson_number	[math]\displaystyle{ \frac{B}{P} }[/math] or Ivey & Immerger? Karan et cie
Krho	[math]\displaystyle{ \kappa_\rho }[/math]	Turbulent diffusivity	turbulent_diffusivity	[math]\displaystyle{ \kappa = \Gamma \varepsilon N^{-2} }[/math]	[math]\displaystyle{ \mathrm{m^2\, s^{-1}} }[/math]
DLL	[math]\displaystyle{ D_{LL} }[/math]	Second-order longitudinal structure function	second_order_longitudinal_structure_function	[math]\displaystyle{ D_{LL} = \big\langle[b^{\prime}(r) - b^{\prime}(r+n\delta{r})]^2\big\rangle }[/math]	[math]\displaystyle{ \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]\displaystyle{ z }[/math]	vertical coordinate -- positive upwards	vertical_coordinate		[math]\displaystyle{ \mathrm{m} }[/math]
G	[math]\displaystyle{ g }[/math]	acceleration of gravity	acceleration_of_gravity	[math]\displaystyle{ \sim 9.81 }[/math]	[math]\displaystyle{ \mathrm{m\, s^{-2}} }[/math]
SALINITY	[math]\displaystyle{ S_a }[/math]	Salinity	Salinity	[math]\displaystyle{ \sim 35 }[/math]
TEMP	[math]\displaystyle{ T }[/math]	Temperature	Temperature	[math]\displaystyle{ \sim -2 \rightarrow 40 }[/math]	[math]\displaystyle{ \mathrm{^{\circ}C } }[/math]
PRES	[math]\displaystyle{ P }[/math]	Pressure	Pressure	[math]\displaystyle{ 0\ \rightarrow\ \sim 1\times10^4 }[/math]	[math]\displaystyle{ \mathrm{dbar} }[/math]
DENSITY	[math]\displaystyle{ \rho }[/math]	Density of water	Density	[math]\displaystyle{ \rho = \rho\left(T,S_a,P \right) }[/math]	[math]\displaystyle{ \mathrm{kg\, m^{-3}} }[/math]
ALPHA	[math]\displaystyle{ \alpha }[/math]	Temperature coefficient of expansion	Temperature_coefficient_of_expansion	[math]\displaystyle{ \alpha = \frac{1}{\rho} \frac{\partial\rho}{\partial T} }[/math]	[math]\displaystyle{ \mathrm{K^{-1}} }[/math]
BETA	[math]\displaystyle{ \beta }[/math]	Saline coefficient of contraction	Saline_coefficient_of_contraction	[math]\displaystyle{ \beta = \frac{1}{\rho} \frac{\partial\rho}{\partial S_a} }[/math]	[math]\displaystyle{ }[/math]
S	[math]\displaystyle{ S }[/math]	Background velocity shear	background_velocity_shear	[math]\displaystyle{ S = \left( \left( \frac{\partial U}{\partial z}\right)^2 + \left( \frac{\partial V}{\partial z}\right)^2 \right)^{1/2} }[/math]	s[math]\displaystyle{ ^{-1} }[/math]
KVISC35	[math]\displaystyle{ \nu_{35} }[/math]	Temperature dependent kinematic viscosity of seawater at a salinity of 35	seawater_kinematic_viscosity_at_35psu	[math]\displaystyle{ \sim 1\times 10^{-6} }[/math]	[math]\displaystyle{ \mathrm{m^2\, s^{-1} } }[/math]
KVISC00	[math]\displaystyle{ \nu_{00} }[/math]	Temperature dependent kinematic viscosity of freshwater	freshwater_kinematic_viscosity	[math]\displaystyle{ \sim 1\times 10^{-6} }[/math]	[math]\displaystyle{ \mathrm{m^2\, s^{-1} } }[/math]
GAMMA_A	[math]\displaystyle{ \Gamma }[/math]	Adiabatic temperature gradient -- salinity, temperature and pressure dependent	Rate of change of temperature due to pressure	[math]\displaystyle{ \sim 1\times 10^{-4} }[/math]	[math]\displaystyle{ \mathrm{K\, dbar^{-1} } }[/math]
N	[math]\displaystyle{ N }[/math]	Background stratification, i.e buoyancy frequency	background_buoyancy_frequency	[math]\displaystyle{ N^2 = g\left[ \alpha\left(\Gamma + \frac{\partial T}{\partial z} \right) - \beta \frac{\partial S_a}{\partial z} \right] }[/math]	[math]\displaystyle{ \mathrm{rad\, s^{-1} } }[/math]

Theoretical Length and Time Scales

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

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

Symbol	Description	Eqn	Units
[math]\displaystyle{ \Delta t }[/math]	Sampling interval	[math]\displaystyle{ \frac{1}{f_s} }[/math]	[math]\displaystyle{ \mathrm{s} }[/math]
[math]\displaystyle{ f_s }[/math]	Sampling rate	[math]\displaystyle{ f_s=\frac{1}{\Delta t} }[/math]	[math]\displaystyle{ \mathrm{s^{-1}} }[/math]
[math]\displaystyle{ \Delta s }[/math]	Sampling volume dimension	[math]\displaystyle{ \Delta s = U_P \Delta t }[/math]	[math]\displaystyle{ \mathrm{m} }[/math]
[math]\displaystyle{ f }[/math]	Cyclic frequency	[math]\displaystyle{ f=\frac{\omega}{2\pi} }[/math]	[math]\displaystyle{ \mathrm{Hz} }[/math]
[math]\displaystyle{ \omega }[/math]	Angular frequency	[math]\displaystyle{ \omega = 2\pi f }[/math]	[math]\displaystyle{ \mathrm{rad\, s^{-1}} }[/math]
[math]\displaystyle{ f_N }[/math]	Nyquist frequency	[math]\displaystyle{ f_N=0.5f_s }[/math]	[math]\displaystyle{ \mathrm{Hz} }[/math]
[math]\displaystyle{ k }[/math]	Cyclic wavenumber	[math]\displaystyle{ k=\frac{f}{U_P} }[/math]	[math]\displaystyle{ \mathrm{cpm} }[/math]
[math]\displaystyle{ \hat{k} }[/math]	Angular wavenumber	[math]\displaystyle{ \hat{k}=\frac{\omega}{U_P} = 2\pi k }[/math]	[math]\displaystyle{ \mathrm{cpm} }[/math]
[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]	[math]\displaystyle{ \mathrm{cpm} }[/math]
[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{ \omega }[/math]	Angular frequency	[math]\displaystyle{ 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