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

Turbulence properties

Parameter name	Symbol	Description	Standard long name	Eqn	Units
EPSI	$\epsilon$	Turbulent kinetic energy dissipation rate	tke_dissipation		$\mathrm{W}\mathrm{k}{\mathrm{g}}^{\mathrm{-}\mathrm{1}}$
RI	$Ri$	Richardson number	richardson_number	$Ri=\frac{N^2}{S^2}$
RI_F	$R{i}_f$	Flux gradient Richardson number	flux_grad_richardson_number	$\frac{B}{P}$ or Ivey & Immerger? Karan et cie
Krho	${\kappa }_{\rho }$	Turbulent diffusivity	turbulent_diffusivity	$\kappa =\mathrm{\Gamma }\epsilon N^{-2}$	${\mathrm{m}}^{\mathrm{2}}{\mathrm{s}}^{\mathrm{-}\mathrm{1}}$
DLL	$D_{LL}$	Second-order longitudinal structure function	second_order_longitudinal_structure_function	$D_{LL}=⟨[b^{\prime }(r)-b^{\prime }(r+n\delta r){]}^2⟩$	m$2^{}$s${-2}^{}$

Fluid properties and background gradients for turbulence calculations

Parameter Name	Symbol	Description	Standard long name	Eqn	Units
S	$S$	Background velocity shear	background_velocity_shear	$S={({\left(\frac{\partial U}{\partial z}\right)}^2+{\left(\frac{\partial V}{\partial z}\right)}^2)}^{1/2}$	s${-1}^{}$
KVISC35	$\nu$	Kinematic viscosity of water for seawater at 35 and 20 $o^{}$C	seawater_kinematic_viscosity_at_35psu	$1\times 10^{-6}$	m2/s
N	$N$	Background stratification, i.e buoyancy frequency	background_buoyancy_frequency	$N=\sqrt{\frac{-g}{\overline{\rho }}\frac{\partial \overline{\rho }}{\partial z}}$	rad/s

Theoretical Length and Time Scales

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

Turbulence Spectrum

Taylor's Frozen Turbulence for converting temporal to spatial measurements $({\overline{u}}_1\frac{\partial }{\partial x}=\frac{\partial }{\partial t})$

• Missing the y-axi variable. CEB proposes:
  • ${\mathrm{\Psi }}_{variable}$ for model/theoretical spectrum of variable e.g., du/dx or u
  • ${\mathrm{\Phi }}_{variable}$ for observed spectrum of variable e.g., du/dx or u
• Lowest frequency and wavenumber resolvable

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