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
|
m s[math]\displaystyle{ ^{-1} }[/math]
|
| NORTH_VEL
|
[math]\displaystyle{ v }[/math]
|
meridional velocity
|
northward_velocity
|
m s[math]\displaystyle{ ^{-1} }[/math]
|
| UP_VEL
|
[math]\displaystyle{ W }[/math]
|
vertical velocity
|
upward_velocity
|
m s[math]\displaystyle{ ^{-1} }[/math]
|
| ERROR_VEL
|
[math]\displaystyle{ u }[/math]
|
error velocity
|
error_velocity
|
m s[math]\displaystyle{ ^{-1} }[/math]
|
| U_VEL
|
[math]\displaystyle{ U }[/math]
|
velocity parellel to mean flow
|
meanflow_velocity
|
m s[math]\displaystyle{ ^{-1} }[/math]
|
| V_VEL
|
[math]\displaystyle{ V }[/math]
|
velocity perpendicular to mean flow
|
crossflow_velocity
|
m s[math]\displaystyle{ ^{-1} }[/math]
|
| Drop_Speed
|
[math]\displaystyle{ W_d }[/math]
|
Profiler fall speed
|
mean_drop_speed
|
m s[math]\displaystyle{ ^{-1} }[/math]
|
| FlowPast_Speed
|
[math]\displaystyle{ U_fp }[/math]
|
Flow speed past sensor
|
mean_velocity_past_turbulence_sensor
|
m s[math]\displaystyle{ ^{-1} }[/math]
|
| AlongBeam_Velocity
|
[math]\displaystyle{ b }[/math]
|
Along-beam velocity from acoustic Doppler sensor
|
observed_velocity_along_an_acoustic_beam
|
m s[math]\displaystyle{ ^{-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
|
m s[math]\displaystyle{ ^{-1} }[/math]
|
| Vertical_Bin_Size
|
[math]\displaystyle{ \delta{z} }[/math]
|
Vertical size of measurement bin for acoustic Doppler sensor
|
vertical_bin_size
|
m
|
| AlongBeam_Distance
|
[math]\displaystyle{ r }[/math]
|
Along-beam distance from acoustic Doppler sensor
|
distance_along_an_acoustic_beam
|
m
|
| AlongBeam_Bin_Size
|
[math]\displaystyle{ \delta{r} }[/math]
|
Along-beam bin size for acoustic Doppler sensor
|
bin_size_along_an_acoustic_beam
|
m
|
| Beam_Angle
|
[math]\displaystyle{ \theta }[/math]
|
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
|
[math]\displaystyle{ \varepsilon }[/math]
|
Turbulent kinetic energy dissipation rate
|
tke_dissipation
|
|
W/kg
|
| 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]
|
m[math]\displaystyle{ ^2 }[/math]s[math]\displaystyle{ ^{-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]
|
m[math]\displaystyle{ ^2 }[/math]s[math]\displaystyle{ ^{-2} }[/math]
|
Fluid properties and background gradients for turbulence calculations
| Parameter Name
|
Symbol
|
Description
|
Standard long name
|
Eqn
|
Units
|
| S
|
[math]\displaystyle{ S }[/math]
|
Background velocity shear
|
background_velocity_shear
|
[math]\displaystyle{ S = \frac{\partial |U|}{\partial z} }[/math]
|
s[math]\displaystyle{ ^{-1} }[/math]
|
| KVISC35
|
[math]\displaystyle{ \nu }[/math]
|
Kinematic viscosity of water for seawater at 35 and 20 [math]\displaystyle{ ^o }[/math]C
|
seawater_kinematic_viscosity_at_35psu
|
[math]\displaystyle{ 1\times 10^{-6} }[/math]
|
m2/s
|
| N
|
[math]\displaystyle{ N }[/math]
|
Background stratification, i.e buoyancy frequency
|
background_buoyancy_frequency
|
[math]\displaystyle{ N = \sqrt{\frac{-g}{\bar{\rho}} \frac{\partial\bar{\rho}}{\partial z}} }[/math]
|
rad/s
|
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{\epsilon/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}{\epsilon}\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{\epsilon}{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]
|
s
|
| [math]\displaystyle{ \Delta s }[/math]
|
Sampling volume dimension
|
|
m
|
| [math]\displaystyle{ f }[/math]
|
Frequency
|
[math]\displaystyle{ \frac{\omega}{2\pi} }[/math]
|
Hz
|
| [math]\displaystyle{ f_n }[/math]
|
Nyquist frequency
|
[math]\displaystyle{ f_n=0.5f_s }[/math]
|
Hz
|
| [math]\displaystyle{ f_s }[/math]
|
Sampling frequency
|
[math]\displaystyle{ f_s=\frac{1}{\Delta t} }[/math]
|
Hz
|
| [math]\displaystyle{ k }[/math]
|
Wavenumbers (angular)
|
[math]\displaystyle{ k=\frac{f}{\bar{u}}=2\pi\hat{k} }[/math]
|
rad/m
|
| [math]\displaystyle{ \hat{k} }[/math]
|
Wavenumbers
|
[math]\displaystyle{ \hat{k}=\frac{k}{2\pi} }[/math]
|
cpm
|
| [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]
|
cpm
|
| [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
|
