Nomenclature
From Atomix
Frame of reference
- Define frame of reference, and notation. Use u,v,w and x,y, and z?
- Dumping a sketch would be useful
---- MOVE THIS TO CONCEPT ---
Reynold's Decomposition
- Variable names for Decomposition of total, mean, turbulent and waves.
- Needs to be decided across the ADV/ADCP working groups
---- MOVE THIS TO FUNDAMENTALS ---
Background (total) velocity
---- MAKE SURE TO BE CONSISTENT WITH NETCDF TABLE --- ---- NETCDF TABLE will have own page (periodic copy&paste of excel sheet)---
| Symbol | Description | Units |
|---|---|---|
| u | zonal velocity | <math> \mathrm{m\, s^{-1}}</math> |
| v | meridional velocity | <math>\mathrm{m\, s^{-1}}</math> |
| <math>u_e</math> | error velocity | <math>\mathrm{m\, s^{-1}}</math> |
| V | velocity perpendicular to mean flow | <math>\mathrm{m\, s^{-1}}</math> |
| <math>W_d</math> | Profiler fall speed | <math>\mathrm{m\, s^{-1}}</math> |
| <math>U_P</math> | Flow speed past sensor | <math>\mathrm{m\, s^{-1}}</math> |
| b | Along-beam velocity from acoustic Doppler sensor | <math>\mathrm{m\, s^{-1}}</math> |
| <math> b^{\prime}</math> | Along-beam velocity from acoustic Doppler sensor with background flow deducted | <math>\mathrm{m\, s^{-1}}</math> |
| <math> \delta{z}</math> | Vertical size of measurement bin for acoustic Doppler sensor | <math>\mathrm{m}</math> |
| r | Along-beam distance from acoustic Doppler sensor | <math>\mathrm{m}</math> |
| <math> \delta{r}</math> | Along-beam bin size for acoustic Doppler sensor | <math>\mathrm{m}</math> |
| <math> \theta</math> | Beam transmit and receive angle relative to instrument axis for acoustic Doppler sensor | <math>^{\circ}</math> |
Turbulence properties
| Symbol | Description | Eqn | Units |
|---|---|---|---|
| <math>\varepsilon</math> | Turbulent kinetic energy dissipation rate | <math>\mathrm{W\, kg^{-1}}</math> | |
| Ri | Richardson number | <math>Ri = \frac{N^2}{S^2}</math> | |
| <math> Ri_f </math> | Flux gradient Richardson number | <math>\frac{B}{P}</math> or Ivey & Imberger? Karan et cie | |
| <math>\kappa_\rho</math> | Turbulent eddy diffusivity via Osborn's model | <math>\kappa = \Gamma \varepsilon N^{-2}</math> | <math>\mathrm{m^2\, s^{-1}}</math> |
| <math>D_{LL}</math> | 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
| Symbol | Description | Eqn | Units |
|---|---|---|---|
| <math>S_a</math> | Salinity | <math> \sim 35 </math> | |
| T | Temperature | <math>\sim -2 \rightarrow 40 </math> | <math> \mathrm{^{\circ}C } </math> |
| P | Pressure | <math>0\ \rightarrow\ \sim 1\times10^4</math> | <math>\mathrm{dbar} </math> |
| <math>\rho</math> | Density of water | <math> \rho = \rho\left(T,S_a,P \right)</math> | <math>\mathrm{kg\, m^{-3}} </math> |
| <math>\alpha</math> | Temperature coefficient of expansion | <math> \alpha = \frac{1}{\rho} \frac{\partial\rho}{\partial T}</math> | <math> \mathrm{K^{-1}}</math> |
| <math>\beta</math> | Saline coefficient of contraction | <math> \beta = \frac{1}{\rho} \frac{\partial\rho}{\partial S_a}</math> | |
| S | 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> | <math> \mathrm{s^{-1}} </math> |
| <math> \nu_{35} </math> | Temperature dependent kinematic viscosity of seawater at a salinity of 35 | <math> \sim 1\times 10^{-6} </math> | <math> \mathrm{m^2\, s^{-1} } </math> |
| <math>\nu_{00}</math> | Temperature dependent kinematic viscosity of freshwater | <math>\sim 1\times 10^{-6} </math> | <math>\mathrm{m^2\, s^{-1} } </math> |
| <math>\Gamma </math> | Adiabatic temperature gradient -- salinity, temperature and pressure dependent | <math>\sim 1\times 10^{-4}</math> | <math>\mathrm{K\, dbar^{-1} } </math> |
| <math>N </math> | Background stratification, i.e 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
| Symbol | Description | Eqn | Units |
|---|---|---|---|
| <math>\tau_N</math> | Buoyancy timescale | <math> \tau_N = \frac{1}{N}</math> | <math> \mathrm{s} </math> |
| <math>T_N</math> | Buoyancy period | <math> T_N = \frac{2\pi}{N}</math> | <math> \mathrm{s} </math> |
| <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 \overline{\rho}/\partial z}</math> | <math> \mathrm{m} </math> |
| <math> L_\rho</math> | Density length scale | <math> L_\rho </math> | <math> \mathrm{m} </math> |
| <math>L_S</math> | Corssin length scale | <math> L_S = \sqrt{\varepsilon/S^3} </math> | <math> \mathrm{m} </math> |
| <math>\eta</math> | Kolmogorov length scale (smallest overturns) | <math>\eta=\left(\frac{\nu^3}{\varepsilon}\right)^{1/4}</math> | <math> \mathrm{m} </math> |
| <math>L_K</math> | Kolmogorov length scale (smallest overturns) | <math>L_K=\left(\frac{\nu^3}{\varepsilon}\right)^{1/4}</math> | <math> \mathrm{m} </math> |
| <math>L_o</math> | Ozmidov length scale, measure of largest overturns in a stratified fluid | <math>L_o=\left(\frac{\varepsilon}{N^3}\right)^{1/2}</math> | <math> \mathrm{m} </math> |
| <math>L_T</math> | Thorp length scale | <math>L_T</math> | <math> \mathrm{m} </math> |
Turbulence Spectrum
These variables are used to express the Turbulence spectrum expected shapes.
CynthiaBluteau (talk) 01:08, 14 October 2021 (CEST) add theses to table.
- <math>\Psi_{\mathrm{variable}}</math> for model/theoretical spectrum of variable e.g., du/dx or u
- <math>\Phi_{\mathrm{variable}}</math> for observed spectrum of variable e.g., du/dx or u
| 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> | Sample spacing | <math> \Delta s = U_P \Delta t </math> | <math> \mathrm{m} </math> |
| <math>\Delta l</math> | Linear dimension of sampling volume (instrument dependent) | <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> | Cyclic wavenumber | <math>k=\frac{f}{U_P}</math> | <math> \mathrm{cpm} </math> |
| <math>\hat{k}</math> | Angular wavenumber | <math>\hat{k}=\frac{\omega}{U_P} = 2\pi k</math> | <math> \mathrm{rad\, m^{-1}} </math> |
| <math>k_\Delta</math> | Nyquist wavenumber, based on sampling volume size <math>\Delta l</math> | <math>k_\Delta=\frac{0.5}{\Delta l}</math> | <math> \mathrm{cpm} </math> |
| <math>k_N</math> | Nyquist wavenumber, via Taylor's hypothesis | <math>k_N=\frac{f_N}{U_P}</math> | <math> \mathrm{cpm} </math> |
