% $Id$

% Purpose: Commands general to fluid dynamics

% Copyright (c) 1998--2009, Charles S. Zender
% This program may be distributed and/or modified under the
% conditions of the LaTeX Project Public License (LPPL), 
% either version 1.2, or (at your option) any later version.
% LPPL: http://www.latex-project.org/lppl.txt

% The original author of this software, Charlie Zender, seeks to improve
% it with your suggestions, contributions, bug-reports, and patches.
% Charlie Zender <surname@uci.edu>, surname=zender
% Department of Earth System Science
% University of California at Irvine
% Irvine, CA 92697-3100

% Dependencies: tdy.sty

% Usage:
% \usepackage{dyn} % Fluid dynamics

% Message printed when LaTeX called
\@ifundefined{ProvidesPackage}{}{
\ProvidesPackage{dyn}[2002/09/22 v1.24 Fluid dynamics]
} % end ProvidesPackage

\usepackage{tdy} % Thermodynamics

% 0. Provided commands
\providecommand{\azi}{\ensuremath{\phi}}\renewcommand{\azi}{\ensuremath{\phi}} % [rdn] Azimuthal angle
\providecommand{\mrd}{\ensuremath{\phi}}\renewcommand{\mrd}{\ensuremath{\phi}} % [rdn] Meridional angle (latitude)
\providecommand{\plr}{\ensuremath{\theta}}\renewcommand{\plr}{\ensuremath{\theta}} % [rdn] Polar angle (zenith angle)
\providecommand{\rdl}{\ensuremath{r}}\renewcommand{\rdl}{\ensuremath{r}} % [m] Radial distance
\providecommand{\rds}{\ensuremath{r}}\renewcommand{\rds}{\ensuremath{r}} % [m] Radius
\providecommand{\znl}{\ensuremath{\lambda}}\renewcommand{\znl}{\ensuremath{\lambda}} % [rdn] Zonal angle (longitude)

% 1. Primary commands
\newcommand{\cross}{\ensuremath{\times}} % [frc] Cross product
\newcommand{\cnfstt}{\ensuremath{p}} % [frc] Confidence statistic
\newcommand{\arm}{\ensuremath{\mathrm{AR}}} % [idx] Autoregression model
\newcommand{\armrdr}{\ensuremath{p}} % [idx] Autoregression model order
\newcommand{\crrcff}{\ensuremath{r}} % [frc] Linear correlation coefficient (Pearson coefficient)
\newcommand{\dmt}{\ensuremath{D}} % [m] Diameter
\newcommand{\dst}{\ensuremath{n}} % Distribution
\newcommand{\frc}{\ensuremath{F}} % [kg m s-2] [N] Force
\newcommand{\grv}{\ensuremath{g}} % [m s-2] Gravity
\newcommand{\hgt}{\ensuremath{z}} % [m] Height
\newcommand{\dpt}{\ensuremath{z}} % [m] Depth (normally positive definite)
\newcommand{\xhatidx}{\ensuremath{\mathbf{\hat{x}}_{\iii}}} % Unit vector in ith direction
\newcommand{\ihat}{\ensuremath{\mathbf{\hat{i}}}} % Unit vector in x-direction
\newcommand{\ivec}{\ensuremath{\vec{\imath}}} % Vector in x-direction
\newcommand{\jhat}{\ensuremath{\mathbf{\hat{j}}}} % Unit vector in y-direction
\newcommand{\jvec}{\ensuremath{\vec{\jmath}}} % Vector in y-direction
\newcommand{\khat}{\ensuremath{\mathbf{\hat{k}}}} % Unit vector in z-direction
\newcommand{\kvec}{\ensuremath{\vec{k}}} % Vector in z-direction
\newcommand{\lngscl}{\ensuremath{L}} % [m] Length scale
\newcommand{\mmn}{\ensuremath{p}} % [kg m s-1] Momentum
\newcommand{\mss}{\ensuremath{M}} % [kg] Mass
\newcommand{\mtrdrv}{\ensuremath{D}} % Material derivative 
\newcommand{\nablavec}{\ensuremath{\vec{\nabla}}} % Vector form of del operator
\newcommand{\pdffnc}{\ensuremath{p}} % Probability density function
\newcommand{\pnt}{\ensuremath{P}} % Generic point
\newcommand{\psn}{\ensuremath{r}} % [m] Position
\newcommand{\rms}{\ensuremath{\mathrm{RMS}}} % Root-mean-square error
\newcommand{\rskrlt}{\ensuremath{\mathrm{RR}}} % [frc] Relative Risk
\newcommand{\sclfld}{\ensuremath{u}} % Generic scalar field
\newcommand{\sdn}{\ensuremath{\sigma}} % Standard deviation
\newcommand{\sfc}{\ensuremath{S}} % Surface
\newcommand{\spd}{\ensuremath{u}} % [m s-1] Speed
\newcommand{\strtnsvsc}{\ensuremath{\tau}} % Viscous stress tensor
\newcommand{\strtns}{\ensuremath{T}} % Stress tensor
\newcommand{\tm}{\ensuremath{t}} % [s] Time
\newcommand{\vct}{\ensuremath{v}} % Generic vector
\newcommand{\vlcngl}{\ensuremath{\omega}} % [rdn s-1] Angular velocity
\newcommand{\vlcu}{\ensuremath{u}} % [m s-1] Velocity expressed as u
\newcommand{\vlc}{\ensuremath{v}} % [m s-1] Velocity
\newcommand{\vlm}{\ensuremath{V}} % [m3] Volume
\newcommand{\wndspd}{\ensuremath{U}} % [m s-1] Scalar wind speed
\newcommand{\xcl}{\ensuremath{a}} % [m s-2] Acceleration
\newcommand{\xsa}{\ensuremath{A}} % [m2] Cross-sectional area
\newcommand{\xsx}{\ensuremath{A}} % [m2] Cross-sectional area

% 2. Derived commands
\newcommand{\azihat}{\ensuremath{\mbox{\boldmath$\hat{\azi}$}}} % Unit vector in azimuthal direction
\newcommand{\crrcffprs}{\ensuremath{\crrcff}} % [frc] Linear correlation coefficient, unranked (Pearson)
\newcommand{\crrcffspr}{\ensuremath{\crrcff_{\mathrm{s}}}} % [frc] Linear correlation coefficient, ranked (Spearman)
\newcommand{\crrcffsqr}{\ensuremath{\crrcff^{2}}} % [frc] Linear correlation coefficient squared
\newcommand{\frcbld}{\ensuremath{\mathbf{\frc}}} % [kg m s-2] Boldface force
\newcommand{\frcgrvbld}{\ensuremath{\mathbf{\frc}_{\grv}}} % [kg m s-2] Boldface force of gravity
\newcommand{\grvbld}{\ensuremath{\mathbf{\grv}}} % [m s-2] Boldface gravity
\newcommand{\grvvec}{\ensuremath{\vec{\grv}}} % [m s-2] Gravity vector
\newcommand{\ihatbld}{\ensuremath{\mathbf{\ihat}}} % Bold unit vector in x-direction
\newcommand{\jhatbld}{\ensuremath{\mathbf{\jhat}}} % Bold unit vector in y-direction
\newcommand{\khatbld}{\ensuremath{\mathbf{\khat}}} % Bold unit vector in z-direction
\newcommand{\mmnbld}{\ensuremath{\mathbf{p}}} % [m2 s-1] Boldface momentum
\newcommand{\mmrone}{\ensuremath{\mmr_{1}}} % [kg kg-1] Mixing ratio one
\newcommand{\mmrtwo}{\ensuremath{\mmr_{2}}} % [kg kg-1] Mixing ratio two
\newcommand{\mrdhat}{\ensuremath{\mbox{\boldmath$\hat{\mrd}$}}} % Unit vector in meridional direction
\newcommand{\mssone}{\ensuremath{\mss_{1}}} % [kg] Mass one
\newcommand{\msstwo}{\ensuremath{\mss_{2}}} % [kg] Mass two
\newcommand{\plrhat}{\ensuremath{\mbox{\boldmath$\hat{\plr}$}}} % Unit vector in polar direction
\newcommand{\prphat}{\ensuremath{\mbox{\boldmath$\hat{e}$}}} % Unit vector in direction of propogation
\newcommand{\psnbld}{\ensuremath{\mathbf{\psn}}} % [m] Boldface position 
\newcommand{\psnvec}{\ensuremath{\vec{\psn}}} % [m] Position vector 
\newcommand{\rdlhat}{\ensuremath{\mathbf{\hat{\rdl}}}} % [m] Unit vector in radial direction
\newcommand{\rdsbld}{\ensuremath{\mathbf{\rds}}} % [m] Boldface radius
\newcommand{\rdssqr}{\ensuremath{\rds^{2}}} % [m2] Square of radius
\newcommand{\rdshatbld}{\ensuremath{\mathbf{\hat{\rds}}}} % [m] Boldface radius hat
\newcommand{\rmsabs}{\ensuremath{\rms_{\mathrm{abs}}}} % Absolute root-mean-square error
\newcommand{\rmsrlt}{\ensuremath{\rms_{\mathrm{rel}}}} % Relative root-mean-square error
\newcommand{\sdnxxx}{\ensuremath{\sdn_{\xxx}}} % Standard deviation of x
\newcommand{\tptone}{\ensuremath{\tpt_{1}}} % [K] Temperature one
\newcommand{\tpttwo}{\ensuremath{\tpt_{2}}} % [K] Temperature two
\newcommand{\vctazi}{\ensuremath{\vct_{\azi}}} % Azimuthal component of generic vector field
\newcommand{\vctbld}{\ensuremath{\mathbf{\vct}}} % Generic vector
\newcommand{\vctmrd}{\ensuremath{\vct_{\mrd}}} % Meridional component of generic vector field
\newcommand{\vctplr}{\ensuremath{\vct_{\plr}}} % Polar component of generic vector field
\newcommand{\vctrdl}{\ensuremath{\vct_{\rdl}}} % Radial component of generic vector field
\newcommand{\vctvec}{\ensuremath{\vec{\vct}}} % Generic vector
\newcommand{\vctxxx}{\ensuremath{\vct_{x}}} % x-component of generic vector field
\newcommand{\vctyyy}{\ensuremath{\vct_{y}}} % y-component of generic vector field
\newcommand{\vctznl}{\ensuremath{\vct_{\znl}}} % Zonal component of generic vector field
\newcommand{\vctzzz}{\ensuremath{\vct_{z}}} % z-component of generic vector field
\newcommand{\vlcbld}{\ensuremath{\mathbf{\vlc}}} % [m s-1] Boldface velocity
\newcommand{\vlcinf}{\ensuremath{\vlc_{\infty}}} % [m s-1] Unperturbed velocity
\newcommand{\vlcvec}{\ensuremath{\vec{\vlc}}} % [m s-1] Velocity vector 
\newcommand{\vlcxxx}{\ensuremath{\vlc_{\xxx}}} % [m s-1] x-component of velocity
\newcommand{\vlcyyy}{\ensuremath{\vlc_{\yyy}}} % [m s-1] y-component of velocity
\newcommand{\vlczzz}{\ensuremath{\vlc_{\zzz}}} % [m s-1] z-component of velocity
\newcommand{\wndspdavg}{\ensuremath{\bar{\wndspd}}} % [m s-1] Wind speed, climatological mean
\newcommand{\xclbld}{\ensuremath{\mathbf{\xcl}}} % [m s-2] Boldface acceleration
\newcommand{\xxxavg}{\ensuremath{\bar{\xxx}}} % Mean value of x
\newcommand{\znlhat}{\ensuremath{\mbox{\boldmath$\hat{\znl}$}}} % Unit vector in zonal direction

% 3. Doubly-derived commands
\newcommand{\vlcxxxtld}{\ensuremath{\tilde{\vlc}_{\xxx}}} % Transposed x-component of velocity
\newcommand{\vlcyyytld}{\ensuremath{\tilde{\vlc}_{\yyy}}} % Transposed y-component of velocity
\newcommand{\vlczzztld}{\ensuremath{\tilde{\vlc}_{\zzz}}} % Transposed z-component of velocity