%SourceDoc aofd.tex
% -------------------------------------------------------------
% This file contains abbreviations, mainly mathematical
% -------------------------------------------------------------
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% This is the environment for the problem sets
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%


% This is for the problem sets of chapter 1.
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\newcommand{\ir}{\mathrm{i}}
\newc{\s}{\,\text{s}\xspace} \newc{\m}{\,\text{m}\xspace}
\newc{\cm}{\,\text{cm}\xspace}
\newc{\km}{\,\text{km}\xspace}
\newc{\kg}{\,\text{kg}\xspace} \newcm{\ps}{\, \text{s}^{-1}\xspace}
\newc{\Kv}{\,\text{K}\xspace}
\newc{\Sv}{\,\text{Sv}\xspace}
\newc{\rms}{\text{rms}}
\newc{\qg}{quasi-geostrophic\xspace}
\newc{\pg}{planetary-geostrophic\xspace}
\newc{\BV}{Brunt--V\"ais\"al\"a\xspace}
\newc{\crn}{\nonumber  \\}
\newc{\qqquad}{\qquad \qquad}
\newc{\cdel}{\cdot \nabla}
\newcommand{\cg}{c_{\mkern -1mu g}}
\newcommand{\cbg}{\bm{c}_{g}}
%\renewcommand{\div}[1][]{\nabla_{#1}\cdot}
\newcommand{\eten}[1]{\ensuremath{\times 10^{#1}}\xspace}
%\newc{\Ro}{\ensuremath{R_o}\xspace}
\newc{\Ro}{\ensuremath{\mathit{Ro}}\xspace}
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\newc{\Ek}{\ensuremath{\mathit{Ek}}\xspace}
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\newc{\Ri}{\ensuremath{\mathit{Ri}}\xspace}
\newc{\Rot}{\ensuremath{\mathit{Ro_\mathrm{t}}}\xspace}
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\newcommand{\pptwo}[2]{{\partial^2 #1 / \partial #2^2}}
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\newc{\bppp}[2]{({\partial #1}/{\partial #2})}
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\newc{\dbfrac}[2]{\left( \dfrac{#1}{#2} \right) }
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\newc{\bdds}[3]{\left(\frac{\d #1}{\d #2}\right)_{\! \! #3}}

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\newc{\K}{\mathcal{K}}
\newcommand{\bta}{\ensuremath{\beta}\xspace}
\newcommand{\ustar}{\ensuremath{{u^*}} }
\newc{\psisp}[1]{\psi^{(#1)}}
\newcommand{\psidag}{\psi^\dagger}
\newc{\psibar}{\overline \psi}
\newc{\Psibar}{\overline \Psi}
\newc{\phibar}{\overline \phi}
\newc{\thetabar}{\overline \theta}
\newc{\varthetabar}{\overline \vartheta}
\newc{\varphibar}{\overline \varphi}
\renewcommand{\hbar}{\overline h}
\newcommand{\hbarr}{\overline h}
%\providecommand{\dtbar}{{\raisebox{2pt}{\mathchar'26}\mkern-12mu \d}}
\providecommand{\dbar}{~{\raisebox{3pt}{--}\mkern-13mu \d \mkern 1mu}}
\providecommand{\dsbar}{\,{\raisebox{2.5pt}{--}\mkern-12.5mu \d \mkern 1mu}}
\newc{\qbar}{\overline q}
\newc{\ubar}{\overline u}
\newc{\vbar}{\overline v}
\newcommand{\mbar}{\overline m}
\providecommand{\wbar}{}
\renewcommand{\wbar}{\overline w}
\newc{\ubbar}{\overline \ub}
\newc{\vbbar}{\overline \vb}
\newc{\bbar}{\overline b}
\newc{\pbar}{\overline p}
\newc{\zbar}{\overline z}
\newc{\rhobar}{\overline \rho}
\newc{\Fbar}{\overline F}
\newc{\Jbar}{\overline J}
\newc{\Sbar}{\overline S}
\newc{\bybar}{\overline \by}
\newcommand{\sigmabar}{\overline \sigma}
\newc{\zetabar}{\overline \zeta}
\newc{\etabar}{\overline \eta}
\newc{\betahat}{\ensuremath{\what \beta}}
\newc{\kbeta}{k_\beta}
\newc{\that}{{\what t}}
\newc{\khat}{\what k}
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\newc{\zetahat}{\ensuremath{\what \zeta}}
\newc{\deltahat}{\what \delta}
\newc{\etahat}{\what \eta}
\newc{\ubhat}{\what\ub}
\newc{\vbhat}{\what\vb}
\newc{\xhat}{{\what x}}
\newc{\xbhat}{{\what \xb}}
\newc{\yhat}{{\what y}}
\newc{\zhat}{{\what z}}
\newc{\uhat}{\what u}
\newc{\vhat}{\what v}
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\newc{\bhat}{\what b}
\newc{\fbhat}{\what{\bm{f}}}
\newc{\phihat}{\what \phi}
\newc{\byhat}{\what \by}
\newc{\hhat}{\ensuremath{\what h}}
\newc{\fhat}{\ensuremath{\what f}}
\newc{\psihat}{\what \psi}
\newc{\Psihat}{\what \Psi}
\newc{\Nhat}{\what N}
\newc{\Nbar}{\overline N}
\newc{\omegahat}{\what \omega}
\newc{\qhat}{\what q}
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\newcommand{\delhat}{\what \nabla}
\newcommand{\divhat}{\what \nabla \cdot}
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\newcommand{\tautil}{\wtilde \tau}
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\newcommand{\wtil}{\wtilde w}
\newcommand{\vtil}{\wtilde v}
\newcommand{\util}{\wtilde u}
\newcommand{\ptil}{\wtilde p}
\newc{\tauhat}{\what \tau}
\newcommand{\Ehat}{\what E}
\newcommand{\Zhat}{\what Z}
\newcommand{\Ebar}{\overline E}
\newcommand{\Zbar}{\overline Z}
\newc{\ug}{u_g}
\newc{\vg}{\ensuremath{v_g}\xspace}
\newc{\Lr}{\Ld}
\newcommand{\Ld}{\ensuremath{L_{d}}\xspace}
\newcommand{\kd}{\ensuremath{k_{d}}\xspace}
\newc{\lr}{\ensuremath{l_r}}
\newc{\lrr}{\ensuremath{\lambda_r}}
\newc{\vrt}{\vartheta}
\newc{\cross}{\bm{\times}}
%\newc{\half}{\tfrac 12}
\newc{\half}{\frac 12}
\newc{\third}{\frac 13}
\newc{\quarter}{\frac 14}
\def\dF{\, \mathrm{d} \bm{F}}
\def\dl{\, \mathrm{d}{l}}
\def\dlb{\, \mathrm{d} \bm{l}}
\def\drb{\mathrm{d} \bm{r}}
\def\dV{\, \mathrm{d}V}
\newc{\dt}{\, \mathrm{d}t}
\newc{\dx}{\, \mathrm{d}x}
\newc{\dy}{\, \mathrm{d}y}
\newc{\dz}{\, \mathrm{d}z}
\newc{\dk}{\, \mathrm{d}k}
\newc{\dr}{\, \mathrm{d}r}
\newc{\dkb}{\, \mathrm{d}\bm{k}}
\newc{\dxb}{\, \mathrm{d}\xb}
\newc{\dvrt}{\, \mathrm{d}\vrt}
\newc{\dpr}{\, \mathrm{d}p}
\newcommand{\dtheta}{\, \mathrm{d}\theta}
\def\dS{\, \mathrm{d} S}
\def\dSb{\, \mathrm{d} \bm{S}}
\def\dA{\, \mathrm{d}{A}}
\newc{\dAb}{\, \mathrm{d} \bm{A}}
\newc{\Dth}{{\D_h \over \D t}}
\newc{\Dto}{{\D_0 \over \D \that}}
\newc{\Fb}{\bm{F} }
\bmdefine\Fb{F}
\newcommand{\Mb}{\bm{M} }
\newcommand{\Sb}{\ensuremath{\bm{S}}\xspace}
\newc\Ab{\ensuremath{\bm{A}}}
\newc\Cb{\ensuremath{\bm{C}}}
\newc\Jb{\ensuremath{\bm{J}}}
\newc\Bb{\ensuremath{\bm{B}}}
\newc\xb{{\bm{x}}}
\bmdefine{\pb}{p}
\bmdefine{\qb}{q}
\bmdefine{\ab}{a}
\bmdefine{\Xb}{X}
\bmdefine{\Yb}{Y}
\bmdefine{\rb}{r}
\newcommand{\rbb}{\mathbf{r}}
%\renewcommand*{\sb}{\bm{s}}
\bmdefine{\sbb}{s}
\bmdefine{\Db}{D}
\def\bb{{\ensuremath{\bm {b}}}}
\def\gb{\bm{g} }
\def\ib{{\bf i}}
\def\jb{{\bf j} }
\newcommand{\kb}{{\bf k}}
\bmdefine{\kbi}{k}
%\newcommand{\kb}{{\bf k}}
\bmdefine{\Vb}{V}
\bmdefine{\Wb}{W}
\def\lb{{\bm l} }
\newc{\fb}{{\ensuremath{\bm {f}}}}
\newc{\fbo}{{\ensuremath{\bm {f}_0}}}
\def\vb{{\ensuremath{\bm {v}}}\xspace}
\def\ub{{\ensuremath{\bm {u}}}\xspace}
\def\wb{{\ensuremath{\bm {w}}}\xspace}
\def\mb{{\ensuremath{\bm {m}}}\xspace}
\def\nb{{\ensuremath{\bm {n}}}\xspace}
\bmdefine{\Ub}{U}
\bmdefine{\cb}{c}
\bmdefine{\psib}{\psi}
\bmdefine{\phib}{\phi}
\def\dll{\delta \lb}
\def\dlrb{\delta \rb}

\newcommand{\by}{\ensuremath{b}}

\newc{\Tb}{{\bm T} }
\newc{\lhs}{left-hands side\xspace}
\newc{\fo}{\ensuremath{f_0}\xspace}
\def\DD#1{{\D#1 \over \D t}}
\newcommand{\DDhat}[1]{{\D#1 \over \D \that }}
\newcommand{\DDDhat}[1]{{\D#1 / \D \that }}
\newcommand{\DDbar}[1]{{\overline{\D}#1 \over \D t}}
\def\DDh#1{{\D_h#1 \over \D t}}
\def\DDo#1{{\D_0#1 \over \D \that}}
\newc{\MD}[1]{{\partial {#1} \over \partial t} + (\vb \cdot \del) #1}
\def\Dt{{\D \over \D t}}
\newcommand{\pp}[3][]{{\partial^{#1} #2 \over \partial #3^{#1}}}
\newcommand{\ppp}[3][]{{\partial^{#1} #2 / \partial #3^{#1}}}
\newcommand{\pppp}[3][]{{\partial^{#1}_{#3} #2 }}
\newcommand{\DDD}[1]{\D{#1} / \D t}
\newcommand{\ddd}[3][]{{\d^{#1} #2 / \d #3^{#1}}}
\newc{\ppa}[1]{{\partial \over \partial #1}}
\newc{\pt}{{\partial \over \partial t}}
\newc{\del}{\nabla }
\newc{\grad}{\nabla}
\newc{\delh}{\nabla_h}
\newc{\cp}{c_{\mkern -1mu p}}
\newc{\cv}{c_{\mkern -1mu v}}
\def\kv{\kappa_v}
\def\kh{\kappa_h}
\newcommand{\kvy}{\kappa^\mathit{vy}}
\newcommand{\kvz}{\kappa^\mathit{vz}}
\newcommand{\kwy}{\kappa^\mathit{wy}}
\newcommand{\kwz}{\kappa^\mathit{wz}}
\newcommand{\srho}{s_{\rho}}
\newcommand{\Kt}{\ensuremath{\tensor{K}}\xspace}
\newcommand{\St}{\ensuremath{\tensor{S}}\xspace}
\newcommand{\At}{\ensuremath{\tensor{A}}\xspace}
\newcommand*{\veps}{\varepsilon}
\newcommand*{\eps}{\epsilon}
\def\delsq{\nabla^2}
\newcommand{\delsqhat}{\what\del^2}
\newcommand{\Jhat}{\what J}
\def\delsqh{\nabla^2_h}
\def\delt{\nabla^2}
\def\delth{\nabla^2_h}
\newcommand{\dd}[3][]{{\d^{#1} #2 \over \d #3^{#1}}}
\newcommand{\dif}{\mathrm{d}}
\renewcommand{\d}{\mathrm{d}}
\newcommand{\f}{\mathrm{f}}
\newcommand{\D}{\mathrm{D}}
%\newcommand{\vres}[1][]{\obar{v^*_{#1}}}
\newcommand{\vres}[1][]{\overline v_{\! #1}^{*}}
\renewcommand{\vres}[1][]{\ensuremath{\overline v_{\! #1}^{*}}\xspace}
\newcommand{\psires}{\psi^*}
\newcommand{\vbres}[1][]{\overline \vb_{\! #1}^{*}}
\newcommand{\ubres}[1][]{\overline \ub_{\! #1}^{*}}
\newcommand{\wres}[1][]{\overline w_{\! #1}^{*}}
%\newcommand{\Fbres}[1][]{\Fb_{#1}^{*}}
\newcommand{\Fbres}{\Fb^{*}}
\newcommand{\pref}{p_{R}}
\newcommand{\rhoref}{\rho_{R}}

%\newcommand{\eqref}[1]{\textup{\tagform@{\ref{#1}}}} % amsmath def
\renewcommand{\eqref}[1]{(\ref{#1})} % gets fonts better

\newcommand{\textmonth}{\ifcase\month \or January \or February\or
March\or April\or May \or June \or July\or August\or September\or October
\or November\or December\fi\xspace}

% Following line always works but is a cheap hack using text fonts in math.
\newcommand{\tensor}[1]{\textit{\textsf{\textbf{#1}}}}

% Following lines are better but may cause TeX to run out of math alphabets.
%\DeclareMathAlphabet{\mathsfsl}{\encodingdefault}{cmss}{bx}{sl} % uses cmr fonts
\DeclareMathAlphabet{\mathsfsl}{\encodingdefault}{hlst}{b}{sl}   % uses lucida
\renewcommand{\tensor}[1]{\mathsfsl{#1}}      % this is the delicate command
                                               % Leave it in if possible


\newcommand\longpage[1][1]{\enlargethispage{#1\baselineskip}}
\newcommand\shortpage[1][1]{\enlargethispage{-#1\baselineskip}}

\providecommand{\bibname}{}
\renewcommand{\bibname}{References}

\newc{\putabcd}{\put(-9.2,7){\small \textit{\textsf{(a)}}}
\put(-4.5,7){\small \textit{\textsf{(b)}}}
\put(-9.2,3.3){\small \textit{\textsf{(c)}}}
\put(-4.5,3.3){\small \textit{\textsf{(d)}}}
}

\newc{\putab}{\put(-8.9,3.3){\small \textit{\textsf{(a)}}}
\put(-4.3,3.3){\small \textit{\textsf{(b)}}}
}
\newcommand{\itemm}{\item\mbox{}}
%\newcommand{\topfigrule}{\vspace*{-3pt}
  %              \rule{\columnwidth}{0.4pt}\vspace{2.6pt} }
% ---------------------------------------------------------------

% Following lines ensure uniformity of mathcal between fontsets.

%\DeclareMathAlphabet{\mathcal}  {OMS}{hlcy}{m}{n}  % uses lucida
%\SetMathAlphabet{\mathcal}{bold}{OMS}{hlcy}{b}{n}  % uses lucida for bold
%\DeclareMathAlphabet{\mathbcal} {OMS}{hlcy}{b}{n}  % don't need this


% \DeclareMathAlphabet{\mathcal}       {U}{mtms}{m}{n}
% \SetMathAlphabet    {\mathcal} {bold}{U}{mtms}{b}{n}

%Let's use cmr, for simplicity and style
%\DeclareMathAlphabet{\mathcal}  {OMS}{cmsy}{m}{n}
%\SetMathAlphabet{\mathcal}{bold}{OMS}{cmsy}{b}{n}
%%\DeclareMathAlphabet{\mathbcal} {OMS}{cmsy}{b}{n} % don't need this

\newcommand{\Fbc}{\bm{\mathcal F}}
\newcommand{\Fc}{\mathcal F}


%\bmdefine{\Fbc}{\mathcal F}
\bmdefine{\Ebc}{\mathcal E}
%%\renewcommand{\Fbc}{\pmb{\mathcal{F}}} % comment out this line if possible
                                        % however, it may lead to too many
                                        % math alphabets (esp with mathtime)

\newcommand{\resetcaptionmargin}{\setcaptionmargin{\captmarg}}
\newcommand{\iteml}[1]{\item\label{#1}}
\newcommand{\bfig}{\begin{figure}}
\newcommand{\efig}{\end{figure}}
\newcommand{\bcen}{\begin{center}}
\newcommand{\ecen}{\end{center}}
%\newcommand{\beql}[1]{\begin{equation}\label{#1}}
\newcommand{\beq}{\begin{equation}}
\newcommand{\eeq}{\end{equation}}


\newcommand{\bsub}{\begin{subequations}}
\newcommand{\esub}{\end{subequations}}

\renewcommand{\diamondsuit}{\blacklozenge}
\renewcommand{\Omega}{\varOmega}
\renewcommand{\Gamma}{\varGamma}
\renewcommand{\Pi}{\varPi}

\renewcommand{\reftextcurrent}{above}
\newcommand{\eqvref}[1]{\eqref{#1}\ \vpageref{#1}}

%%% Local Variables:
%%% mode: latex
%%% TeX-master: "aofd"
%%% End:
