Blank spaces in equations

I'm writing a paper and I want to replicate this set of equations in my latex document. But when I'm trying to do the align with & many times I get error. \begin{eqnarray}
\label{Eq:GeosWind}
\frac{\partial u}{\partial t} &+& \overrightarrow{v}\nabla u + \frac{1}{\rho}\frac{\partial p}{\partial x}  -fv +f^{\ast}w \mp v \frac{\vert\overrightarrow{v}\vert}{r}  + F_x = 0 \label{a}\\
\frac{\partial v}{\partial t} + \overrightarrow{v}\nabla u + \frac{1}{\rho}\frac{\partial p}{\partial y} + fu \pm u \frac{\vert\overrightarrow{v}\vert}{r} +F_y = 0 \label{b}\\
\frac{\partial w}{\partial t} + \overrightarrow{v}\nabla w + \frac{1}{\rho}\frac{\partial p}{\partial y} -g -f^{\ast}u  + F_z = 0 \label{c}\\
I &&   II    III   IV    V    VI   VII
\end{eqnarray}

Here's a solution with alignat (7columns) and eqparbox. I also loaded the esdiff and esvect packages for a simpler typing of partial differential, and nicer arrow tips:

\documentclass{article}
\usepackage[b]{esvect}
\usepackage{esdiff}
\usepackage{eqparbox}
\newcommand{\eqmathbox}[M] {\eqmakebox[#1]{$\displaystyle#2$}}
\usepackage{amsmath}

\begin{document}

\begin{alignat}{7}
\diffp{u}{t} &+{} &\vv{v}\nabla u & +{} & \frac{1}{\rho}\diffp{p}{x} & & & -{} & fv & +{} & f^{\ast}w & \mp{} & v \frac{\vert\vv{v}\vert}{r}& + F_x = 0 \label{a}\\
\diffp{v}{t} &+{} & \vv{v}\nabla u & + {} & \frac{1}{\rho}\diffp{p}{ y} & & & +{} & fu & & & \pm{} &\eqmathbox[VI]{u\frac{\vert\vv{v}\vert}{r}} & +F_y = 0 \label{b}\\
\eqmathbox[I]{\diffp{w}{t}} &+{} &\eqmathbox[II] {\vv{v}\nabla w } & +{} & \eqmathbox[III]{\frac{1}{\rho}\diffp{p}{y}} &-{} & \eqmathbox[IV]{g} & -{} & \eqmathbox[V]{f^{\ast}u} & & & & & + F_z = 0\label{c} \\
\eqmakebox[I]{I} & & \eqmakebox[II]{II}& & \eqmakebox[III]{III} & & \eqmakebox[IV]{IV}& & \eqmakebox[V]{V} & & & & \eqmakebox[VI]{VI} & \phantom{ + }\text{VII} \notag
\end{alignat}%

\end{document} • +1. A very minor nit to pick: The first instances of + in rows 1 and 2 should be generated by &+{} instead of by &{}+, right?
– Mico
Jul 9 '20 at 3:48
• @Mico: Not so minor. The reason, I guess, was the way I ended in this code: I initialy wrote a standard alignat wiithout the roman numbers, then redistributed some of the & so as to centre these numbers w.r.t. the above maths expressions, enclosed in \eqmathboxes — and the ampersands were so many… Thanks again! Jul 9 '20 at 8:57
• I've deleted one final stray } character. :-)
– Mico
Jul 9 '20 at 9:20
• Thanks for your help. I've been a few hours trying to align the equations. So, alignat is a better way to that and the white spaces are represented with {}. Right? Jul 10 '20 at 2:59
• Not exactly – the distinctive feature of alignat, as opposed to align, is that it adds no space between the alignment columns: it up to you to add the spacing. Here , I added {} after + to ensure it's considered by latex as a mathbin, with the ad hoc spacing on each side (because there's a & before, it would be a mathord without this trick. Jul 10 '20 at 9:39