You can turn the tree using a sidewaysfigure from the rotating package, but it still won't fit on your page. Very likely you have more \textheight than the default article - even if you are in one of the few places which eschews ISO sizes, the default margins are so great you are probably reducing them - but unless you are using A3 or (possibly?) US legal, this isn't going to fit.
So you have to do something else. I experimented with splitting the text in more nodes and you could also make the font size smaller or reduce the padding in or between the nodes, but it isn't going to look good.
Moreover, I don't know if this is important or not, but you have nodes with the same names in two branches of the tree. Maybe that's just for the minimal example, but I'm guessing your tree has at least rough symmetry geometrically between the two, even if the node content is actually different.
[If it isn't just for the example, is there a reason 'Hydrostatic Balance Equation' is the last child in one branch and the last but one in the other?]
I suggest you make better use of both dimensions by switching style for the subtrees rooted in root's grandchildren. The edges library provides a folder style, though the specific style below took me an embarrassingly long time to get right.
forking tree is just shorthand for the style you were using;major is a style which sets the shadow etc. for the root and adjusts the placement;folders down switches to the folder style, which doesn't respond well to styling subtrees without a bit of fiddling;
where level=1{folders down}{} applies this to root's children i.e. level 1 in forest terms (the root level being 0)
align grandchild folders aligns all the nth grandchildren of the root node (but it would be easy to tweak it to work from some non-root node).
My images suck due to an Okular bug, but I'm hoping this one may be a bit better.
\documentclass{article}
\usepackage{mathtools}
\usepackage{forest}
\usetikzlibrary{shadows}
\useforestlibrary{edges}
\tikzset{every shadow/.style={shadow xshift=5pt,shadow yshift=-5pt}}
% ateb: https://tex.stackexchange.com/a/718524/ addaswyd o gwestiwn s28: https://tex.stackexchange.com/q/718466/
\forestset{% addaswyd o ateb: https://tex.stackexchange.com/a/690629/
folders down/.style={
for tree={
grow'=0,
folder,
},
for current and siblings={anchor=north west, child anchor=north},
},
forking tree/.style={
calign=edge midpoint,
for tree={
fit=band,
font=\sffamily,
line width=1pt,
edge+={line width=1pt},
draw,
align=center,
},
forked edges,
},
major/.style={%
drop shadow,
for children={fork sep'=2ex},
},
define long step={grandchildren}{}{sort by=n,sort={branch={children,children}}},
define long step={grandchildren at n}{n args=1}{%
filter={grandchildren}{>On={n}{#1}}%
},
align grandchild folders/.style={%
before computing xy={%
if={ > On> {n children}{1} } {
tempcounta/.max={>O{n}}{grandchildren},
tempcountb'=0,
for nodewalk={%
fake=first,
while={ >OR< {n children}{tempcounta} }{fake=next},
children
}{%
tempcountb/.option=n,
tempdima/.min={ > O{s} }{fake=parent,fake=parent,grandchildren at n/.register=tempcountb},
for nodewalk={%
fake=parent,fake=parent,grandchildren at n/.register=tempcountb
}{s/.register=tempdima}
},
}{},
},
},
}
\begin{document}
\pagestyle{empty}%
\begin{forest}
forking tree,
where level=1{folders down}{},
align grandchild folders,
[Strong Diabatic Heating, major,
fill=white
[Synoptic-Scale Dynamics
[Thermodynamic Equation
[(1)]
]
[PV Equation
[(2)]
]
[Continuity Equation
[(3)]
[(4)]
]
[Horizontal Momentum Equation
[(5)]
]
[Hydrostatic Balance Equation
[(6)]
]
]
[Mesoscale Dynamics
[Thermodynamic Equation
[(7)]
[(8)]
]
[Vorticity Equation
[(9)]
]
[Continuity Equation
[(10)]
[(11)]
]
[Hydrostatic Balance Equation
[(12)]
]
[Mesoscale Horizontal Divergence Equation
[(13)]
]
]
]
\end{forest}
\begin{align}
i^2 &= -1 \label{eqn:i}\\
\sqrt{1} &= \pm 1 \label{eqn:1}\\
v &= ut + \frac{1}{2}at^2 \label{eqn:v}\\
\sin^2\theta + \cos^2\theta &= 1 \label{eqn:theta}\\
\text{??} &= 42 \label{eqn:h2g2}
\end{align}
\end{document}
EDIT
Here are a couple of other possibilities which don't involve restructuring your tree. I use \small from your duplicate question and also assume you are using A4, since the tree is too wide otherwise, even rotated.
The first option puts both tree and equations in a float. You might use \caption with this. The second simply puts them in an environment which is turned. Both use the rotating package mentioned above.
\documentclass[a4paper]{article}
\usepackage{forest}
\usetikzlibrary{shadows}
\useforestlibrary{edges}
\usepackage{amsmath}
\usepackage{rotating}
\usepackage[left=2.5cm,right=1cm,top=1.25cm,bottom=2cm]{geometry}
\tikzset{every shadow/.style={shadow xshift=5pt,shadow yshift=-5pt}}
\begin{document}
\begin{sidewaysfigure}
\centering
\begin{forest}
forked edges,
for tree={
font=\small\sffamily,
line width=1pt,
edge+={line width=1pt},
draw,
align=left,
tier/.option=level,
},
s sep'+=20pt,
[Strong Diabatic Heating,drop shadow,
fill=white
[Synoptic-Scale Dynamics
[Thermodynamic \\ Equation
[(1)]
]
[PV Equation
[(2)]
]
[Continuity \\ Equation
[(3)]
[(4)]
]
[Hor. Momentum \\ Equation
[(5)]
]
[Hydrostatic Balance \\ Equation
[(6)]
]
]
[Mesoscale Dynamics
[Thermodynamic\\ Equation
[(7)]
[(8)]
]
[Vorticity\\ Equation
[(9)]
]
[Continuity \\ Equation
[(10)]
[(11)]
]
[Hydrostatic Balance \\ Equation
[(12)]
]
[Mesoscale Horizontal \\Divergence Equation
[(13)]
]
]
]
\end{forest}
\begin{align}
i^2 &= -1 \label{eqn:ai}\\
\sqrt{1} &= \pm 1 \label{eqn:a1}\\
v &= ut + \frac{1}{2}at^2 \label{eqn:av}\\
\sin^2\theta + \cos^2\theta &= 1 \label{eqn:atheta}\\
\text{??} &= 42 \label{eqn:ah2g2}
\end{align}
\end{sidewaysfigure}
\begin{sideways}
\parbox{\textheight}{%
\centering
\begin{forest}
forked edges,
for tree={
font=\small\sffamily,
line width=1pt,
edge+={line width=1pt},
draw,
align=left,
tier/.option=level,
},
s sep'+=20pt,
[Strong Diabatic Heating,drop shadow,
fill=white
[Synoptic-Scale Dynamics
[Thermodynamic \\ Equation
[(1)]
]
[PV Equation
[(2)]
]
[Continuity \\ Equation
[(3)]
[(4)]
]
[Hor. Momentum \\ Equation
[(5)]
]
[Hydrostatic Balance \\ Equation
[(6)]
]
]
[Mesoscale Dynamics
[Thermodynamic\\ Equation
[(7)]
[(8)]
]
[Vorticity\\ Equation
[(9)]
]
[Continuity \\ Equation
[(10)]
[(11)]
]
[Hydrostatic Balance \\ Equation
[(12)]
]
[Mesoscale Horizontal \\Divergence Equation
[(13)]
]
]
]
\end{forest}
\begin{align}
i^2 &= -1 \label{eqn:i}\\
\sqrt{1} &= \pm 1 \label{eqn:1}\\
v &= ut + \frac{1}{2}at^2 \label{eqn:v}\\
\sin^2\theta + \cos^2\theta &= 1 \label{eqn:theta}\\
\text{??} &= 42 \label{eqn:h2g2}
\end{align}}
\end{sideways}
\end{document}
articlepage.