I really do not fully understand what you want to achieve, but I am wondering if the following goes in the right direction.
\documentclass[fleqn]{article}
\usepackage{amsmath}
\begin{document}
With:
\begin{align*}
m_1&= 0.4 . \\
m_2&= 0.25 .\\
K_f&= \sqrt{2T_v(1-m_{2}^2)\left(\frac{m_1^2}{m_2^2}-m_2+1-m_1^2\right)^{-1}} . \\
T_v&= \frac{L_v}{V_\mathrm{moy}}
\end{align*}
With:
\begin{align*}
V_{0}(t,\omega)&:~\text{Speed on point $V_0$}.\\
V_\mathrm{mea}&:~\text{Mean speed}.\\
B(t,\omega)&:~\text{Noise}.
\end{align*}
\end{document}

EDIT: If you want to move the equations to the left, use
\documentclass[fleqn]{article}
\usepackage{amsmath}
\setlength{\mathindent}{0pt} % from https://tex.stackexchange.com/a/8744/121799
\begin{document}
\noindent
With:
\begin{align*}
m_1&= 0.4 . \\
m_2&= 0.25 .\\
K_f&= \sqrt{2T_v(1-m_{2}^2)\left(\frac{m_1^2}{m_2^2}-m_2+1-m_1^2\right)^{-1}} . \\
T_v&= \frac{L_v}{V_\mathrm{moy}}
\end{align*}
With:
\begin{align*}
V_{0}(t,\omega)&:~\text{Speed on point $V_0$}.\\
V_\mathrm{mea}&:~\text{Mean speed}.\\
B(t,\omega)&:~\text{Noise}.
\end{align*}
\end{document}

And if you want the alignment anchor to be on the left, use
\documentclass[fleqn]{article}
\usepackage{amsmath}
\setlength{\mathindent}{0pt}
\begin{document}
\noindent
With:
\begin{align*}
&m_1= 0.4 . \\
&m_2= 0.25 .\\
&K_f= \sqrt{2T_v(1-m_{2}^2)\left(\frac{m_1^2}{m_2^2}-m_2+1-m_1^2\right)^{-1}} . \\
&T_v= \frac{L_v}{V_\mathrm{moy}}
\end{align*}
With:
\begin{align*}
&V_{0}(t,\omega):~\text{Speed on point $V_0$}.\\
&V_\mathrm{mea}:~\text{Mean speed}.\\
&B(t,\omega):~\text{Noise}.
\end{align*}
\end{document}

None of these options look too nice to me, but this is a matter of taste.
\\outside of tables and alignments and certainly never do\\ \\which generatesUnderfull \hbox (badness 10000)which is the maximum measure of badness that TeX assigns – David Carlisle Mar 08 '18 at 18:59