A new two$-$equation turbulence model is desired. The first variable is the turbulent kinetic energy, k$,$ and the second variable is the $$eddy acceleration,$$ a$.$ Assuming a has units of length$/($time$)2,$ using dimensional analysis determine the functional relationship of the eddy $($turbulent$)$ viscosity, $,$ the rate of turbulent energy dissipation, $\backslash$epsi $,$ and the scaling of turbulence length, l$,$ on k and a$.$