  In this investigation, we theoretically studied the transports of kinetic
energy and scalar variance in turbulence driven by a scalar-based volume force
in $M{\nabla}^{\beta} s'$ form associated with scalar fluctuations $s'$ in
wavenumber space relies on flux conservation equation. The equation has one
real solution and two complex solutions, which lead to four different cascade
processes, including inertial subrange (constant fluxes of kinetic energy and
scalar variance), CEF subrange (quasi-constant flux of kinetic energy), CSF
subrange (quasi-constant flux of scalar variance), and a new subrange with both
non-constant fluxes of kinetic energy and scalar variance in addition to
dissipation subrange. ${\beta}$ controls the cascade processes and the scaling
exponents. For the real solution, in the CEF subrange, ${\xi}_u$ is always
-5/3, while ${\xi}_s=-(6{\beta}+1)/3$. In the CSF subrange,
${\xi}_u=(4{\beta}-11)/5$ and ${\xi}_s=-(2{\beta}+7)/5$ which are both
consistent with the theory of Zhao and Wang (2021). Relying on ${\beta}$, the
transport of kinetic energy and scalar variance can be distinguished as four
cases. (1) When $\beta<3/2$ (except $\beta=2/3$), the CEF and CSF subranges are
coexisted, with the former located on the lower wavenumber side of the latter.
At ${\beta}=2/3$, a new inertial subrange with both ${\xi}_u$ and ${\xi}_s$
equal to -5/3 is present. (2) When $3/2<=\beta<2$, only the CEF subrange is
predicted. (3) At $\beta=2$, special and singular exponents of ${\xi}_u=-1$,
${\xi}_s=-3$, ${\lambda}_u=1$, and ${\lambda}_s=-1$ can be found, if $MN=1$.
Otherwise, a CSF subrange is predicted. (4) When $2<\beta<=4$, only the CSF
subrange is predicted. Thus, a complete transport picture of both kinetic
energy and scalar variance has been established for the type of forced
turbulence.
