  We have performed a simulation study of Langmuir turbulence in the Earth's
ionosphere by means of a Zakharov model with parameters relevant for the F
layer. The model includes dissipative terms to model collisions and Landau
damping of the electrons and ions, and a linear density profile, which models
the ionospheric plasma inhomogeneity whose length scale is of the order 10--100
km. The injection of energy into the system is modeled by a constant source
term in the Zakharov equation. Langmuir turbulence is excited ``on-demand'' in
controlled ionospheric modification experiments where the energy is provided by
an HF radio beam injected into the overhead ionospheric plasma. The ensuing
turbulence can be studied with radars and in the form of secondary radiation
recorded by ground-based receivers. We have analyzed spectral signatures of the
turbulence for different sets of parameters and different altitudes relative to
the turning point of the linear Langmuir mode where the Langmuir frequency
equals the local plasma frequency. By a parametric analysis, we have derived a
simple scaling law, which links the spectral width of the turbulent frequency
spectrum to the physical parameters in the ionosphere. The scaling law provides
a quantitative relation between the physical parameters (temperatures, electron
number density, ionospheric length scale, etc.) and the observed frequency
spectrum. This law may be useful for interpreting experimental results.
