  We present a semi-analytic model for the interstellar medium that considers
local processes and structures of turbulent star-forming gas. A volume element
of the interstellar medium is described as a multiphase system, comprising a
cold and a warm gas phase in effective (thermal plus turbulent) pressure
equilibrium, and a stellar component. Since turbulence has a critical impact on
the shape of the gaseous phases, on the production of molecular hydrogen and on
the formation of stars, the consistent treatment of turbulence energy -- the
kinetic energy of unresolved motions -- is an important new feature of our
model. Besides turbulence production by supernovae and by the cooling
instability, we also take into account the forcing by large scale motions.
  We formulate a set of ordinary differential equations, which statistically
describes star formation and the exchange between the different budgets of mass
and energy in a region of the interstellar medium with given mean density,
size, metallicity and external turbulence forcing. By exploring the behaviour
of the solutions, we find equilibrium states, in which the star formation
efficiencies are consistent with observations. Kennicutt-Schmidt-like relations
naturally arise from the equilibrium solutions, while conventional star
formation models in numerical simulations impose such relations with observed
efficiency parameters as phenomenological calibrations.
  Beyond the semi-analytic approach, a potential application is a complete
subgrid scale model of the unresolved multi-phase structure, star formation and
turbulence in simulations of galaxies or in cosmological simulations. The
formulation presented in this article combines various models focusing on
particular processes and yet can be adopted to specific applications, depending
on the range of resolved length scales.
