The model MACH3 (Model for Applied Complex Hydrodynamics, 3-dimensional) is the numerical conversion of the primitive equations system of the hydrothermodynamics. MACH3 is diabatic, baroclinic, and eddy-resolving, and it comprises the second order turbulence closure developed by Dr. Helmut Frey. MACH3 calculates prognostically: MACH3 calculates diagnostically: currents, transport pressure and density field sea surface elevation trift velocities temperature mean energetics, eddy- and turbulence-energetics salinity frontal zone index various tracer concentrations temperature-, salinity- and density-stratification 3-dimensional turbulence (indirectly) vertical convection   any further derivable quantities MACH3 can be forced by tides, wind, heat fluxes between atmosphere and waters, air pressure, river discharges, backwater and precipitation. MACH3 is tested and verified already in detail, and was already applied successfully on investigations in the German Bight and on process studies. The high capacity of MACH3 facilitates the physically adequate prognostic calculation of even such high-complex mesoscale processes as formation and decay of fronts, eddies, and thermal and haline stratification. This high capacity is based not at least on the complex turbulence closure and on mathematical-numerical methods, which ensure enstrophy-conserving momentum advection and eddy-conserving, diffusion-minimized scalar advection along the streamlines.