We numerically investigate the mode properties of the V-groove silicon nitride trench waveguides based on the experimental results. The trench waveguides are suitable for nonlinear applications. By manipulating the waveguide thicknesses, the waveguides can achieve zero dispersion or a maximized nonlinear parameter of 0.219 W-1·m-1 at 1550 nm. Broadband four-wave mixing with a gain of 5.545 m-1 is presented as an example. The waveguides can also be applied in sensing applications with an optimized evanescent intensity ratio. By etching away the top flat slabs, wider trapezoidal trench waveguides can be utilized for plasmonic sensing thanks to their TE fundamental modes.