Thermal losses from hot to cold ends of a Stirling cycle regenerator as a result of streamwise conduction and thermal dispersion in the matrix significantly degrade performance. Cross-stream conduction and thermal dispersion aids in reducing inlet flow and temperature nonuniformities. Thus, quantification of conduction and thermal dispersion is important for design. Thermal dispersion can be divided into a flow-driven eddy dispersion component, and, in the flow direction, a flow-driven advection dispersion component. Because regenerator design choices affect the components differently, it is advantageous to evaluate them separately. The focus of this paper is the measurement of the eddy component of dispersion. This component is caused by mixing within the pores by eddies created by flow separation off the solid-phase elements. Because of poor access to void spaces within a porous medium, no direct measurements have been made, and eddy dispersion models have been derived indirectly. In the current program, a large-scale porous matrix consisting of stacked wire screens with a porosity of 90% is installed in a flow rig, which is operated at an engine-representative Reynolds number. Measurements are made of eddy transport of momentum normal to the flow direction at the exit plane of the matrix using multiple hot-film sensors. The relationship of such a turbulent transport term to cross-stream and streamwise eddy thermal dispersion in the volumetric-averaged energy equation for the regenerator matrix is developed. An eddy dispersion model based upon a coefficient from the measurements and the functional form of the Prandtl mixing length model is proposed. This correlation agrees with several in the literature. Such agreement supports this measurement method.