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Non‐linear internal waves (NLIW) are important to processes such as heat transfer, nutrient replenishment and sediment transport on continental shelves. Our unique field observations of shoaling NLIW of elevation revealed a variety of different wave shapes, varying from relatively symmetric waves, to waves with either steepened leading‐ or trailing‐faces; many had evidence of trapped cores. The wave shape was related to the position of maximum density overturns and diapycnal mixing. We observed both shear (where sheared currents overcome the stabilizing effects of stratification) and convective (where the local velocity exceeds the wave propagation speed) instabilities. The elevated diapycnal mixing (>10−3 m2s−1) and heat flux (>500 Wm−2) were predominantly local to the NLIW of elevation packets, and were transported onshore 10s kilometers with the wave packets. We demonstrate that wave steepness may be a useful bulk property for the parameterization of wave‐averaged diapycnal heat flux. Plain Language Summary: Predicting the distribution of constituents such as nutrients, heat, sediment and pollutants on the continental shelf is key to processes such as: the safe operation of offshore infrastructure; understanding the variation in primary productivity; the prediction of marine heat waves; and environmental impact assessments of new activities. Non‐linear internal waves, waves that travel within the stratified water column, are likely to have a significant impact on constituent transport; however, they are poorly understood. Here we present unique observations that quantify the properties of a class of these nonlinear internal waves, known as waves of elevation. These waves can break in a similar way to surface waves at the beach, leading to dramatic increases in turbulent mixing over horizontal length scales of 10s kilometers. We have used our observations to define the amount of vertical heat transport induced by the breaking waves as a function of wave steepness. The vertical heat transport can be used as a proxy to estimate the vertical nutrient transport. This study has made a step change in quantifying the impact of NLIW of elevation on vertical transport. Key Points: Nonlinear internal waves of elevation can form both convective and shear instabilities, resulting in enhanced diapycnal mixing and heat fluxBreaking continues as the nonlinear waves propagate onshore, influencing diapycnal mixing and vertical heat flux over 10s of kilometersThe elevated heat flux associated with the nonlinear internal waves of elevation increases with the wave steepness [ABSTRACT FROM AUTHOR]