The shape of the head of a turbidity current is consistent with an inflow of the ambient medium into the current along clefts and tunnels regularly spaced along and back from the overhanging front of the head. The rate of inflow of the ambient medium into the head is expressed mathematically, and it is shown that the bed shear stresses exerted in the region of the head vary transversely across the region with a spatial periodicity. The deducd force structure of the head region explains the hitherto puzzling occurrence on turbidite soles of regular bands or clusters of flute marks aligned parallel with flow. It is also shown that the near-bed flow in the head is strongly three-dimensional, and this may help to explain the commonly observed non-parallelism of the sole markings observed on single bedding surfaces. The rates of inflow of the ambient medium into the head are found to be large enough to account for the density reduction necessary for the transformation of a liquified sediment slump into a turbidity current in a journey down the continental slope and upper rise.