In an accelerating tidal flow the near-bed velocity profile departs from the usual logarithmic form. The amount of the departure may not necessarily be large, but is nevertheless important when the profiles are used to calculate the bed roughness length and shear stress. A form for the accelerated profile is derived in terms of an ‘acceleration length’. Profiles measured off the SW coast of England are fitted to this expression, and give a value for a constant γ appearing in it. Published laboratory oscillatory flow profiles are also fitted; in this case the constant γ is larger due to the greater relative bed roughness. Von Karman's constant is obtained from the field data and found to be equal to 0.40, closer to laboratory values than to the now widely used atmospheric value of 0.35. Some evidence is found, however, to support a slow decrease in von Karman's constant with increasing boundary-layer thickness to roughness length ratio.