A modified law‐of‐the‐wall applied to oceanic bottom boundary layers

Near the bottom, the velocity profile in the bottom boundary layer over the continental shelf exhibits a characteristic law‐of‐the‐wall that is consistent with local estimates of friction velocity from near‐bottom turbulence measurements. Farther from the bottom, the velocity profile exhibits a deviation from the law‐of‐the‐wall. Here the velocity gradient continues to decrease with height but at a rate greater than that predicted by the law‐of‐the‐wall with the local friction velocity. We argue that the shape of the velocity profile is made consistent with the local friction velocity by the introduction of a new length scale that, near the boundary, asymptotes to a value that varies linearly from the bottom. Farther from the boundary, this length scale is consistent with the suppression of velocity fluctuations either by stratification in the upper part of the boundary layer or by proximity to the free surface. The resultant modified law‐of‐the‐wall provides a good representation of velocity profiles observed over the continental shelf when a local estimate of the friction velocity from coincident turbulence observations is used. The modified law‐of‐the‐wall is then tested on two very different sets of observations, from a shallow tidal channel and from the bottom of the Mediterranean outflow plume. In both cases it is argued that the observed velocity profile is consistent with the modified law‐of‐the‐wall. Implicit in the modified law‐of‐the‐wall is a new scaling for turbulent kinetic energy dissipation rate. This new scaling diverges from the law‐of‐the‐wall prediction above 0.2 D (where D is the thickness of the bottom boundary layer) and agrees with observed profiles to 0.6 D .