FY 1983

Effects of time-varying viscosity on oscillatory turbulent channel flow

Lavelle, J.W., and H.O. Mofjeld

J. Geophys. Res., 88(C12), 7607–7616, doi: 10.1029/JC088iC12p07607 (1983)

A semi-analytic model of a time-dependent bottom boundary layer has been constructed in which flow and time-variable eddy viscosity are interdependent. Evaluated in the case of oscillatory forcing at tidal frequencies, the model shows that neglecting time-variations in viscosity results in underestimates of maximum bottom stress and distortion of the flow profile near times of flow reversal. Acceleration and variable viscosity also add terms proportional to zln(z/z) and z to the conventional steady-state ln(z/z) profile near the bottom. Inferences based on the logarithmic profile for measurements made in time-dependent boundary layers may consequently yield inaccurate estimates of roughness length and friction velocity. Stress is seen to lag flow at points away from the bottom, as has been observed in measurements, though bottom stress always leads flow aloft. Bottom stress is found to depend linearly on the free-stream velocity in the limit of time-varying viscosity. In the limit of strongly time-varying viscosity, bottom stress is more nearly quadratic. The friction coefficients are reasonably time-independent only when the phase lead, , between bottom stress, , and free-stream velocity, U, is incorporated into the bottom friction expression. A generalized bottom drag law for oscillatory flow encompassing all these features takes the form = g|U(t/T+)| U(t/T+), where has a value between 0 and 1, and is typically a few tens of degrees. In the examples evaluated, when = 0, g (conventionally called r) ranges from 2–15 × 10 cm/s, and when = l, g (conventionally called CD) ranges from 1–5 × 10, the variation in both cases depending on surface Rossby number.