Field observations in San Francisco Bay of subtidal channels that drain through intertidal mudflats indicate that substantial periodic stratification develops in very shallow flows with distinct asymmetries between flood and ebb conditions. The greatest variability in salinity and stratification occurs during the wet winter months. Very strong longitudinal salinity gradients develop across the intertidal zone, between salty subtidal water and fresher water draining into the marsh upstream. Tidal straining of the longitudinal gradient creates the periodic stratification, stratifying through ebbs and destratifying through floods. The stratification can be very strong in very shallow flows, with N2 > 0.1 s-2 in about 0.5 m water depth. Analysis of the data with dimensionless numbers shows that at times the stratification is strong enough to suppress turbulence and mixing. The asymmetry in stratification between ebbs and floods results in asymmetries in eddy viscosity and eddy diffusivity, with lower values during the stratified ebbs. Because of the intertidal elevation of the system, the strong longitudinal salinity gradient is regenerated each time the mudflats and marsh drain. The system approaches a tidally periodic steady state where the flow dynamics are dominated by the sharp front of salty water that advects into the intertidal zone on the rising tide and exits the system by each lower low water. The field data are supported by a numerical model with simple mudflat/channel bathymetry. Both the field and numerical work indicate that the shallow, low energy flows in mudflat channels transition between strongly stratified suppressed turbulence and relatively unstratified active turbulence each tidal cycle.