Velocity and shear stress profiles for tidal effected channels

• The explicit formulas of velocity profile and shear stress profile are deduced.
• The bed shear stress expression under the tide is derived in theory.
• The surface elevation variation and the phase differences are taken into account.
• The tidal current velocity profile is expressed as a simple-structured function.
• The bed shear stress of the tidal flow is infrequent conclusion.

Tidal current is a periodic movement of unsteady and non-uniform, which owns obvious acceleration and deceleration process. The vertical distributions of velocity and shear stress in tidal flow possess the extraordinary features from the unidirectional flow. From the fundamental tidal movement equation, a simple-structure velocity profile formula is deduced which is capable of describing the velocity states from bypass to fully-developed, and it can express the velocity distribution of which the maximum velocity is not near the water surface. Based on the velocity profile, the tidal shear stress profile expression is derived and it can depict the characteristics commendably that the shear stress obeys the concave distribution within accelerating flow and a convex distribution within decelerating flow. Meanwhile, the computed values of the surface shear stress, on the conditions of acceleration or deceleration, conform to the fact the surface shear stress is not always equal to zero. Following the results of field observations, indoor experiments and numerical models, the bed shear stress is rather a variable dominated by tidal phase than a constant during the tide. The bed shear stress formula in the tide is derived with the definition raised by Soulsby, which is verified with the measured materials. The results are good agreeing with the field data.