Fluid Driven by Tangential Velocity and Shear Stress: Mathematical Analysis, Numerical Experiment, and Implication to Surface Flow

Table 1

The difference of solutions for the long cavity flow associated with the velocity and stress boundary condition. u, v, and w are velocity in x, y, and z direction, respectively. Subscripts 𝑣 and 𝑠 stand for the velocity and stress condition, respectively.

𝑡 (s)	‖𝑝𝑠−𝑝𝑣‖∞ (Pa)	‖𝑢𝑠−𝑢𝑣‖∞ (m/s)	‖𝑣𝑠−𝑣𝑣‖∞ (m/s)	‖𝑤𝑠−𝑤𝑣‖∞ (m/s)
50	0.641	0.056	1.66𝐸−3	0.0121
500	4.30𝐸−3	9.42𝐸−5	1.51𝐸−4	8.95𝐸−5