An unsteady-state two-dimensional velocity field in the xy plane is given by where t is the time is hours, a and b are the amplitudes of the temporal velocity fluctuations, ω = 2π/T is the frequency...

An unsteady-state two-dimensional velocity field in the xy plane is given by

where t is the time is hours, a and b are the amplitudes of the temporal velocity fluctuations, ω = 2π/T is the frequency of the velocity fluctuations, and T is the period of the fluctuations. Consider a particular case where a = 15 cm/s, b = 20 cm/s, and T = 12 h. Estimate the streakline for particles released continuously from (x, y) = (0 m, 0 m) starting at t = 0 h and ending at t = 12 h. Use 1-h time increments in estimating the streakline.