Navier-Stokes and continuity equations are utilized to simulate fully developed laminar Dean flow with an oscillating time-dependent pressure gradient. These equations are solved analytically with the appropriate boundary and initial conditions in terms of Laplace domain and inverted to time domain using a numerical inversion technique known as Riemann-Sum Approximation (RSA). The flow is assumed to be triggered by the applied circumferential pressure gradient (azimuthal pressure gradient) and the oscillating time-dependent pressure gradient. The influence of the various flow parameters on the flow formation are depicted graphically. Comparisons with previously established result has been made as a limit case when the frequency of the oscillation is taken as 0 (ω = 0). It was revealed that maintaining the frequency of oscillation, the velocity and skin frictions can be made increasing functions of time. An increasing frequency of the oscillating time-dependent pressure gradient and relatively a small amount of time is desirable for a decreasing velocity and skin frictions. The fluid vorticity decreases with further distance towards the outer cylinder as time passes. Findings confirm that increasing the frequency of oscillation weakens the fluid velocity and the drag on both walls of the cylinders.

中文翻译：

---

振荡时间相关压力梯度对 Dean 流量的影响：瞬态解决方案

Navier-Stokes 和连续性方程用于模拟具有振荡时间相关压力梯度的完全发展的层流 Dean 流。这些方程使用适当的边界和初始条件根据拉普拉斯域进行解析求解，并使用称为 Riemann-Sum Approximation (RSA) 的数值反演技术反演到时域。假设流动是由施加的圆周压力梯度（方位角压力梯度）和振荡的时间相关压力梯度触发的。以图形方式描述了各种流动参数对流动形成的影响。当振荡频率为 0 (ω = 0) 时，作为极限情况与先前建立的结果进行比较。结果表明，保持振荡频率，速度和皮肤摩擦可以成为时间的增函数。振荡依赖于时间的压力梯度的频率增加和相对少量的时间对于降低速度和皮肤摩擦是合乎需要的。随着时间的流逝，流体涡度随着朝向外圆柱体的距离进一步减小而减小。研究结果证实，增加振荡频率会削弱流体速度和气缸两壁上的阻力。