Vortical source-sink flow against a wall: The initial value problem and exact steady states
Vortical source-sink flow against a wall: The initial value problem and exact steady states
复制标题
靠墙的涡流源汇流：初始值问题和精确稳态
DOI：
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发表时间：
2006
期刊：
影响因子：
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通讯作者：
N. R. McDonald
中科院分区：
文献类型：
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作者：
E. Johnson;N. R. McDonald
具有等涡度的流体从沿壁的线源排出。得到了确定最终稳态的非线性问题的精确解析解。在离源足够近的地方，流动是无旋的和各向同性的，在垂直尺度Q∕ω（表示面积通量Q和涡度ω）上沿壁面向右移动（表示ω>0）。当扰动沿垂直和无旋转流体之间的界面无衰减地传播时，流动是线性稳定的。对随时间变化的运动方程的完全非线性数值积分表明，从静止开始的流动确实接近于稳态。对于垂直源-汇对和靠壁的垂直源双重，也得到了类似的精确稳态解。时间相关积分表明，对于足够小的扰动，稳态在任意大的时间内不变，但被有限的扰动所破坏。
Fluid of uniform vorticity is expelled from a line source against a wall. An exact analytical solution is obtained for the nonlinear problem determining the final steady state. Sufficiently close to the source, the flow is irrotational and isotropic, turning on the vortical scale Q∕ω (for area flux Q and vorticity ω) to travel along the wall to the right (for ω>0). The flow is linearly stable with perturbations propagating unattenuated along the interface between vortical and irrotational fluid. Fully nonlinear numerical integrations of the time-dependent equations of motion show that flow started from rest does indeed closely approach the steady state. Similar exact steady solutions are obtained for a vortical source-sink pair and vortical source doublet against a wall. Time-dependent integrations show that the steady state is unchanged at arbitrarily large times for sufficiently small disturbances but is disrupted by finite perturbations.