Displacement thickness

Remarks

Example: for the linear profile $u = U y / \delta$ for $0 \le y \le \delta$ and $u = U$ for $y > \delta$, one gets $\delta^* = \int_0^\delta (1 - y / \delta) \, dy = \delta / 2$ and $\theta = \int_0^\delta \frac{y}{\delta}\big(1 - \frac{y}{\delta}\big) dy = \delta / 6$, so $H = 3$.

Non-example: a profile with $u = U (1 - (1 + y)^{-1})$ tends to $U$ too slowly: $1 - u / U = (1 + y)^{-1}$ is not integrable, so $\delta^*$ is not defined.

The mass flux deficit $\int_0^\infty (U - u) \, dy$ equals $U \delta^*$. For the Blasius layer $\delta^* \approx 1.72 \sqrt{\nu x / U}$ and $H \approx 2.59$.