= Bound vortex
A \b[bound vortex] in an aerodynamic model is a vortex-filament representation attached to the modeled lifting body, rather than a wake element convected downstream. In <lifting-line theory>, a spanwise distribution of <circulation> $\Gamma(y)$ represents the wing loading. The word bound describes the representation's relation to the body; it does not identify a literal tube of fluid fixed inside the wing.
The local <Kutta–Joukowski theorem> connects the modeled circulation to lift per unit span:
$$
L'(y)=\rho U\Gamma(y),\qquad
c_l(y)=\frac{2\Gamma(y)}{Uc(y)}.
$$
The MIT derivation uses that connection to couple the section law to the induced flow.<Prandtl's Lifting Line Introduction (16.100) by MIT OpenCourseWare>[Pages 2–3, Kutta–Joukowski relation and lifting-line construction]{ref} Here $c(y)$ is <airfoil chord>; the sign of $\Gamma$ is chosen consistently with positive lift.
An original example stipulates $\rho=1.2$ kg/m$^3$, $U=40$ m/s and $\Gamma=5$ m$^2$/s at one section. The predicted $L'$ is 240 N/m. For chord 0.50 m, $q=960$ Pa and $c_l=240/(960\cdot0.50)=0.50$. The same circulation at a different chord need not give the same sectional coefficient.
The finite-span model includes the wake. A <horseshoe vortex> joins a finite bound segment to trailing legs; continuously varying spanwise circulation generates a distributed trailing <vortex sheet>. Adjacent modeled segments with circulations 5 and 3 m$^2$/s have a circulation difference of magnitude 2 m$^2$/s, which determines the intervening wake-filament strength under the chosen orientation. Omitting those trailing contributions would omit the <downwash> that couples the wing sections.
Total lift follows from $L=\rho U\int\Gamma(y)\,dy$, but that single integral does not uniquely determine the distribution. Different span loadings can have equal total lift and different <lift-induced drag>; the originating force calculation keeps the circulation distribution when evaluating drag.<Force Calculations for Lifting Line (16.100) by MIT OpenCourseWare>[Pages 1–3, lift integral and induced-drag calculation]{ref}
A proposed apparatus comparison reconstructs section loading from surface pressures and independently measures the downstream velocity field. Agreement tests the lifting-line representation and wake prediction. A force reading alone cannot locate a unique physical vortex filament, and the model does not resolve the full viscous flow near the surface.
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