📂Fluid Mechanics

Definition of the Lamb Number in Fluid Dynamics

Definition¹

In fluid dynamics, consider a sphere of mean radius $a$ rotating with angular frequency $\Omega$, with gravitational acceleration $g$, and let $H$ be the thickness of the layer of fluid on the sphere. Then the following dimensionless quantity is called the Lamb number. $$ \mathrm{La} = {\frac{ \left( 2 \Omega a \right)^{2} }{ g H }} $$

Explanation

$H$ may be regarded as the same mean depth $H$ that appears in the shallow water equations. Although the formula makes no direct mention of the Coriolis force, the numerator of the Lamb number contains $\Omega a$, so a large $\mathrm{La}$ means that the rotational speed at the equator is large, which tells us that, on the scale of a celestial body, the Coriolis force is dominant.