Depending on the non-dimensional Reynolds number, fluid flow can be either laminar or turbulent, where the transition between these types of flow has been characterized for various flow conditions including internal flows (pipes, ...) and external flows (flat plates, spheres, cylinders, ...).[1][2][3] The Reynolds number is basically a ratio of inertial to viscous forces, such that low Reynolds numbers indicate laminar flow (disturbances are damped by viscosity), whereas high Reynolds numbers indicate turbulent flow. Early experiments on laminar-turbulent transition were undertaken by Osbourne Reynolds at the University of Manchester, and further experiments have examined different circumstances under which transition can occur over many orders of magnitude of Reynolds numbers (at least 1,000 to 100,000).[4]
The location of transition is called the transition point. Examples of transition include Tollmien-Schlichting waves and boundary layer transition. Transition can also be strongly affected by other factors such as upstream disturbances, surface roughness and cross-flow. Therefore transition can occur over a range of Reynolds numbers, rather than always occurring at a single value.
Aerothermal heat fluxes on spacecraft like the Apollo or Orion capsules are strongly affected by whether the flow over the heat shield is laminar or turbulent (see also Nusselt number).[5] For example, convective heat transfer is higher for turbulent flow than for laminar flow.[6] Similarly, the drag coefficient and lift coefficient on aircraft wings depend strongly on the (often variable) location of the transition point. For example, flat plate (skin friction) drag is higher for turbulent flow than for laminar flow.[7] Similar analyses of transition flow can be undertaken in other fields where fluid drag is critical, including auto racing, yacht racing, and competitive swimwear.
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