Related Experiment Video
Updated: Aug 10, 2026

The Diffusion of Passive Tracers in Laminar Shear Flow
Published on: May 1, 2018
Power-law scaling in Bénard-Marangoni convection at large Prandtl numbers
1Max-Planck-Institute for the Physics of Complex Systems, Nöthnitzer Strasse 38, 01187 Dresden, Germany.
Abstract:
Bénard-Marangoni convection at large Prandtl numbers is found to exhibit steady (nonturbulent) behavior in numerical experiments over a very wide range of Marangoni numbers Ma far away from the primary instability threshold. A phenomenological theory, taking into account the different character of thermal boundary layers at the bottom and at the free surface, is developed. It predicts a power-law scaling for the nondimensional velocity (Peclet number) and heat flux (Nusselt number) of the form Pe approximately Ma(2/3), Nu approximately Ma(2/9). This prediction is in good agreement with two-dimensional direct numerical simulations up to Ma=3.2 x 10(5).
Related Concept Videos
Bernoulli's Principle
Bernoulli's principle has several applications. It is used...
Viscosity
The SI unit of viscosity is...
Poiseuille's Law and Reynolds Number
Viscosity
Couette Flow
Steady, Laminar Flow in Circular Tubes

