# Richardson Number - thermal convection

## Description

The Richardson number (Ri) is named after Lewis Fry Richardson (1881 – 1953). It is the dimensionless number that expresses the ratio of potential to kinetic energy. In certain fields the Froude number is more commonly used and is the reciprocal of the square root of the Richardson number or Ri = 1/Fr^2.

In thermal convection problems, Richardson number represents the importance of natural convection relative to the forced convection. The Richardson number in this context is defined as shown.

## Variables

Ri | Richardson number (dimensionless) |

g | Standard gravity |

β | thermal expansion coefficient (1/K) |

T_{hot} | hot wall temperature (K) |

T_{ref} | reference temperature (K) |

L | characteristic length (m) |

V | characteristic velocity (m/s) |