A gravity current appears when fuid of one density propagates into another fluid of an different density, and the motion is mainly in the horizontal direction. A gravity current is formed when we open the door of a heated house and cold air from outside flows over the floor into the less dense warm air inside. A gravity current is formed when we pour honey on a pancake and we let it spread out on its own. Gravity currents originate in many natural and industrial circumstances and are present in the atmosphere, lakes and oceans as winds, cold or warm streams or currents, polluted discharges, etc.

The study of gravity currents has generated a quite large literature, including some partial review papers (e.g., Gri ths 1986; Felix 2002; Huppert 2006) and the well known book of Simpson (1997). The start of quantitative study (or modeling) of the gravity current is attributed to von K arm an in 1940 (see Huppert 2006 and x 5.5 below), but the related dam-break problem (see x 2.5) was solved by Saint-Venant about a century earlier. It is of course impossible to cite and summarize in detail all these topics, contributions, discussions, and suggestions.

The objective here is to present a more-or-less unifed theoretical approach for the interpretation and prediction of the gravity current flow. The attempt is to develop this theory from first principle and focus mostly on methods and results with a wide range of applicability or with apparent potential for extensions.

On the other hand, we try to maintain the mathematical simplicity of the presentation. The analytical (or semi-analytical) results are of course only approximations. Their acceptance requires a confidence-building process. To this end comparisons with experimental and Navier-Stokes simulation data will be discussed.