The spectral signature of salt fingers

-The spectra of either temperature, salinity or vertical velocity which might be measured by a sensor moving through a field of salt fingers are considered. A theoretical calculation is presented which attempts to incorporate the deviations from squareness and perfect orientation of the salt fingers. The resulting spectra rise to a peak close to ~o = (x/2)kv and decrease rapidly for larger to, where to is the temporal frequency of the spectrum, k the dominant wave number of the salt fingers and v the horizontal velocity of the sensor. A spectrum of vertical velocity of laboratory-generated salt fingers is shown to be in close agreement with the theoretical prediction. OVER THE last twenty years the concept of salt fingers has evolved from being 'An oceanographical curiosity' (STOMMEL, ARONS and BLANCHARD, 1956) to being an observed fact (WILLIAMS, 1974, 1975). By using a collimated laser beam, Williams' instrument obtained a series of photographs 5 cm in diameter of salt fingers in the Mediterranean outflow which were very similar to those easily observed in a laboratory. While an instrument which allows one to actually 'see' phenomena occurring at a depth of over 1000 m is a very valuable new tool, it is not feasible to use it to obtain a quantitative estimate of what proport ion of a (large) section of ocean is saltfingering at any particular time. This estimate is important because it will differentiate between the notion that salt fingers occur in a significant fraction of the ocean, as conjectured by HUPPERT and MANINS (1973), and the notion that they occur in only very isolated spots. Recently, efforts have been made to use a small temperature and salinity sensor which could be towed behind a ship to yield data which might be analysed to determine over what fraction of the path the sensor was moving through a salt-finger field. But how will the record appear when the sensor is in a salt-finger field; that is, what is an observable signature of salt fingers ? The examination of this question is the aim of the present note. A careful investigation of the raw line trace, output by the sensor, would be a very timeconsuming and not very profitable task. The best means of identification of salt fingers would seem to come from the spectrum, and we concentrate on this here. We calculate only the spectrum due to salt fingers; those portions of the record not due to salt fingers will contribute to the background spectrum and in practice this influence could be removed either before or after calculation of the spectrum. The simplest representation of a salt-finger field reflects the fact that individual salt fingers are very much longer than they are thick and have a nearly square plan form (SHIRTCLIFFE and TURNER, 1970). Thus all variables are of the form ~b = ~b0 sin kx sin ky, (1) where ~b represents temperature, salinity or vertical velocity of amplitude q~o, k is a wave number related to the large-scale temperature and salinity gradients and x and y are orthogonal, horizontal axes. The form (1) has been shown by HUPPERT and MANINS (1973) to be the only one representing a steady-state, square salt-finger field with purely vertical motion. * Department of Applied Mathematics and Theoretical Physics, Silver Street, Cambridge, CB3 9EW. England.