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This sketch illustrates the definition of the Turner angle, Tu(degree), with corresponding Density ratio value indicated. Double-diffusion is scaled in low, medium, and strong conditions.[1]
The Turner angleTu, introduced by Ruddick(1983) [2] and named after J. Stewart Turner, is a parameter used to describe the local stability of an inviscid water column as it undergoes double-diffusive convection. The temperature and salinity attributes, which generally determine the water density, both respond to the water vertical structure. By putting these two variables in orthogonal coordinates, the angle with the axis can indicate the importance of the two in stability. Turner angle is defined as:[1]
where tan−1 is the four-quadrant arctangent; α is the coefficient of thermal expansion; β is the equivalent coefficient for the addition of salinity, sometimes referred to as the "coefficient of saline contraction"; θ is potential temperature; and S is salinity. The relation between Tu and stability is as shown [3]
If −45° < Tu < 45°, the column is statically stable.
If −90° < Tu < −45°, the column is unstable to diffusive convection.
If 45° < Tu < 90°, the column is unstable to salt fingering.
If −90° > Tu or Tu > 90°, the column is statically unstable to Rayleigh–Taylor instability.
^ abYou, Yuzhu (November 2002). "A global ocean climatological atlas of the Turner angle: implications for double-diffusion and water-mass structure". Deep Sea Research Part I: Oceanographic Research Papers. 49 (11): 2075–2093. doi:10.1016/S0967-0637(02)00099-7.
^Ruddick, Barry (October 1983). "A practical indicator of the stability of the water column to double-diffusive activity". Deep Sea Research Part A. Oceanographic Research Papers. 30 (10): 1105–1107. doi:10.1016/0198-0149(83)90063-8.
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