Gradient-based similarity theory

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gradient-based similarity theory

While most similarity theories in atmospheric sciences rely on scales based on fluxes of momentum, heat, and other scalars, the potential for self-correlation in these flux-based similarities and their nonmonotonic trends have led many researchers to propose gradient-based alternatives. This is especially true during periods of stable thermal stratification, when gradients are also statistically better defined than fluxes (small fluxes, large gradients). According to the gradient-based similarity, scales under stable thermal stratification should be based on the vertical gradients of velocity, potential temperature, and scalar concentrations. The resulting dimensionless groups that emerge (i.e., the gradient-based similarity functions) depend on the local gradient Richardson number Rig. Their analytical form can be obtained based on observations. In the explicit approach, the mixing length is included as the length scale. Elimination of the mixing length leads to the implicit approach, which includes scales based also on various moments of turbulence (e.g, vertical velocity variance, the dissipation rate, etc.). Since the implicit gradient-based scales and similarity functions are not directly dependent on height, they are expected to be universally valid not only in the atmospheric surface layer, but also in the entire stable boundary layer, as well as in other stably stratified turbulent flows.

Sorbjan, Z., 2010: Gradient-based scales and similarity laws in the stable boundary layer. Quart. J. Roy. Meteor. Soc., 136, 1243–1254, doi:10.1002/qj.638.
——, 2016: Universal properties of the stably stratified atmospheric boundary layer. Quart. J. Roy. Meteor. Soc., 142, 805–810, doi:10.1002/qj.2682.

Term edited 18 July 2016.

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