Advances and Deficiencies in Studies of Turbulence and Relevance to Integration into Larger-Scale Atmospheric Models

Dear Colleagues,

In a general sense, turbulence covers a wide range of scales, from centimetres (and even millimetres) to thousands of kilometres. However, its behaviour varies enormously over this range. At the smallest scales, it is considered to be broadly isotropic, and this is often assumed up to scales of hundreds of metres. At larger scales, up to a few kilometres, it is considered anisotropic, but still clearly three-dimensional and related to its smaller-scale quasi-isotropic cousins. At scales beyond 10 km of depth, it is considered largely two-dimensional in nature, and in the lower atmosphere, it competes with gravity-waves for dominance. At scales of thousands of kms, a new class of turbulence develops, referred to as geostrophic 2-D turbulence. Within each range, further sub-ranges exist, such as the viscous, inertial, and buoyancy range.

These different levels of turbulence profoundly affect larger-scale mean flows. However, the range of scales is so large that integrating all scales at once in any model is impossible, and some form of parameterization is required, and these parameterizations tend to be overly simplistic. For example, the diffusion coefficient is often taken to be K = e/N², where e is the energy dissipation rate and N is the Vaisala–Brunt frequency. This assumes isotropic homogeneous turbulence. However, for further advances, better parameterizations are needed. Small-scale turbulence is rarely homogeneous at scales beyond a few hundred metres. It is often very intermittent and inhomogeneous, and in places like the stratosphere, the dynamical motions comprise regions of strong turbulence surrounded by regions where laminar viscous flow dominates. This massive intermittency changes the relationship between small and larger-scale flows. Other forms of mixing exist as well: gravity waves are important here, and as they break, they of course produce 3-D turbulence. However, even without breaking, they can cause large-scale mixing through the combined stochastic interaction of Stokes drifts of the waves. Such diffusion has never been integrated into large-scale computer models.

Even at scales of a few metres, turbulence is not actually isotropic, but eddies can be quite ellipsoidal in shape and can have non-horizontal mean tilts, significantly affecting their impact on the mean state. Even experimental measurements of turbulence strengths with radar have recently drawn attention, with the relative sizes of the beams and pulse lengths compared to the key turbulence scales resulting in different dependencies of e on radar-spectral widths, thereby raising uncertainties about the full impact of turbulence.

In this Special Issue, we especially seek papers that look again at how we may most effectively couple the actions of turbulence (at all scales) into larger-scale atmospheric models. Papers do not need to solve all aspects of this complex problem but should address at least one aspect that might contribute to better parameterizations of the impact of turbulent energy dissipation and momentum diffusion on larger-scale flows.

Prof. Dr. Wayne Hocking
Guest Editor

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• turbulence
• energy dissipation
• diffusion
• scaling
• parameterization
• coupling
• non-linearities
• spatial and temporal inhomogeneity