Vertical wind shears, turbulence and non‐turbulence in the troposphere and stratosphere

Abstract

A theoretical calculation is made of σ(h), the standard deviation of vertical wind shears, in terms of the turbulence energy dissipation rate ε and Brunt‐Väisälä frequency ω_B. This calculation provides a theoretical basis for the empirical power law relation σ(h) = A h^m obtained by rocket and balloon wind soundings; it also provides a scaling of σ(h) with atmospheric conditions. The intervals h ranging from about 50m to 1000m are determined by buoyancy subrange turbulence, and smaller shear intervals are determined by inertial subrange turbulence. The theoretical σ(h) allows ε to be predicted from vertical wind soundings in the troposphere and stratosphere. The predicted value of ε in the troposphere agrees with the value obtained by Kung. However, the predicted stratospheric value of ε is larger than obtained by Lilly et al. from HICAT flights. This discrepancy in stratospheric ε is attributed to non‐turbulent, low frequency, short scale, quasi‐horizontal motions of the stratosphere; motions that contribute to vertical wind soundings but not to gust measurements by horizontal HICAT flights.