On the spectrum of atmospheric motions (Ludwig-Prandtl Memorial Lecture

Kurzfassung

Spectra of atmospheric motions describe the distribution of kinetic and potential energy as a function of scales. The spectrum of horizontal motions in the free troposphere and the lower stratosphere at horizontal scales from a few 10 m to several 1000 km has often been shown to follow a power law with logarithmic spectral slopes near -3 at large scales and near -5/3 at smaller scales. The motions are highly anisotropic. Inertial subrange turbulence occurs only occasionally. The horizontal spectrum of vertical velocity has been discussed relatively little. Vertical wind drives conversion between potential and kinetic energy, vertical fluxes, cloud formation and turbulence. This study started from measurements of velocity and temperature spectra in field campaigns investigating atmospheric dynamics over oceans and mountains with the DLR research aircraft HALO. Accurate measurements are demanding because the wind speed is often small compared to the aircraft speed. The measured spectrum of vertical velocity showed unexpected peaks at scales corresponding to the depth of the atmosphere. We discuss the Helmholtz decomposition of horizontal velocity in rotational and divergent velocity components. We then show that the horizontal spectrum of vertical velocity is kinematically connected to the spectrum of horizontal divergent motions. The observed peaks occur when the divergent motions are vertically coherent and when the horizontal spectrum of divergent velocity reaches spectral slopes larger than -2. Details can be found in a recent publication (J. Atmos. Sci., 2019, doi: 10.1175/JAS-D-19-0160.1). This lecture is dedicated to Ludwig Prandtl (1875-1953) who contributed fundamentally to fluid mechanics, including meteorology.