The Diurnal Variation of the Wind

The equations of motion are numerically integrated under assumptions which represent the diurnal variation of the wind. The coefficient of eddy viscosity varies periodically with time as well as nonlinearly with height. The time variation is represented by two trigonometric terms giving a 20-fold change between maximum and minimum eddy viscosity. Several different functions were used to depict the vertical variation of the eddy viscosity, among which were an increasing, but bounded, exponential function, and also an exponential function which first increased with height and then decreased to a residual value. The boundary conditions imposed were, firstly, that the wind vanishes (or approaches a constant value) at the lower boundary; and, secondly, that the wind becomes geostrophic at some arbitrarily selected upper level. The solutions were in general agreement with observed data and showed the spiral characteristic of the planetary boundary layer. However, there is disagreement between theory and observation in some important features.