Skewed, exponential pressure distributions from Gaussian velocities

A simple analytical argument is given to show that the distribution function of the pressure and that of its gradient have exponential tails when the velocity is Gaussian. A calculation of moments implies a negative skewness for the pressure. Explicit analytical results are given for the case of the velocity being restricted to a shell in wave number. Numerical pressure distributions are presented for Gaussian velocities with realistic spectra. For real turbulent flows, one expects that the pressure distribution should retain exponential tails while the pressure gradients should develop stretched-exponential distributions. In the context of the theory, available numerical and laboratory data are examined for the pressure, along with data for the wall shear stress in a boundary layer.