Nonlinear Processes in Geophysics www.nonlin-processes-geophys.net 1023-5809 1607-7946 13 1 2006 10.5194/npg-13-119-2006 http://www.nonlin-processes-geophys.net/13/119/2006/ http://www.nonlin-processes-geophys.net/13/119/2006/npg-13-119-2006.html http://www.nonlin-processes-geophys.net/13/119/2006/npg-13-119-2006.pdf 119 123 2006-04-27 On the dependence of third- and fourth-order moments on stability in the turbulent boundary layer A. Maurizi a.maurizi@isac.cnr.it Institute of Atmospheric Sciences and Climate via Gobetti 101,I-40129 Bologna, Italy Analysis of published data on the third- and fourth-order moments of vertical velocity in the atmospheric boundary layer is performed, and it is shown that turbulence is non-Gaussian even when almost symmetric. It is also proposed that the relationship between third- and fourth-order moments depends on stability. New data from a wind tunnel experiment roughly support this hypothesis. The analysis presented can explain some differences among datasets, and provides a starting point for investigation on the dependence of third- and fourth-order moments on stability. Alberghi, S., Maurizi, A., and Tampieri, F.: Relationship between the vertical velocity skewness and kurtosis observed during sea-breeze convection, J. Appl. Meteorol., 41, 885-889, 2002. Anfossi, D., Ferrero, E., Sacchetti, D., and Trini Castelli, S.: Comparison among empirical probability density functions of the vertical velocity in the surface layer based on higher order correlations, Boundary-Layer Meteorol., 82, 193-218, 1997. Baskaran, V., Smits, A J., and Joubert, P N.: A turbulent flow over a curved Hill. Part 2. Effects of streamline pressure gradient, J. Fluid Mech., 232, 377-402, 1991. Bradshaw, P.: The analogy between streamline curvature and buoyancy in turbulent shear flow, J. Fluid Mech., 36, 179-191, 1969. Chatwin, P C. and Sullivan, P.: A simple and unifying physical interpretation of scalar fluctuation measurements from many turbulent shear flows, J. Fluid Mech., 212, 533-556, 1990. Durst, F., Jovanovic, J., and Kanevce, L.: Probability density distributions in turbulent wall boundary-layer flow, in: Turbulent Shear Flow 5, edited by: ~Durst, F., Launder, B E., Lumley, J L., Schmidt, F W., and Whitelaw, J H., Springer, 197-220, 1987. Gryanik, V M. and Hartman, J.: A turbulence closure for the convective boundary layer based on a two-scale mass-flux approach, J. Atmos. Sci., 59, 2729-2744, 2002. Hartman, J., Kottmeier, C., and Raasch, S.: Rolls vortices and planetary boundary-layer development during a cold air outbreak, Boundary-Layer Meteorol., 84, 45-65, 1997. Kendall, S M. and Stuart, A.: The Advanced Theory of Statistics, vol 1, C. Griffin & Co., London, 4th edn., 1977. Lenschow, D H., Mann, J., and Kristensen, L.: How long is long enough when measuring fluxes and other turbulence statistics?, J. Atmos. Oceanic Technol., 11, 661-673, 1994. Lewis, D M., Chatwin, P C., and Mole, N.: Investigation of the collapse of the skewness and kurtosis exhibited in atmospheric dispersion data, Nuovo Cimento C, 20, 385-398, 1997. Losch, M.: On the validity of the Millionshchikov hypothesis for open-ocean deep convection, Geophys. Res. Lett., 31, L23301, doi:10.1029/2004GL021412, 2004. Maurizi, A. and Lorenzani, S.: On the influence of the Eulerian velocity $pdf$ closure on the eddy diffusion coefficient, Boundary-Layer Meteorol., 95, 427-436, 2000. Maurizi, A. and Lorenzani, S.: Lagrangian time scales in inhomogeneous non-Gaussian turbulence, Flow, Turbulence and Combustion, 67, 205-216, 2001. Maurizi, A. and Tampieri, F.: Velocity probability density functions in Lagrangian dispersion models for inhomogeneous turbulence, Atmos. Environ., 33, 281-289, 1999. Maurizi, A., Trombetti, F., Sabatino, S D., and Tampieri, F.: Reliability of Third-Order Moments Parameterization for Models of Turbulent Boundary Layer Over Gentle Topography, Nuovo Cimento C, 20C, 273-286, 1997. Tampieri, F., Maurizi, A., and Alberghi, S.: Lagrangian models of turbulent dispersion in the atmospheric boundary layer, in Ingegneria del vento in Italia 2000. Atti del $6^o$ convegno nazinale di ingegneria del vento - INVENTO 2000, edited by:~Solari, G., Pagnini, L C., and~Piccardo, G., SGEditoriali (Padova), 37-50, 2000. Wyngaard, J C.: An experimental investigation of the small-scale structure of turbulence in a curved mixing layer, PhD thesis, Pennsylvania State University, 1967. Wyngaard, J C. and Weil, J C.: Transport asymmetry in skewed turbulence, Phys. Fluids A, 3, 155-162, 1991.