CEE Seminar: Co-spectral Budgets Link Energy Distributions in Eddies to Bulk Flow Properties in Hydrology & Micrometeorology

Abstract: Connections are explored between spectral descriptions of turbulence and the mean velocity profile in wall-bounded flows using a budget for the co-spectral density. The co-spectrum is derived using a standard model for the wall normal velocity variance and a linear Rotta-like return-to-isotropy closure modified to include the isotropozition of the production for the pressure-strain effects. The approach provides a connection between well-established constants such as the von Karman and Kolmogorov constants, and the Rotta constant known to vary with the flow configuration. Depending on the choices made about small-scale intermittency corrections, the logarithmic mean velocity profile or a power-law profile with an exponent that depends on the intermittency correction are derived, thereby offering a new perspective on a long-standing debate about the shape of the mean velocity profile in the equilibrium region¹. The twice-integrated co-spectral budget with respect to scale and depth is then used to explain the variation in the friction factor with Reynolds number in smooth pipes² with attention to the switch from power-law (Blasius scaling) to log-law (Colebrook’s formula).  A general discussion on how to link the ‘microstates’ of eddies (i.e. energy distribution in eddies) to macroscopic flow properties used in operational hydrology and micrometeorology (i.e. bulk flow relations such as Manning’s formula, Monin-Obukhov similarity theory, stably stratified flow properties, Strickler scaling for roughness elements, etc….) is also featured.

References:

¹Katul, G.G., A. Porporato, C. Manes, and C. Meneveau, 2013, Co-spectrum and mean velocity in turbulent boundary layers, Physics of Fluids, 25, 091702;

²Katul, G.G. and C. Manes, 2014, Cospectral budget of turbulence explains the bulk properties of smooth pipe flow, Physical Review E, 90, 063008

Bio: Gabriel G. Katul received his B.E. degree in 1988 at the American University of Beirut (Beirut, Lebanon), his M.S. degree in 1990 at Oregon State University and his Ph.D degree in 1993 at the University of California, Davis.  He is currently the Theodore S. Coile Professor of Hydrology and Micrometeorology at the Nicholas School of the Environment and the Department of Civil and Environmental Engineering at Duke University. Research in Katul's lab focuses on micrometeorology and near-surface hydrology with emphasis on heat, momentum, carbon dioxide, water vapor, ozone, particulate matter (including aerosols, pollen and seeds) and water transport in the soil-plant-atmosphere system, as well as their implications to a plethora of hydrological, ecological, atmospheric and climate change-related questions.

Katul served as an associate editor for Advances in Water Resources (1998-2014), Boundary Layer Meteorology (1998-present), Water Resources Research (2004-2009) and the Vadoze Zone Journal (2000-2003), and served as one of the four editors-in-chief for Advances in Water Resources (2011-2014).  He was a visiting fellow at the Commonwealth Science and Industrial Research Organization (Australia) in 2002, at University of Helsinki (Finland) in 2009 and a Fulbright-Italy Distinguished Fellow at Politecnico di Torino (Itay) in 2010. He also served as a visiting fellow at École polytechnique fédérale de Lausanne (Switzerland) in 2013 and at Nagoya University (Japan) in 2014. He received several honorary awards, including an honorary certificate by La Seccion de Agrofisica de la Sociedad Cubana de Fisica in Habana (in 1998), an editor’s citation for excellence in refereeing from the American Geophysical Union (in 2008), the Macelwane medal and became thereafter a fellow of the American Geophysical Union (in 2002).  In 2012, he received the Hydrologic Science Award from the American Geophysical Union.  He served as the Secretary General for the Hydrologic Science Section at the American Geophysical Union (2006-2008).