#### Boundary Layer, Urban Meteorology and Land-Surface Processes

## Ekman Revisited: The case of the phantom PGF.

### Ethan Cook

School of Meteorology

#### 04 December 2015, 2:00 PM

National Weather Center, Room 5600

120 David L. Boren Blvd.

University of Oklahoma

Norman, OK

In a seminar given in April of this year (A very basic model for velocity statistics of an Ekman-like neutral turbulent layer) the presenter proposed that, for a stationary, horizontally homogeneous flow, the Green’s Function integral substituted for the perturbation pressure gradient force (PGF) in a constant-density atmosphere could be approximated using a ‘flux gradient’ expression as used to approximate the Reynolds stresses in the turbulent Ekman Model. Objections raised by faculty to the application of the Boussinesq analogy to the perturbation PGF led to reexamination of the idea and discovery of some important errors.

The role of deviations in PGF from hydrostatic and geostrophic-reference in the ‘classic’ Ekman formulation remains in some sense obvious, as pressure forces clearly provide the mode of momentum transfer between adjacent volumes of air. Furthermore, the use of a flux gradient model to simplify the forcing expression for the PDF Transport Equations is still desirable. In this seminar, we will present an alternative formulation of the mean conditional forcing to that presented in the initial seminar. Special emphasis will be given to addressing the errors noted previously.

Boundary Layer, Urban Meteorology and Land-Surface Processes Seminar Series website