Formulas for Parcel Velocity and Vorticity in a Rotating Cartesian Coordinate System
Advanced Search
Select up to three search categories and corresponding keywords using the fields to the right. Refer to the Help section for more detailed instructions.

Search our Collections & Repository

For very narrow results

When looking for a specific result

Best used for discovery & interchangable words

Recommended to be used in conjunction with other fields



Document Data
Clear All
Clear All

For additional assistance using the Custom Query please check out our Help Page


Formulas for Parcel Velocity and Vorticity in a Rotating Cartesian Coordinate System

Filetype[PDF-231.45 KB]


  • Journal Title:
    Journal of the Atmospheric Sciences
  • Personal Author:
  • NOAA Program & Office:
  • Description:
    Formulas in an Eulerian framework are presented for the absolute velocity and vorticity of individual parcels in inviscid isentropic flow. The analysis is performed in a rectangular Cartesian rotating coordinate system. The dependent variables are the Lagrangian coordinates, initial velocities, cumulative temperature, entropy, and a potential. The formulas are obtained in two different ways. The first method is based on finding a matrix integrating factor for the Euler equations of motion and a propagator for the vector vorticity equation. The second method is a variational one. Hamilton’s principle of least action is used to minimize the fluid’s absolute kinetic energy minus its internal energy and potential energy subject to the Lin constraints and constraints of mass and entropy conservation. In the first method, the friction and diabatic heating terms in the governing equations are carried along in integrands so that the generalized formulas lead to Eckart’s circulation theorem. Using them to derive other circulation theorems, the helicity-conservation theorem, and Cauchy’s formula for the barotropic vorticity checks the formulas further. The formulas are suitable for generating diagnostic fields of barotropic and baroclinic vorticity in models if some simple auxiliary equations are added to the model and integrated stably forward in time alongside the model equations.
  • Keywords:
  • Source:
    Journal of the Atmospheric Sciences, 72(10), 3908-3922
  • DOI:
  • ISSN:
  • Format:
  • Publisher:
  • Document Type:
  • Rights Information:
  • Compliance:
  • Main Document Checksum:
  • Download URL:
  • File Type:

Supporting Files

  • No Additional Files
More +

You May Also Like

Checkout today's featured content at

Version 3.26.1