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On the problem of boundary conditions in isentropic coordinates

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Abstract

The main advantages of constant potential enthalpy as a vertical coordinate are weaker horizontal velocity gradients in frontal regions and a higher vertical resolution. A disadvantage is the intersection of isentropes with the ground and folding of these surfaces. A numerical model is proposed to overcome the difficulties imposed by the intersection of isentropes with the ground. The model contains a physical and computational domain. The top and bottom surfaces of the computational domain are isentropes whereas the physical domain of the flow confined above by a free surface of constant pressure, and the bottom of this domain is the surface of the earth. In the present study the top surfaces of these two domains coincide (θ T, PTare constants in space and time). The model was tested for the study of frontogenesis and cyclogenesis and integrated for 7 days. The results correspond to enstrophy-conserving finite difference scheme.

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Abbreviations

Cp :

specific heat at constant pressure = 1004

f:

Coriolis parameter

g:

gravity

M:

Montgomery potential

NL:

No. of layers

P:

pressure

Pg :

surface pressure = 1000 mb

q:

a variable

R:

gas constant = 287.0

T:

temperature in °K

u:

zonal velocity

U:

mass flux inX-direction

v:

meridional velocity

V:

mass flux inY-direction

XM:

length of the channel = 4800 km

YM:

width of the channel = 3200 km

Z:

potential vorticity

β:

beta-parameter (df/dy) =1.16 × 10−11 m−1 s−1

ΔPg:

5 mb

Δx:

Δy = 200 km

Δt:

480 s

Δθg :

1200 m2 s−2

ϕ:

geopotential (=gz)

ζ:

relative vorticity

κ:

R/CP

π:

Exner function

θ:

potential enthalpy

θg :

potential enthalpy at the ground = 288C p/πgm2 s−2

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Authors and Affiliations

  1. Centre for Atmospheric Sciences, Indian Institute of Technology, 110016, New Delhi, India

    H. C. Upadhyaya & R. Sadourny

  2. Laboratoire de Meteorologie Dynamique, ENS-Physique, 24, Rue Lhomond, 75231, Paris, France

    R. Sadourny

Authors
  1. H. C. Upadhyaya
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  2. R. Sadourny
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Upadhyaya, H.C., Sadourny, R. On the problem of boundary conditions in isentropic coordinates. Proc. Indian Acad. Sci. (Earth Planet Sci.) 101, 35–46 (1992). https://doi.org/10.1007/BF02839171

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  • DOI: https://doi.org/10.1007/BF02839171

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