Energetics of a developing wave in the westerlies

Harald Lejenäs

doi:10.3402/tellusa.v25i1.9641

Energetics of a developing wave in the westerlies

Tellus

Volume 25 (1973): Issue 1

By: Harald Lejenäs

Open Access

|Jan 1973

Abstract

The terms expressing conversion between eddy kinetic and zonal kinetic energy and between eddy available and eddy kinetic energy are studied, in order to establish the contribution of barotropic and baroclinic processes respectively to the increase of eddy kinetic energy in an amplifying disturbance. After specification of initial fields the tendencies

∂/∂t[C(K_E,K_Z)] and ∂/∂t [[C(A_E,K_E)]]

at time t = 0 are solved analytically using the quasi-geostrophic equations of motion and the ω-equation. Comparisons between this method, which depends on the specification of initial fields, and the ordinary eigen-value method are made, and it is found that the results are similar. The problem of solving the combined barotropic-baroclinic case is complicated using the eigen-value method, but investigation of the initial tendencies of the energy conversion terms gives an insight into this problem in an easy way.

References

Bretherton , F. P . 1966 . Critical layer instability in baroclinic flows. Quart. J. R. Met. Soc . 92 . 325 – 334 .
Search in Google Scholar Back to article
Brown , J. A . 1969 . A numerical investigation of hydrodynamic instability and energy conver-sions in the quasi-geostrophic atmosphere. J. Atmos. Sci. 26, Part I, 352-365; Part II, 366 - 375 .
Search in Google Scholar Back to article
Charney , J. G . 1947 . The dynamics of long waves in a baroclinic westerly current. J. Meteor . 4 , 135 – 162 .
Search in Google Scholar Back to article
Charney , J. G. and Stern , M. E . 1962 . On the stability of internal baroclinic jets in a rotating atmos-phere. J. Atmos. Sci . 19 , 159 – 172 .
Search in Google Scholar Back to article
Derome , J. F. and Wiin-Nielsen , A . 1966 . On the baroclinic stability of zonal flow in simple model atmospheres. The University of Michigan, Dept. of Meteorology and Oceanography, Technical report no. 2.
Search in Google Scholar Back to article
Eady , E. T . 1949 . Long waves and cyclone waves. Tellus I, No . 3 , 33 – 52 .
Search in Google Scholar Back to article
Fischer , G . 1968 . Ein Beitrag zum Problem der barotropen Instabilität. Beitr. Phys. Atmos . 41 , 9 – 25 .
Search in Google Scholar Back to article
Fischer , G and Renner, V. . 1971 . Numerical and analytical studies on the energy conversions in a baroclinic model. J. Atmos. Sci. 28 , 512 - 522 .
Search in Google Scholar Back to article
Foote , J. R. and Lin , C. C . 1951 . Some recent investiga-tions in the theory of hydrodynamic stability. Quart. appl. Math . 8 , 265 – 280 .
Search in Google Scholar Back to article
Gates , W. L . 1961 . Static stability measures in the atmosphere. J. Meteor . 18 , 526 – 553 .
Search in Google Scholar Back to article
Green , J. S. A . 1960 . A problem in baroclinic sta-bility. Quart. J. Roy. Meteor. Soc . 86 , 237 – 251 .
Search in Google Scholar Back to article
Hirota , I . 1968 . On the dynamics of long and ultra-long waves in a baroclinic zonal current. J. Met. Soc. Japan 46 , 234 – 249 .
Search in Google Scholar Back to article
Jacobs , S. J and Wiin-Nielsen, A. . 1966 . On the stability of a barotropic basic flow in a stratified atmosphere. J. Atmos. Sci. 23 , 682 - 687 .
Search in Google Scholar Back to article
Kuo , H.-L . 1949 . Dynamic instability of two-dimensional non-divergent flow in a barotropic atmosphere. J. Meteor . 6 , 105 – 122 .
Search in Google Scholar Back to article
Kuo , H.-L . 1953 . On the production of mean zonal currents in the atmosphere by large disturbances. Tellus 5 , 475 – 493 .
Search in Google Scholar Back to article
Lipps , F. B . 1962 . Stability of jets in a divergent barotropic fluid. J. Atm. Sci . 20 , 120 – 129 .
Search in Google Scholar Back to article
Lippe , F. B . 1965 . The stability of an asymmetric zonal current in the atmosphere. J. Fluid Mech . 11 , 397 – 407 .
Search in Google Scholar Back to article
Lipps , F. B . 1966 . Momentum transfer across an asymmetric jet. J. Atm. Sci . 23 , 213 – 222 .
Search in Google Scholar Back to article
Lorenz , E. N . 1960 . Energy and numerical weather prediction. Tellus 12 , 364 – 373 .
Search in Google Scholar Back to article
Ogura , Y . 1957 . Wave solutions of the vorticity equation for the 21-dimensional model. J. Meteor . 14 , 60 – 64 .
Search in Google Scholar Back to article
Phillips , N . 1951 . A simple three-dimensional model for the study of large-scale extratropical flow patterns. J. Meteor . 8 , 381 – 394
Search in Google Scholar Back to article
Pedlosky , J . 1964 . The stability of currents in the atmosphere and the ocean. J. Atmos. Sci. 21, Part I, 201-219, Part II, 342 - 353 .
Search in Google Scholar Back to article
Platzman , G. W . 1952 . The increase or decrease of mean-flow energy in large-scale horizontal flow in the atmosphere. J. Meteor . 9 , 347 – 358 .
Search in Google Scholar Back to article
Rayleigh, Lord , 1880 . On the stability, or insta-bility, of certain fluid motions. Scientific Papers 1, 474-487. Cambridge Univ. Press.
Search in Google Scholar Back to article
Rayleigh, Lord , 1913 . On the stability of the laminar motion of an inviscid fluid. Scientific Papers 6, 197-204. Cambridge Univ. Press.
Search in Google Scholar Back to article
Tollmien , W . 1935 . EM allgemeines Kriterium der Instabilitiit laminarer Geschwindigkeitsvertei-lungen. Nachr. Ges. Wiss. Göttingen, Math.-Phys. Klasse 50 , 79 – 114 .
Search in Google Scholar Back to article
Wiin-Nielsen , A . 1962 . On truncation errors due to vertical differences in various numerical predic-tion models. Tellus 14 , 261 – 280 .
Search in Google Scholar Back to article
Yanai , M. and Nitta , T . 1968 . Finite difference approximations for the barotropic instability problem. J. Met. Soc. (Japan) 46 , 389 – 403 .
Search in Google Scholar Back to article