Abstract
The purpose of this note is to estimate the accuracy and practical limitations of applying linear theory at a critical level over a realistic range of atmospheric stabilities for an idealized surface terrain. These estimates are made by comparing the results of a linear model with a nonlinear numerical model at a critical level. Essentially similar results are obtained from each model for wave stress, wave breaking height and wave dissipation through the critical level. Because gravity waves can be either evanescent or internal depending on the relative sizes of the Scorer parameter and the wavenumber of the ground surface disturbance, the somewhat paradoxical result develops that wave breaking and non-linearity increase with increasing bulk Richardson number. It is recommended that steady linear wave theory be used in gravity wave drag parameterizations provided near real time profiles of background velocity and temperature are available.
Similar content being viewed by others
References
Baines, P. G.: 1995, Topographic Effects in Stratified Flows, Cambridge University Press, 482 pp.
Booker, J. R. and Bretherton, F. P.: 1967, ‘The Critical Layer for Internal Gravity Waves in a Shear Flow’, J. Fluid Mech. 27, 513–539.
Delisi, D. P. and Dunkerton, T. J.: 1989, ‘Laboratory Observations of Gravity Wave Critical-Layer Flows’, Pure Appl. Geophys. 130, 445–461.
D¨ ornbrack, A.: 1996, ‘Turbulent Mixing by Breaking Gravity Waves’, J. Fluid Mech.submitted.
D¨ ornbrack, A., Gerz, T., and Schumann, U.: 1995, ‘Turbulent Breaking of Overturning Gravity Waves Below a Critical Level’, Appl. Scient. Res.54, 163–176.
D¨ ornbrack, A. and Schumann, U.: 1993, ‘Numerical Simulation of Turbulent Convective Flows Over Wavy Terrain’, Boundary-Layer Meteorol.65, 323–355.
Eliassen, A. and Palm, E.: 1960, ‘On the Transfer of Energy in Stationary Mountain Waves’, Geofy-siske Publikasjoner XXII, 1–23.
Fritts, D. C.: 1984, ‘Gravity Wave Saturation in the Middle Atmosphere: A Review of Theory and Observations’, Rev. Geophys. Space Phys.22, 275–308.
Fritts, D. C. and Geller, M. A.: 1976, ‘Viscous Stabilization of Gravity Critical Level Flows’, J. Atmos. Sci.33, 2276–2284.
Hazel, P.: 1967, ‘The Effect of Viscosity and Heat Conduction on Internal Gravity Waves at a Critical Level’, J. Fluid Mech.30, 775–783.
Kim, Y.-J. and Arakawa, A.: 1995, ‘Improvement of Orographic Gravity Wave Parameterization using a Mesoscale Gravity Wave Model’, J. Atmos. Sci.52, 1875–1902.
Koop, C. G. and McGee, B.: 1986, ‘Measurements of Internal Gravity Waves in a Continiously Stratified Shear Flow’, J. Fluid Mech.172, 453–480.
Nappo, C. J. and Andrèn, A.: 1995, ‘A Parameterization of Subgrid Scale Gravity-Wave Generated Turbulence in a Mesoscale Boundary Layer Model’, 11th Symp. on Boundary Layers and Turbu-lence, 27–31 March, Charlotte, NC. American Meteorological Society, Boston, MA, 341–343.
Nappo, C. J. and Chimonas, G.: 1992, ‘Wave Exchange Between the Ground Surface and a Boundary-Layer Critical Level’, J. Atmos. Sci.49, 1075–1091.
Merrill, J. T. and Grant, J. R.: 1979, ‘A Gravity Wave – Critical Level Encounter Observed in the Atmosphere’, J. Geophys. Res.84, 6315–6320.
Smith, R. B.: 1979, ‘The Influence of Mountains on the Atmosphere’, Adv. in Geophysics 21, 87–230.
Thorpe, S. A.: 1968, ‘A Method of Producing a Shear Flow in a Stratified Fluid’, J. Fluid Mech.32, 693–704.
Thorpe, S. A.: 1981, ‘An Experimental Study of Critical Layers’, J. Fluid Mech.103, 321–344.
Worthington, R. M. and Thomas, L.: 1996, ‘Radar Measurements of Critical Layer Absorption in Mountain Waves’, Quart. J. Roy. Meteorol. Soc.122, 1263–1282.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Dörnbrack, A., Nappo, C.J. A NOTE ON THE APPLICATION OF LINEAR WAVE THEORY AT A CRITICAL LEVEL. Boundary-Layer Meteorology 82, 399–416 (1997). https://doi.org/10.1023/A:1000270821161
Issue Date:
DOI: https://doi.org/10.1023/A:1000270821161