Critical Levels of the Sea Breeze Сirculation within the Framework of Linear Theory

M. V. Shokurov✉, N. Yu. Kraevskaya

Marine Hydrophysical Institute of RAS, Sevastopol, Russian Federation

✉ e-mail: shokurov.m@gmail.com

Abstract

Purpose. The present paper is aimed at solving (within the framework of linear theory) a problem on the influence of critical levels on an inertia-gravity wave with the scale typical of the sea breeze circulation in the presence of an average background synoptic flow (perpendicular to the coast) with a vertical shear.

Methods and Results. To solve the problem, the generalized Taylor – Goldstein equation was used with the regard for rotation. The coefficients’ behavior, having been analyzed, showed that at the equator, for a gravity internal wave (generated by a heat source on the surface) with the daily frequency, there existed a single critical level, at which the wave was absorbed. In the tropics, an inertia-gravity wave of the daily period passes through two critical levels and the attenuation region located between them. At the mid-latitudes, the generated wave, starting from the surface, is in the attenuation zone, then passes the critical level and propagates above it. To analyze the solution behavior, the Cauchy problem on the wave passage through the critical level was solved. The solution near the critical level was obtained numerically.

Conclusions. For the selected values of stratification and background wind speed, the absorption coefficients of the vertical momentum flux were calculated for the equator and those of the vertical angular momentum flux – for the tropics and middle latitudes. The absorption coefficient value at the equator is in complete agreement with the results obtained in the earlier published papers. Comparing the values of the absorption coefficients of the vertical momentum flux/vertical angular momentum flux at different latitudes, one can note that the strongest attenuation takes place at 15°, and the weakest one – at 45°.

Keywords

linear theory, sea breeze circulation, internal inertia-gravity waves, critical level, stratification, shear flow

Acknowledgements

The investigation was carried out within the framework of the state assignment of the MHI RAS on theme FNNN-2021-0002 “Fundamental studies of the processes of interaction in the ocean-atmosphere system, which determine the regional spatial and temporal variability of the natural environment and climate”. The authors are thankful to the reviewer for the useful comments that contributed to improving the article.

Original russian text

Original Russian Text © M. V. Shokurov, N. Yu. Kraevskaya, 2022, published in MORSKOY GIDROFIZICHESKIY ZHURNAL, Vol. 38, Iss. 6, pp. 620-636 (2022)

For citation

Shokurov, M.V. and Kraevskaya, N.Yu., 2022. Critical Levels of the Sea Breeze Circulation within the Framework of Linear Theory. Physical Oceanography, 29(6), pp. 602-618. doi:10.22449/1573-160X-2022-6-602-618

DOI

10.22449/1573-160X-2022-6-602-618

References

  1. Haurwitz, B., 1947. Comments on the Sea-Breeze Circulation. Journal of the Atmospheric Sciences, 4(1), pp. 1-8. doi:10.1175/1520-0469(1947)004<0001:COTSBC>2.0.CO;2
  2. Rotunno, R., 1983. On the Linear Theory of the Land and Sea Breeze. Journal of the Atmospheric Sciences, 40(8), pp. 1999-2009. doi:10.1175/15200469(1983)040<1999:OTLTOT>2.0.CO;2
  3. Niino, H., 1987. The Linear Theory of Land and Sea Breeze Circulation. Journal of the Meteorological Society of Japan. Ser. II, 65(6), pp. 901-921. doi:10.2151/jmsj1965.65.6_901
  4. Steyn, D.G. and Mckendry, I.G., 1988. Quantitative and Qualitative Evaluation of a ThreeDimensional Mesoscale Numerical Model Simulation of a Sea Breeze in Complex Terrain. Monthly Weather Review, 116(10), pp. 1914-1926. doi:10.1175/15200493(1988)116<1914:QAQEOA>2.0.CO;2
  5. Gille, S.T. and Llewellyn Smith, S.G., 2014. When Land Breezes Collide: Converging Diurnal Winds over Small Bodies of Water. Quarterly Journal of the Royal Meteorological Society, 140(685), pp. 2573-2581. doi:10.1002/qj.2322
  6. Anjos, M. and Lopes, A. 2019. Sea Breeze Front Identification on the Northeastern Coast of Brazil and Its Implications for Meteorological Conditions in the Sergipe Region. Theoretical and Applied Climatology, 137, pp. 2151-2165. doi:10.1007/s00704-018-2732-x
  7. Simpson, J.E., 1982. Gravity Currents in the Laboratory, Atmosphere, and Ocean. Annual Review of Fluid Mechanics, 14, pp. 213-234. doi:10.1146/annurev.fl.14.010182.001241
  8. Mitsumoto, S., Ueda, H. and Ozoe, H., 1983. A Laboratory Experiment on the Dynamics of the Land and Sea Breeze. Journal of the Atmospheric Sciences, 40(5), pp. 1228-1240. doi:10.1175/1520-0469(1983)040<1228:ALEOTD>2.0.CO;2
  9. Pearce, R.P., 1955. The Calculation of a Sea‐Breeze Circulation in Terms of the Differential Heating across the Coastline. Quarterly Journal of the Royal Meteorological Society, 81(349), pp. 351-381. doi:10.1002/qj.49708134906
  10. Pielke, R.A., 1974. A Three-Dimensional Numerical Model of the Sea Breezes over South Florida. Monthly Weather Review, 102(2), pp. 115-139. doi:10.1175/15200493(1974)102<0115:ATDNMO>2.0.CO;2
  11. Chen, X., Zhang, F. and Zhao, K., 2016. Diurnal Variations of the Land-Sea Breeze and Its Related Precipitation over South China. Journal of the Atmospheric Sciences, 73(12), pp. 4793-4815. doi:10.1175/JAS-D-16-0106.1
  12. Kimura, R. and Eguchi, T., 1978. On Dynamical Processes of Seaand Land-Breeze Circulation. Journal of the Meteorological Society of Japan. Ser. II, 56(2), pp. 67-85. doi:10.2151/jmsj1965.56.2_67
  13. Porson, A., Steyn, D.G. and Schayes, G., 2007. Sea-Breeze Scaling from Numerical Model Simulations, Part I: Pure Sea Breezes. Boundary-Layer Meteorology, 122(1), pp. 17-29. doi:10.1007/s10546-006-9090-4
  14. Antonelli, M. and Rotunno, R., 2007. Large-Eddy Simulation of the Onset of the Sea Breeze. Journal of the Atmospheric Sciences, 64(12), pp. 4445-4457. doi:10.1175/2007JAS2261.1
  15. Schmidt, F.H., 1947. An Elementary Theory of the Landand Sea-Breeze Circulation. Journal of the Atmospheric Sciences, 4(1), pp. 9-20. doi:10.1175/15200469(1947)004<0009:AETOTL>2.0.CO;2
  16. Walsh, J.E., 1974. Sea Breeze Theory and Applications. Journal of the Atmospheric Sciences, 31(8), pp. 2012-2026. doi:10.1175/1520-0469(1974)031>2012:SBTAA>2.0.CO;2
  17. Qian, T., Epifanio, C.C. and Zhang, F., 2009. Linear Theory Calculations for the Sea Breeze in a Background Wind: The Equatorial Case. Journal of the Atmospheric Sciences, 66(6), pp. 1749-1763. doi:10.1175/2008JAS2851.1
  18. Jiang, Q., 2012. On Offshore Propagating Diurnal Waves. Journal of the Atmospheric Sciences, 69(5), pp. 1562-1581. doi:10.1175/JAS-D-11-0220.1
  19. Du, Y. and Rotunno, R., 2018. Diurnal Cycle of Rainfall and Winds near the South Coast of China. Journal of the Atmospheric Sciences, 75(6), pp. 2065-2082. doi:10.1175/JAS-D-170397.1
  20. Booker, J.R. and Bretherton, F.P., 1967. The Critical Layer for Internal Gravity Waves in a Shear Flow. Journal of Fluid Mechanics, 27(3), pp. 513-539. doi:10.1017/S0022112067000515
  21. Miles, J.W., 1961. On the Stability of Heterogeneous Shear Flows. Journal of Fluid Mechanics, 10(4), pp. 496-508. doi:10.1017/S0022112061000305
  22. Jones, W.L. 1967. Propagation of Internal Gravity Waves in Fluids with Shear Flow and Rotation. Journal of Fluid Mechanics, 30(3), pp. 439-448. doi:10.1017/S0022112067001521
  23. Grimshaw, R., 1975. Internal Gravity Waves: Critical Layer Absorption in a Rotating Fluid. Journal of Fluid Mechanics, 70(2), pp. 287-304. doi:10.1017/S0022112075002030
  24. Slepyshev, A.A. and Vorotnikov, D.I., 2017. Vertical Transport of Momentum by the InertialGravity Internal Waves in a Baroclinic Current. Physical Oceanography, (4), pp. 3-15. doi:10.22449/1573-160X-2017-4-3-13
  25. Du, Y., Rotunno, R. and Zhang, F., 2019. Impact of Vertical Wind Shear on Gravity Wave Propagation in the Land-Sea-Breeze Circulation at the Equator. Journal of the Atmospheric Sciences, 76(10), pp. 3247-3265. doi:10.1175/JAS-D-19-0069.1

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