Gravity wave radiation from unsteady rotational flow in an f-plane shallow water system

Norihiko Sugimoto, Keiichi Ishioka, Shigeo Yoden

Research output: Contribution to journalArticle

8 Citations (Scopus)

Abstract

Spontaneous gravity wave radiation from an unsteady rotational flow is investigated numerically in an f-plane shallow water system. Unlike the classical Rossby adjustment problem, where free development of an initially unbalanced state is investigated, we consider development of a barotropically unstable zonal flow which is initially balanced but maintained by zonal mean forcing. Gravity waves are continuously radiated from a nearly balanced rotational flow region even when the Froude number is so small that balance dynamics is thought to be a good approximation for the full system. The source of gravity waves is discussed by analogy with the theory of aero-acoustic sound wave radiation (the Lighthill theory). It is shown that the source regions correspond to regions of strong rotational flow. The gradual change of rotational flow causes gravity wave radiation. We propose an approximation for these strong sources on the assumption that the dominant flow in the jet region is non-divergent rotational flow. In addition, we calculate the zonally symmetric component of gravity waves far from the source regions, solving the Lighthill equation. Using scaling analyses for perturbations, these gravity waves can be calculated with only one approximated source term that is related to the latitudinal gradient of the fluid depth and the latitudinal mass flux. In spite of its simplicity, this approximation not only explains the physical cause of gravity wave radiation, but gives an amount of source close to that obtained by classical approximation derived from vortical motion.

Original languageEnglish
Pages (from-to)731-754
Number of pages24
JournalFluid Dynamics Research
Volume39
Issue number11-12
DOIs
Publication statusPublished - 2007 Nov
Externally publishedYes

Fingerprint

rotational flow
Rotational flow
Gravity waves
shallow water
gravity waves
electromagnetic radiation
Radiation
Water
approximation
Acoustic waves
Froude number
causes
sound waves
Mass transfer
adjusting
scaling
perturbation
gradients
Fluids
acoustics

Keywords

  • Gravity wave radiation
  • Jet
  • Rotational flow
  • Shallow water equation
  • Shear instability

ASJC Scopus subject areas

  • Mechanical Engineering
  • Statistical and Nonlinear Physics

Cite this

Gravity wave radiation from unsteady rotational flow in an f-plane shallow water system. / Sugimoto, Norihiko; Ishioka, Keiichi; Yoden, Shigeo.

In: Fluid Dynamics Research, Vol. 39, No. 11-12, 11.2007, p. 731-754.

Research output: Contribution to journalArticle

Sugimoto, Norihiko ; Ishioka, Keiichi ; Yoden, Shigeo. / Gravity wave radiation from unsteady rotational flow in an f-plane shallow water system. In: Fluid Dynamics Research. 2007 ; Vol. 39, No. 11-12. pp. 731-754.
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