TY - JOUR

T1 - Gravity wave radiation from unsteady rotational flow in an f-plane shallow water system

AU - Sugimoto, Norihiko

AU - Ishioka, Keiichi

AU - Yoden, Shigeo

N1 - Funding Information:
Numerical experiment was performed with VPP800 and HPC2500 at the Academic Center for Computing and Media Studies, Kyoto University, at the Information Technology Center, Nagoya University, and the KDK system of Research Institute for Sustainable Humanosphere (RISH) at Kyoto University as a collaborative research project. GFD-DENNOU Library was used for drawing the figures. ISPACK-0.61 was used for numerical simulation and analysis. N. Sugimoto was supported by Grant-in-Aids for the 21st Century COE programs “Elucidation of the Active Geosphere” and “Frontiers of Computational Science”. This work was also supported by a Grant-in-Aid for Young Scientists (B) (19740290) from the Ministry of Education Culture, Sport, Science and Technology in Japan. We thank Prof. T. Kambe for his helpful suggestions to the extension of the aero-acoustic sound wave radiation theory to our study. We also want to thank Prof. S. Kida, Prof. Y.-Y. Hayashi, Prof. K. Ishii, and two anonymous referees for their constructive comments.

PY - 2007/11

Y1 - 2007/11

N2 - 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.

AB - 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.

KW - Gravity wave radiation

KW - Jet

KW - Rotational flow

KW - Shallow water equation

KW - Shear instability

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U2 - 10.1016/j.fluiddyn.2007.07.001

DO - 10.1016/j.fluiddyn.2007.07.001

M3 - Article

AN - SCOPUS:35748972047

VL - 39

SP - 731

EP - 754

JO - Fluid Dynamics Research

JF - Fluid Dynamics Research

SN - 0169-5983

IS - 11-12

ER -