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Instability of Baroclinic Tidal Flow in a Stratified Fjord

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  • 1 School of Ocean Sciences, Bangor University, Anglesey, United Kingdom, and Physical Oceanography Laboratory, Ocean University of China, Qingdao, China
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Abstract

The Taylor–Goldstein equation is used to investigate the stability of a baroclinic tidal flow observed in a stratified fjord. The flow is analyzed at hourly intervals when turbulent dissipation measurements were made. The critical gradient Richardson number is often close to the Miles–Howard limit of 0.25, but sometimes it is substantially less. Although during 8 of the 24 periods examined the flow is marginally stable, it is either very stable or very unstable in others. For the unstable flow, the e-folding period of the fastest growing disturbances is 83–455 s, about 46% of the buoyancy period at the levels where the fastest growing disturbances have their maximum amplitude. These disturbances to the flows have wavelengths about 20%–72% of the water depth and have mostly a second-mode structure. Simultaneous measurements of the flow and turbulence allow for testing of the hypothesis that the growth rates of the most unstable disturbances are related to the turbulent dissipation rates. Dissipation is found to depend on the growth rates, but only to a power of about 1.2; there is a stronger (power 1.8) dependence on the buoyancy frequency.

* Current affiliation: State Key Laboratory of Marine Environmental Science, Xiamen University, Xiamen, China.

Corresponding author address: Dr. Zhiyu Liu, State Key Laboratory of Marine Environmental Science, Xiamen University, 422 Siming South Road, Xiamen 361005, China. Email: zyliu@xmu.edu.cn

Abstract

The Taylor–Goldstein equation is used to investigate the stability of a baroclinic tidal flow observed in a stratified fjord. The flow is analyzed at hourly intervals when turbulent dissipation measurements were made. The critical gradient Richardson number is often close to the Miles–Howard limit of 0.25, but sometimes it is substantially less. Although during 8 of the 24 periods examined the flow is marginally stable, it is either very stable or very unstable in others. For the unstable flow, the e-folding period of the fastest growing disturbances is 83–455 s, about 46% of the buoyancy period at the levels where the fastest growing disturbances have their maximum amplitude. These disturbances to the flows have wavelengths about 20%–72% of the water depth and have mostly a second-mode structure. Simultaneous measurements of the flow and turbulence allow for testing of the hypothesis that the growth rates of the most unstable disturbances are related to the turbulent dissipation rates. Dissipation is found to depend on the growth rates, but only to a power of about 1.2; there is a stronger (power 1.8) dependence on the buoyancy frequency.

* Current affiliation: State Key Laboratory of Marine Environmental Science, Xiamen University, Xiamen, China.

Corresponding author address: Dr. Zhiyu Liu, State Key Laboratory of Marine Environmental Science, Xiamen University, 422 Siming South Road, Xiamen 361005, China. Email: zyliu@xmu.edu.cn

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