Planetary, Inertia‐Gravity and Kelvin waves on the f ‐plane and β ‐plane in the presence of a uniform zonal flow

<p>A linear wave theory of the Rotating Shallow Water Equations (RSWE) is developed in a channel on either the mid-latitude f-plane/&#946;-plane or on the equatorial &#946;-plane in the presence of a uniform mean zonal flow that is balanced geostrophically by a meridional gradient of the fluid surface height. We show that this surface height gradient is a potential vorticity (PV) source that generates Rossby waves even on the f-plane similar to the generation of these waves by PV sources such as the &#946;&#8211;effect, shear of the mean flow and bottom topography. Numerical solutions of the RSWE show that the resulting planetary (Rossby), Inertia-Gravity (Poincar&#233;) and Kelvin-like waves differ from their counterparts without mean flow in both their phase speeds and meridional structures. Doppler shifting of the &#8220;no mean-flow&#8221; phase speeds does not account for the difference in phase speeds, and the meridional structure does not often oscillate across the channel but is trapped near one the channel's boundaries in mid latitudes or behaves as Hermite function in the case of an equatorial channel. The phase speed of Kelvin-like waves is modified by the presence of a mean flow compared to the classical gravity wave speed but their meridional velocity does not vanish. The gaps between the dispersion curves of adjacent Poincar&#233; modes are not uniform but change with the zonal wavenumber, and the convexity of the dispersion curves also changes with the zonal wavenumber. In some cases, the Kelvin-like dispersion curve crosses those of Poincar&#233; modes, but it is not an evidence for the existence of instability since the Kelvin waves are not part of the solutions of an eigenvalue problem.&#160;</p>

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On the Interaction Between Kelvin Waves and the Mean Zonal Flow

Journal of the Atmospheric Sciences ◽

10.1175/1520-0469(1971)028<0162:otibkw>2.0.co;2 ◽

1971 ◽

Vol 28 (2) ◽

pp. 162-169 ◽

Cited By ~ 31

Author(s):

V. E. Kousky ◽

J. M. Wallace

Keyword(s):

Zonal Flow ◽

Kelvin Waves ◽

The Mean

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Dynamical Aspects of the General Circulation and the Stability of Zonal Flow

Tellus A Dynamic Meteorology and Oceanography ◽

10.3402/tellusa.v3i4.8656 ◽

1951 ◽

Author(s):

Hsiao-Lan Kuo

Keyword(s):

General Circulation ◽

Zonal Flow ◽

The Stability

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Kelvin waves on helical vortex tube in swirling flow

Journal of Physics Conference Series ◽

10.1088/1742-6596/980/1/012003 ◽

2018 ◽

Vol 980 ◽

pp. 012003

Author(s):

M A Tsoy ◽

S G Skripkin ◽

P A Kuibin ◽

S I Shtork ◽

S V Alekseenko

Keyword(s):

Vortex Tube ◽

Swirling Flow ◽

Kelvin Waves ◽

Helical Vortex

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Low-cost Solutions for Velocimetry in Rotating and Opaque Fluid Experiments using Ultrasonic Time of Flight

Experimental Techniques ◽

10.1007/s40799-021-00469-x ◽

2021 ◽

Author(s):

Fabian Burmann ◽

Jerome Noir ◽

Stefan Beetschen ◽

Andrew Jackson

Keyword(s):

Acoustic Waves ◽

Flow Measurement ◽

Low Cost ◽

Time Of Flight ◽

Zonal Flow ◽

Gravitational Acceleration ◽

Complex Flow ◽

Ultrasonic Time ◽

Theoretical Predictions ◽

Complex Flow Structure

AbstractMany common techniques for flow measurement, such as Particle Image Velocimetry (PIV) or Ultrasonic Doppler Velocimetry (UDV), rely on the presence of reflectors in the fluid. These methods fail to operate when e.g centrifugal or gravitational acceleration leads to a rarefaction of scatterers in the fluid, as for instance in rapidly rotating experiments. In this article we present two low-cost implementations for flow measurement based on the transit time (or Time of Flight) of acoustic waves, that do not require the presence of scatterers in the fluid. We compare our two implementations against UDV in a well controlled experiment with a simple oscillating flow and show we can achieve measurements in the sub-centimeter per second velocity range with an accuracy of $\sim 5-10\%$ ∼ 5 − 10 % . We also perform measurements in a rotating experiment with a complex flow structure from which we extract the mean zonal flow, which is in good agreement with theoretical predictions.

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