Role of Wavenumber-1 Disturbances in Redistributing Angular Momentum in TC Eyes: Implication from High-Resolution AMVs

It has been elucidated by many studies that barotropic instabilities in tropical cyclone (TC) like vortices redistribute vorticity to change the radial distribution of angular momentum and that this mechanism induce changes in the low-level circulation in TC eyes, which is important in determining TC strength. However, their observational evidence had been scarce and indirect until recently because of the lack of precipitating particles suitable for Doppler radar observations and the difficulty in densely covering by aircraft observations. This situation was changed by the recent third-generation geostationary satellites that can observe clouds of TCs at high frequencies on the order of a minute. We have been developing methods to obtain atmospheric motion vectors (AMVs) at high frequency, resolution, and accuracy from high-frequency imaging. Based on the analyses of the AMVs, we show that the azimuthally wavenumber-1 disturbances play important roles in redistributing (potential) vorticity and angular momentum, whose importance has been overlooked presumably due in part to the absence of the exponentially growing wavenumber-1 barotropic instability. [This presentation is based on Horinouchi et al. (2023) and subsequent unpublished materials.]

By using an experimentally conducted 30-second imaging of Himawari-8, we derived high-resolution AMVs from the visible images of the low-level clouds in the eye of Typhoon Haishen (2020) from the daytime observations when it had a clear eye (Sep 4, 2020). It was found that a wavenumber-1 disturbance was present throughout the analysis period. It propagated cyclonically at an angular velocity near the maximum rotational-flow angular velocity with respect to radius. This feature is consistent with the algebraically growing wavenumber-1 disturbance studied theoretically by Nolan and Montgomery (2000), which causes trochoidal motion in the eye and its energy grows linearly with time. The amplitude of the observed disturbance also exhibited a mild growth. It was further shown that it transported angular momentum inward, which is quantitatively comparable to the observed increase in the angular velocity of rotation near the eye center.

We also derived high-resolution AMVs from the visible images of low-level clouds in the eyes of Typhoons Lan (2017) and Nanmadol (2022). They also had persistent wavenumber-1 disturbances that propagated at the angular velocity near the maximum rotational-flow angular velocities along radius. To our knowledge, the only previous observation of such wavenumber-1 disturbances having similar angular-velocity relationship is that reported by Marks et al (2008) who accidentally resulted in conducting a long aircraft operation in the eye of Hurricane Hugo. However, from the fact that they existed in all the three cases we analyzed (as well as further thoughts from the morphology of clouds in many TC eyes), we suggest that it is likely that they exist in TC eyes frequently, at least when they have clear eyes.

A possible reason for their ubiquity is that such wavenumber-1 disturbance evolves slowly. The aforementioned theory is derived as an asymptotic solution at sufficiently long time, and the initial disturbance must have a finite amplitude, so this is quite different from the exponential modal growth in the linear stability problem. Hendricks et al (2009) studied long-term behavior of barotropically unstable vortices. They found that many cases exhibit a “slow-monopole” behavior, in which a region of low vorticity is left after the decay of the initial modal instability and that the region is expelled in the long run. This behavior is likely understood in terms of the algebraically growing instability, which eventually expels the low-vorticity region. It should also be noted that the actual TC eyes evolve gradually, so fast modal instability and slow algebraic instability might coexist or occur alternately.

Studies on the wavenumber-1 disturbances and their roles in real (or realistic) TCs are still limited. Both observational and numerical studies would be needed to fully elucidate them.

References

Hendrics et al. (2009), https://doi.org/10.1175/2008JAS2820.1

Horinouchi et al. (2023), https://doi.org/10.1175/MWR-D-22-0179.1

Marks et al. (2008), https://doi.org/10.1175/2007MWR2073.1

Nolan and Montgomery (2000), https://doi.org/10.1175/1520-0469(2000)057<3514:TAGOWO>2.0.CO;2