Helicity: A Possible Indicator of Negative Feedback Initiation of Tropical Cyclone–Ocean Interaction

The development of large‐scale vortex dynamo during tropical cyclogenesis through the mutual intensification of primary and secondary circulation in terms of helical evolution is well studied. However, the influence of atmospheric helicity on ocean surface heat and moisture fluxes associated with tropical cyclone (TC) evolution is yet to be understood. At its development stage, the heat and moisture flux from the ocean surface increases with the increase in intensity of the TC. This time, TC‐Ocean interaction works in a positive feedback mechanism. However, after a particular stage, the very intense wind of the TC causes strong turbulent mixing in the underlying ocean. Hence, the upper ocean layer temperature starts decreasing, leading to a decrease in heat and moisture flux exchange to the TC. We have analyzed the emergence of vortex helical structure in TC and the role of helicity in modulating surface heat and moisture fluxes. The result shows that helical development is associated with the axisymetrization of the vertical velocity and diabatic heating at the middle and upper troposphere. There is no definite TC intensity at which the initiation of negative feedback of TC‐upper ocean interaction occurs. However, the increase in helicity above 200 × 10−2 ms−2 reversed the TC‐ocean interaction trend. Therefore, TC helicity evolution and upper ocean interaction are essential to understand TC evolution.

in large and more intense vortices.A non-zero mean helicity indicates the break of mirror symmetry in atmospheric turbulence, which may result in large-scale vortex instability.A deep convective tower with cyclonic vorticity-a vortical hot tower works to form the secondary overturning circulation, which generates helicity and links the primary and secondary circulation on the system scale, forming a spiral structure.It thereby supports large-scale vortex by providing positive feedback between these two circulations.The ocean's role in developing and maintaining tropical cyclone circulation through moisture and heat fluxes is well known.TC forms when the sea surface temperature (SST) of the underlying ocean is greater than or equal to 26°C, and its intensity is very sensitive to changes in the upper ocean thermal distribution.The increased moisture and latent heat flux from the ocean moistens the boundary layer (BL) and produces conductive conditions for TC genesis and development (Gao et al., 2020;Lin et al., 2005).Emanuel (1986) treated TC as a Carnot heat engine absorbing energy from the ocean surface and releasing it at the upper troposphere.He also suggested that underlying SST is a determining factor for estimating maximum potential intensity.TC is an example of extreme air-sea interaction.Strong wind stress during TC causes strong turbulent mixing in the upper layer of the ocean and underlying cold water entrainment into the mixed layer.At this stage, increasing TC intensity causes stronger turbulent mixing, which leads to a decrease in SST and, hence, a reduction of heat and moisture flux.Therefore, a negative feedback mechanism plays a role in the ocean to atmosphere heat and moisture flux.Observation showed that TC-induced SST cooling ranges from 1°C to 6°C (Price, 1981).The negative feedback of decreasing SST with increasing TC intensity has been discussed by Chang and Anthes. (1979), Bender and Ginis (2000), Shay et al. (2000), Lin et al. (2009), andPasquero et al. (2021).Simulations have indicated that TC-induced decrease in SST has a prime role in the variation of TC intensity.This study aims to understand the significance of TC helicity feedback to cyclone-induced heat and moisture flux.

Data and Methods
The 3-hourly India Meteorological Department (IMD) tropical cyclone best track data for maximum surface wind and minimum sea level pressure has been used in this study.Reanalysis data sets have been developed using the Advanced Research Weather Research and Forecasting (ARW) model coupled with a 1D simple ocean model and 3-Dimensional Ensemble Variational (3DEnVAR) techniques for assimilation of Global Data Assimilation System (GDAS) satellite radiance data and scatterometer derived ocean surface wind data assimilation.The Global Forecast System (GFS) analysis data was used to initialize the model to generate high resolution (2 km × 2 km) reanalysis.The model has been configured in two way nesting domain consisting of three domains with horizontal resolutions of 18 km (first domain), 6 km (second domain), and 2 km (third domain).Vertically, the model is configured with 64 levels with the model top 10 hPa.We adopted the Dudhia scheme to represent short-wave radiation physics parameterization and the Rapid Radiative Transfer Model (RRTM scheme) to represent long-wave radiation physics.The physical schemes used in the model are the Thompson scheme for cloud microphysics, the Kain-Frisch scheme for cumulus physics parameterizations, Unified Noah LSM, the Thompson scheme to represent land surface physics, Mellor Yamada Janjic-Turbulence Kinetic Energy (MYJ-TKE) scheme for planetary boundary layer physics.A comprehensive description of the model configuration used in this study has been detailed by Munsi et al. (2021).The developed reanalysis has been used in this study to analyze the dynamics.
Total helicity density in three dimensions at a given space point (H) used for this study has been calculated using the formula: Where   = î  + ĵ  + k  = wind vector having (u,v,w) as (zonal, meridional, vertical) components and 𝐴𝐴 ( î𝐢, ĵ𝐣 , k𝐤 ) as unit vectors in the respective direction.

Helical Development of the TC Vortex
Growth of helicity during the development of TC adequately reflects the tendency of wind speed and pressure changes.It thus can be used as an indicative feature for the TC intensity variation (Glebova et al., 2009).
Enhancement in wind speed and vertical shear leads to a sharp increase in helicity.In the development and maintenance of large-scale vortexes, small-scale helical convective systems are considered as a possible energy source.Forming a single large-scale helical vortex in place of numerous small-scale convective cells is energetically advantageous for heterogeneous heated helical turbulence (Levina, 2006).Moiseev et al. (1983) proposed that the intensification and sustainability of large-scale vortex disturbances are due to the transfer of energy from small-scale convective helical turbulence, termed turbulent vortex dynamo.Non-zero mean helicity is a criterion of mirror symmetry breaking of atmospheric turbulence, which may generate large-scale instability (Frisch & Kolmogorov, 1995).Sukhanovskii et al. (2017) showed that negative azimuthal helicity is generated in a large radial velocity gradient area when convergent flow replaces the divergent one.Its interaction with the anticyclonic motion provides negative azimuthal helicity.On the other hand, positive helicity is the outcome of the cyclonic vortex and convective plumes.The velocity fields are disrupted by convective plumes, which lead to a large vertical velocity gradient in the radial direction.In the study by Munsi et al. (2023), the helical evolution of three TCs, Fani, Luban, and Ockhi, originating over the north Indian Ocean, has been analyzed.The pathway of generation of the knotted vortex through the mutual intensification of primary and overturning secondary circulation, which makes the vortex self-sustaining, has been explored in that study.
This section analyzes the evolution in the convective vortex when the whole circular eyewall region at the lower troposphere showed non-zero helicity density, and the time is defined as T2 (Figure 1).Before 12 hr of T2 (said T1), a few weak patches of helicity were observed that were poorly organized (Figure 1).The formation of a helical vortex has been shown in Figure 1 for the said three TCs.The time in hours has been counted starting from the 0th hr at the India Meteorological Department (IMD)-declared depression stage.Until the 24 to 27th hr (hereafter time T1), no helical formation in the lower level vortex has been observed for TC Fani and Luban.
After 12 hr, at the 36-39th hr (hereafter time T2), a formation of the helical vortex has been observed at the lower troposphere.For TC Ockhi, the emergence of this vortex has been seen at the 9th hr.During the formation of the helical vortex, the southeast sector of the eyewall region showed a negative H value associated with radial velocity gradient when convergent flow at the lower troposphere starts relacing divergent one (Sukhanovskii et al., 2017) for TC Fani and Ockhi.Though, with the intensification of TCs, the H in the whole eyewall region becomes highly positive due to the dominance of convective plumes with cyclonic vorticity.
The evolution of the convective vortex during this helical vortex emergence time at the lower troposphere has been analyzed in Figure 2 (TC Fani), Figure 3 (TC Luban), and Figure 4 (TC Ockhi).These figures show the variation of vertical velocity (first column), diabatic heating rate (second column), and absolute vertical vorticity, which is the sum of relative vertical vorticity and Coriolis parameter (third column) at times T1 and T2 in a 4° × 4° area around the TC center.At time T1, a discrete thin lower vertical velocity band away from the center of the TC has been observed, and the band becomes more discontinuous with the increase of altitude.A lower diabatic heating rate at the lower troposphere and discrete patches of positive vorticity, mainly at the eastern sector Figure 5 shows the spatial distribution of Column-Integrated Moist Static Energy (CIMSE) overlaid on 850 hPa streamlines in a 4° × 4° area around the TC center at time T1 (first column) and T2 (second column).MSE has been calculated from the formula MSE = C p T + L c q + gz.Here, C p is the heat capacity of dry air at constant pressure, has been taken as a constant 1,004 J K −1 kg −1 , q is the specific humidity, T is the temperature and L c is the latent heat of condensation (2.5 × 10 6 J kg −1 ).It is observed that initially (T1), the CIMSE is not well organized around the center of the TC, and streamlines show the circulation pattern.After 12 hr (T2), the maximum CIMSE converges at the TC center, and the streamline showed comma shaped coiling structure around the eye, possibly due to the establishment of secondary circulation.For confirmation, we have plotted the radius-height cross-section of relative angular momentum superimposed with the equivalent potential temperature during helical vortex formation (Figure 6).The figure indicates the dominance of rotation and the increase in angular momentum throughout the column, especially in the middle and upper troposphere (Figure 6).The relative angular momentum becomes stronger and moves radially inward toward the core of TC at the time T2.Downward displacement of the isentropic surface shows the downward advection of heat (diabatic heating) in the TC column and strengthens the circulation.

TC Helicity Feedback to Heat and Moisture Flux
A helical structure, a unique feature of convective vortices, is formed by developing primary tangential and vertical secondary circulation, providing moisture and heat supply from the ocean surface.The merging of helical convective cells increases the horizontal scale of vortices, which is associated with a sharp increase in kinetic energy and a significant increase in heat transfer (Levina & Burylov, 2006).Their study pointed out that heat flux enhancement through a layer has been observed with an increase in the mean helicity value of a flow.Furthermore, a sharp increment in the heat transfer was observed above a threshold value of stability and later, in unstable conditions, after the merging of vortex structures.In the previous studies (Glebova et al., 2009;Levina & Montgomery, 2010a, 2010b;Onderlinde & Nolan, 2014), it has been shown that helicity is an indicatory characteristic to address the evolution of TC.The helicity index is a proxy for estimating the destructive impact and intensity of TC turbulence (Kurgansky, 2008).At the genesis and development stages of TCs, positive feedback works between the TC-ocean system.With the strengthening of TC, the moisture flux grows because of increasing surface wind speed.It enhances the ocean's moisture supply, increasing the latent heat energy, which drives the TC circulation.However, when the TC grows to a higher intensity, the increased wind stress produces strong turbulent mixing.As a result, it causes a decrease in SST.The cooling of the sea surface reduces heat flux to the atmosphere; consequently, the storm intensity decreases.During this period, a negative feedback mechanism exists between the ocean and the atmosphere (Bender et al., 1993).
Figure 7a shows the time series of 2° × 2° area-averaged heat and moisture flux along with the evolution of minimum sea level pressure and maximum surface wind speed as the proxy of TC intensity.The increasing enthalpy flux (both sensible heat flux and moisture flux) with increasing intensity of TC Fani showed extreme heat flux up to 100 Wm −2 and moisture flux 3.0 × 10 −4 kg m −2 s −1 .Then, a further increase in intensity above 48 ms −1 of maximum surface wind and pressure drop below 955 hPa showed a decreasing trend of heat and moisture flux 45 hr before the TC attained its maximum intensity (MI).However, a secondary maximum in the intensification stage was observed just before MI.The enthalpy flux decreased 36 hr before TC Luban reached its MI state with maximum heat flux up to 40 Wm −2 and moisture flux 1.5 × 10 −4 kg m −2 s −1 .The intensity of Luban during the flux reversal trend was 22 ms −1 in maximum surface wind and 995 hPa in minimum sea level pressure.For TC Ockhi, heat, and moisture flux values were increased with wind speed up to the 60th hr when it had a maximum heat flux value of 60 Wm −2 and moisture flux value of 2.0 × 10 −4 kg m −2 s −1 .After that, the enthalpy flux started decreasing when the TC intensity exceeded the maximum surface wind of 35 ms −1 , and the minimum sea level pressure dropped to 980 hPa about 12 hr before it attained its MI.While analyzing the time series of heat and momentum flux with the evolution of area-averaged H at the lower troposphere (integrated from surface to 900 hPa) at the 2° × 2° area around the TC center (Figure 7b), it is observed that, at the initial stage, the heat and moisture flux increased with the increasing helicity density.
For TC Fani and Luban, decreasing trends in heat and moisture flux were exhibited after H values increased more than 200 × 10 −2 ms −2 , irrespective of TC maximum surface wind speed or minimum sea level pressure.It may be due to the representation of the screw-like motion of helicity, which better characterizes the churn-up of upper ocean layers.In the case of Ockhi, we observe that between 50 and 65 hr, the H values were around 190 × 10 −2 ms −2 when the enthalpy flux showed immense fluctuation, unlike the other two TCs.After that, enthalpy sharply decreased at around 70-72 hr.Further investigations are required by considering different intensity TC cases and also in the other TC basins to clarify the importance of helicity evolution in reversing the heat and moisture flux trend.

Entropy
Entropy, an environmental factor, plays a vital role in studying the dynamics (Frank & Ritchie, 2001).It grows by the dissipation of turbulent kinetic energy and the exchange of enthalpy (Bister & Emanuel, 1998).The advantage of the analysis of entropy as a proxy of TC intensity has been discussed by Tapiador (2008).The rapid increase in the entropy radially inward toward the TC center can be attributed to the highest value of specific entropy (Emanuel, 2003).Entropy also contributes to the distribution of convective available potential energy (CAPE), which affects the spiral rain band activity, diabatic heating rate, boundary inflow, and the inner core size of the TC (Xu & Wang, 2010).The warming of the TC vortex is strongly governed by moist entropy distribution (Rotunno & Emanuel, 1987).
In this section, we have studied the vertical distribution of the specific moist entropy calculated as in Carrillo and Raymond (2005), Raymond (2013), and Juračić and Raymond (2016): γ is the mixing ratio of water vapor.C v and C d are the specific heat of water vapor and dry air at constant pressure, taken as 1,850 and 1,005 J K −1 kg −1 , respectively.T r , 273.15 K, is the freezing point water.R v (461.5 J K −1 kg −1 ) and R d (287.05J K −1 kg −1 ) are the gas constants of water vapor and dry air, respectively.T represents the air temperature in Kelvin, P d and P v are the dry air pressure and water vapor pressure in hPa.The reference pressure P r is taken as 1,000 hPa, and the triple point pressure of water P tp is taken as 6.1078 hPa.L c (2.5 × 10 6 J kg −1 ) is the latent heat of condensation.
As ocean surface temperature underneath the TC decreases the vertical mixing of ocean water, the moisture-holding capacity of relatively cold air above the sea surface also decreases.Therefore, even though there is a decrease in moisture flux, the low-level relative humidity may be close to 100% (Figure 8).A very dry layer in the middle troposphere at the dissipation stage of TC Ockhi has been observed, which is associated with the dry air intrusion in the TC inner core disrupting the convection, leading to rapid weakening (Lingala et al., 2022).The surface flux is a contributing factor to entropy distribution (Bister & Emanuel, 1998) and TC core temperature field (Rotunno & Emanuel, 1987).The moist entropy started advecting downward at this time (Figure 8), at around the 105th hr of TC Fani, 54th hr of Luban, and 60th hr of TC Ockhi.Advection of low-entropy air in the TC core decreases the heat engine efficiency (Tang & Emanuel, 2010), disrupting the convection.Also, changes in the entropy have an important role in the distribution of convective available potential energy, diabatic heating, boundary layer inflow (Xu & Wang, 2010) and hence effecting the TC overturning circulation.Therefore, the downward advection of entropy affects the toroidal (secondary) circulation and hence the helical structure of the TC.Further detailed study is required with a focus on entropy distribution and the corresponding helicity variation.

Conclusions
The life cycle of TC depends on moisture and heat flux through air-sea interaction at the upper ocean layer.Helicity is an indicative characteristic of TC evolution.In this study, we have analyzed the feedback of TC and the upper ocean by figuring out the TC intensity evolution with the variation of lower tropospheric helicity density, moisture, and heat flux at the air-sea interface.At the formation stage of the vortex, the southeast sector of the eyewall region showed a negative H for TC Fani and Ockhi.However, at the developed stage, the helicity density in the whole eyewall region becomes highly positive due to the dominance of convective plumes with cyclonic vorticity.At the time of helical formation, maximum CIMSE tends to converge at the TC center, and the streamline started showing comma comma-shaped coiling structure in place of the circulation pattern.

Figure 1 .
Figure 1.Distribution of helicity density in a 4° × 4° area around the TC center during the formation of the helical vortex and at the maximum intensified stage.

Figure 2 .
Figure 2. Distribution of vertical velocity (first column), diabatic heating (second column), and absolute vertical vorticity (third column) in a 2° × 2° area around the TC center at time T1 (first row) and T2 (second row) of TC Fani.

Figure 3 .
Figure 3. Distribution of vertical velocity (first column), diabatic heating (second column), and absolute vertical vorticity (third column) in a 2° × 2° area around the TC center at time T1 (first row) and T2 (second row) of TC Luban.

Figure 4 .
Figure 4. Distribution of vertical velocity (first column), diabatic heating (second column), and absolute vertical vorticity (third column) in a 2° × 2° area around the TC center at time T1 (first row) and T2 (second row) of TC Ockhi.

Figure 6 .
Figure 6.Azimuthally averaged relative angular momentum (shaded) of three TCs at time T1 and T2, superposed with equivalent potential temperature (K).

Figure 7 .
Figure 7. (a) Time series of maximum surface wind, minimum sea level pressure from IMD best track data, area-averaged heat, and moisture flux at the 2° × 2° area around the TC center.(b) Time series of area-averaged H at the lower troposphere (surface to 900 hPa), surface heat, and moisture flux at the 2° × 2° area around the TC center.