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Abstract In the inner core of a tropical cyclone, turbulence not only exists in the boundary layer (BL) but can also be generated above the BL by eyewall and rainband clouds. Thus, the treatment of vertical turbulent mixing must go beyond the conventional scope of the BL. The turbulence schemes formulated based on the turbulent kinetic energy (TKE) are attractive as they are applicable to both deep and shallow convection regimes in the tropical cyclone (TC) inner core provided that the TKE production and dissipation can be appropriately determined. However, TKE schemes are not self-closed. They must be closed by an empirically prescribed vertical profile of mixing length. This motivates this study to investigate the sensitivity of the simulated TC intensification to the sloping curvature and asymptotic length scale of mixing length, the two parameters that determine the vertical distribution of a prescribed mixing length. To tackle the problem, both idealized and real-case TC simulations are performed. The results show that the simulated TC intensification is sensitive to the sloping curvature of mixing length but only exhibits marginal sensitivity to the asymptotic length scale. The underlying reasons for such sensitivities are explored analytically based on the Mellor and Yamada level-2 turbulence model and the analyses of azimuthal-mean tangential wind budget. The results highlight the uncertainty and importance of mixing length in the numerical prediction of TCs and suggest that future research should focus on searching for physical constraints on mixing length, particularly in the low- to midtroposphere, using observations and large-eddy simulations. Significance StatementThe parametric representation of subgrid-scale turbulent mixing is one of the major sources of uncertainty in numerical predictions of tropical cyclones (TCs). This study investigates how the numerical prediction of TC intensification is affected by the turbulent mixing length, a length scale that is required to close a turbulence scheme formulated based on the turbulent kinetic energy (TKE). The research highlights the uncertainty and importance of mixing length in numerical prediction of TCs and suggests that future research should focus on searching for physical constraints on the mixing length, particularly in the low- to midtroposphere, using observations and large-eddy simulations. 

Abstract An analytical method for diagnosing the interaction between the primary and secondary circulations of a tropical cyclone (TC) and vortex intensification is developed. It includes a diagnostic equation describing the mean secondary circulation of a TC in an unbalanced framework by including the radial eddy forcing in the analytical system. It is an extension of the Sawyer–Eliassen equation (SEE) developed from the strict gradient-wind balance. This generalized SEE (GSEE) remediates some of the limitations of SEE and can be used to diagnose both balanced and unbalanced dynamical processes during the TC evolution. Using GSEE, this study investigates how the tangential and radial eddy forcing affects the TC intensification simulated by the Hurricane Weather Research and Forecasting Model (HWRF) with differently parameterized turbulent mixing. The diagnostic results show that the supergradient component of radial eddy forcing contributes positively to the acceleration of the peak tangential wind, whereas the subgradient component of the radial eddy forcing tends to lower the height of peak tangential wind. The relative importance of negative and positive effects of tangential eddy forcing on TC intensification varies depending on the details of turbulence parameterization. For a turbulent kinetic energy (TKE) scheme used in this study, a large sloping curvature of mixing length in the low troposphere causes the tangential eddy forcing to produce a net positive tangential wind tendency near the location of the peak tangential wind. In contrast, a small sloping curvature of mixing length generates a net negative tangential wind tendency at the peak tangential wind. Significance StatementThe interaction between the primary and secondary circulations of a tropical cyclone (TC) plays a key role in TC evolution. Historically, the secondary circulation induced by turbulence and convection is often described by a so-called Sawyer–Eliassen equation (SEE). While SEE has provided much insight into the TC dynamics in the past, the assumption of gradient-wind balance used by SEE prevents it from understanding TC unbalanced dynamics. To remediate the limitation, we extended the analytical framework into the unbalanced regime by including radial eddy forcing in the analytical system and derived a generalized SEE (GSEE). Using GSEE, this study investigates how tangential and radial eddy forcing affects TC intensification. The result highlights the importance of multiple roles that turbulence plays in the intensification of TCs. 

Numerical experiments using the WRF model were conducted to analyze the sensitivity of Typhoon Mangkhut intensification simulations to seven widely used planetary boundary layer (PBL) parameterization schemes, including YSU, MYJ, QNSE, MYNN2, MYNN3, ACM2, and BouLac. The results showed that all simulations generally reproduced the tropical cyclone (TC) track and intensity, with YSU, QNSE, and BouLac schemes better capturing intensification processes and closely matching observed TC intensity. In terms of surface layer parameterization, the QNSE scheme produced the highest Ck/Cd ratio, resulting in stronger TC intensity based on Emanuel’s potential intensity theory. In terms of PBL parameterization, the YSU and BouLac schemes, with the same revised MM5 surface layer scheme, simulated weaker turbulent diffusivity Km and shallower mixing height, leading to stronger TC intensity. During the intensification period, the BouLac, YSU, and QNSE PBL schemes exhibited stronger tangential wind, radial inflow within the boundary layer, and updraft around the eye wall, consistent with TC intensity results. Both PBL and surface layer parameterization significantly influenced simulated TC intensity. The QNSE scheme, with the largest Ck/Cd ratio, and the YSU and BouLac schemes, with weaker turbulent diffusivity, generated stronger radial inflow, updraft, and warm core structures, contributing to higher storm intensity. 

The question of at what resolution the large eddy simulations (LESs) of a tropical cyclone (TC) high wind area may converge largely remains unanswered. To address this issue, LESs with five resolutions of 300 m, 100 m, 60 m, 33 m, and 20 m are performed in this study to simulate a high wind area near the radius of maximum wind of Typhoon Chanthu (2021) using the Weather Research and Forecasting (WRF) model. The results show that, for a limited area LES, model grid resolution may alter the local turbulence structure to generate significantly different extreme values of temperature, moisture, and winds, but it only has a marginal impact on the median values of these variables throughout the vertical column. All simulations are able to capture the turbulent roll vortices in the TC boundary layer, but the structure and intensity of the rolls vary substantially in different resolution simulations. Local hectometer-scale eddies with vertical velocities exceeding 10 m s−1 are only observed in the 20 m resolution simulation but not in the coarser resolution simulations. The ratio of the resolved turbulent momentum fluxes and turbulent kinetic energies (TKEs) to the total momentum fluxes and TKEs appears to show some convergence of LESs when the grid resolution reaches 100 m or finer, suggesting that it is an acceptable grid resolution for LES applications in TC simulations. 

Key Points Lateral entrainment of air from the moat region into eyewall and rainbands of a tropical cyclone (TC) satisfies the instability criterion Positive buoyancy flux induced by the entrainment is an important source of turbulent kinetic energy for the eyewall and rainband clouds Lateral entrainment instability should be included in turbulent mixing parameterizations in TC forecast models 

Key Points A method to concoct non‐stationary data series is proposed Eddy covariance and wavelet analysis methods underestimate turbulent momentum flux under non‐stationary condition by about 50% Mexican hat wavelet method has the potential to accurately calculate flux of non‐stationary turbulence after correction