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Existing hypotheses for the dynamical dependence of tropical cyclone genesis and size on latitude depend principally on the Coriolis parameter f. These hypotheses are tested via dynamical aquaplanet experiments with uniform thermal forcing in which planetary rotation rate and planetary radius are varied relative to Earth values; the control simulation is also compared to a present-day Earth simulation. Storm genesis rate collapses to a quasi-universal dependence on f that attains its maximum at the critical latitude, where the inverse-f scale and Rhines scale are equal. Minimum genesis distance from the equator is set by the equatorial Rhines (or deformation) scale and not by a minimum value of f. Outer storm size qualitatively follows the smaller of the two length scales, including a slow increase with latitude equatorward of 45° in the control simulation, similar to the Earth simulation. The latitude of peak size scales with the critical latitude for varying planetary radius but not rotation rate, possibly because of the dependence of genesis specifically on f. The latitudes of peak size and peak packing density scale closely together. Results suggest that temporal effects and interstorm interaction may be significant for size dynamics. More generally, the critical latitude separates two regimes: 1) a mixed wave–cyclone equatorial belt, where wave effects are strong and the Rhines scale likely limits storm size, and 2) a cyclone-filled polar cap, where wave effects are weak and cyclones persist. The large-planet limit predicts a world nearly covered with long-lived storms, equivalent to the f plane. Overall, spherical geometry is likely important for understanding tropical cyclone genesis and size on Earthlike planets.

It is important to understand how tropical cyclones (TCs) decay over the ocean as this is a critical pre‐landfall stage. A modified exponential decay model (β$\\beta $model) with two parameters α$\\alpha $and β$\\beta $is proposed. The scale parameter α$\\alpha $defines the decay scale, while the shape parameter β$\\beta $determines whether the decay rate decelerates or accelerates over time. Global fittings indicate that around 40% of TCs exhibit decelerating decay (β≤1)$(\\beta \\le 1)$ , while the majority (about 60%) show accelerating decay (β>1)$(\\beta > 1)$ . Correlation analysis reveals a strong negative correlation between the scale parameter α$\\alpha $and the initial Coriolis parameter (r=−0.96)$(r=-0.96)$and a positive correlation between the shape parameter β$\\beta $and the meridional component of the initial translation velocity (r=0.75)$(r=0.75)$ . The β$\\beta $model provides a comprehensive understanding of how TCs decay with time and how environmental conditions affect the decay scale and evolution. Plain Language Summary Tropical cyclones (TCs), also known as hurricanes or typhoons, are powerful storms that cause significant damage when they hit land. However, these storms do not remain equally strong throughout their lifespan. Our research investigates how TCs decay over time over the ocean. To help understanding, a modified exponential model (β$\\beta $model) with two parameters α$\\alpha $and β$\\beta $is used to describe the time evolution of TC intensity during the decay. The α$\\alpha $is a decay scale constant which describes how much TC decays over a certain decay period. The shape parameter β$\\beta $shows the change of decay rate at each time step during the decay. Two types of decay are identified: decelerating decay (β≤1)$(\\beta \\le 1)$ , where the decay rate slows down over time; and accelerating decay (β>1)$(\\beta > 1)$ , where the decay rate speeds up over time. The smaller decay scale α$\\alpha $is associated with a higher latitude at which TCs start to decay. TCs are more likely to show a decelerating decay (β≤1)$(\\beta \\le 1)$with a lower meridional translation velocity. The β$\\beta $model provides a comprehensive description of the temporal decay of TC intensity and an insightful understanding of potential factors controlling the decay behaviors. Key Points A two‐parameter modified exponential model is proposed to interpret the temporal decay of tropical cyclones (TCs) over ocean Two types of temporal decay are identified: 40% of global TCs exhibit decelerating decay, while 60% show accelerating decay The decay scale (α) is smaller with higher latitude, while the shape parameter (β) is smaller with lower meridional velocity

An idealized framework of steady barotropic flow past an isolated seamount in a background of constant stratification (with frequency N ) and rotation (with Coriolis parameter f ) is used to examine the formation, separation, instability of the turbulent bottom boundary layers (BBLs), and ultimately, the genesis of submesoscale coherent vortices (SCVs) in the ocean interior. The BBLs generate vertical vorticity ζ and potential vorticity q on slopes; the flow separates and spawns shear layers; barotropic and centrifugal shear instabilities form submesoscale vortical filaments and induce a high rate of local energy dissipation; the filaments organize into vortices that then horizontally merge and vertically align to form SCVs. These SCVs have O (1) Rossby numbers ( ) and horizontal and vertical scales that are much larger than those of the separated shear layers and associated vortical filaments. Although the upstream flow is barotropic, downstream baroclinicity manifests in the wake, depending on the value of the nondimensional height , which is the ratio of the seamount height to that of the Taylor height , where L is the seamount half-width. When , SCVs span the vertical extent of the seamount itself. However, for , there is greater range of variation in the sizes of the SCVs in the wake, reflecting the wake baroclinicity caused by the topographic interaction. The aspect ratio of the wake SCVs has the scaling , instead of the quasigeostrophic scaling .

This work revisits the statistics of observed tropical cyclone outer size in the context of recent advances in our theoretical understanding of the storm wind field. The authors create a new dataset of the radius of 12 m s−1 winds based on a recently updated version of the QuikSCAT ocean wind vector database and apply an improved analytical outer wind model to estimate the outer radius of vanishing wind. The dataset is then applied to analyze the statistical distributions of the two size metrics as well as their dependence on environmental parameters, with a specific focus on testing recently identified parameters possessing credible theoretical relationships with tropical cyclone size. The ratio of the potential intensity to the Coriolis parameter is found to perform poorly in explaining variation of size, with the possible exception of its upper bound, the latter of which is in line with existing theory. The rotating radiative–convective equilibrium scaling of Khairoutdinov and Emanuel is also found to perform poorly. Meanwhile, mean storm size is found to increase systematically with the relative sea surface temperature, in quantitative agreement with the results of a recent study of storm size based on precipitation area. Implications of these results are discussed in the context of existing tropical climate theory. Finally, an empirical dependence of the central pressure deficit on outer size is found in line with past work.

A theory is presented for the Great Plains low-level jet in which the jet emerges in the sloping atmospheric boundary layer as the nocturnal phase of an oscillation arising from diurnal variations in turbulent diffusivity (Blackadar mechanism) and surface buoyancy (Holton mechanism). The governing equations are the equations of motion, mass conservation, and thermal energy for a stably stratified fluid in the Boussinesq approximation. Attention is restricted to remote (far above slope) geostrophic winds that blow along the terrain isoheights (southerly for the Great Plains). Diurnally periodic solutions are obtained analytically with diffusivities that vary as piecewise constant functions of time and slope buoyancies that vary as piecewise linear functions of time. The solution is controlled by 11 parameters: slope angle, Coriolis parameter, free-atmosphere Brunt–Väisälä frequency, free-atmosphere geostrophic wind, radiative damping parameter, day and night diffusivities, maximum and minimum surface buoyancies, and times of maximum surface buoyancy and sunset. The Holton mechanism, by itself, results in relatively weak wind maxima but produces strong jets when paired with the Blackadar mechanism. Jets with both Blackadar and Holton mechanisms operating are shown to be broadly consistent with observations and climatological analyses. Jets strengthen with increasing geostrophic wind, maximum surface buoyancy, and day-to-night ratio of the diffusivities and weaken with increasing Brunt–Väisälä frequency and magnitude of minimum slope buoyancy (greater nighttime cooling). Peak winds are maximized for slope angles characteristic of the Great Plains.

An intraseasonal genesis potential index (ISGPI) for Northern Hemisphere (NH) summer is proposed to quantify the anomalous tropical cyclone genesis (TCG) frequency induced by boreal summer intraseasonal oscillation (BSISO). The most important factor controlling NH summer TCG is found as 500-hPa vertical motion (ω 500) caused by the prominent northward shift of large-scale circulation anomalies during BSISO evolution. The ω 500 with two secondary factors (850-hPa relative vorticity weighted by the Coriolis parameter and vertical shear of zonal winds) played an effective role globally and for each individual basin in the northern oceans. The relative contributions of these factors to TCG have minor differences by basins except for the western North Atlantic (NAT), where low-level vorticity becomes the most significant contributor. In the eastern NAT, the BSISO has little control of TCG because weak convective BSISO and dominant 10–30-day circulation signal did not match the overall BSISO life cycle. The ISGPI is shown to reproduce realistic intraseasonal variability of TCG, but the performance is phase-dependent. The ISGPI shows the highest fidelity when BSISO convective anomalies have the largest amplitude in the western North Pacific and the lowest when they are located over the north Indian Ocean and eastern North Pacific. Along the NH major TCG zone, the TCG probability changes from a dry to a wet phase by a large factor ranging from 3 to 12 depending on the basins. The new ISGPI for NH summer can simulate more realistic impact of BSISO on TC genesis compared to canonical GPI derived by climatology.

In this study, we examine the role of curvature in modifying frontal stability. We first evaluate the classical criterion that the Coriolis parameter f multiplied by the Ertel potential vorticity (PV) q is positive for stable flow and that instability is possible when this quantity is negative. The first portion of this statement can be deduced from Ertel’s PV theorem, assuming an initially positive fq . Moreover, the full statement is implicit in the governing equation for the mean geostrophic flow, as the discriminant, fq , changes sign. However, for curved fronts in cyclogeostrophic or gradient wind balance (GWB), an additional term enters the discriminant owing to conservation of absolute angular momentum L . The resulting expression, (1 + Cu) fq < 0 or Lq < 0, where Cu is a nondimensional number quantifying the curvature of the flow, simultaneously generalizes Rayleigh’s criterion by accounting for baroclinicity and Hoskins’s criterion by accounting for centrifugal effects. In particular, changes in the front’s vertical shear and stratification owing to curvature tilt the absolute vorticity vector away from its thermal wind state; in an effort to conserve the product of absolute angular momentum and Ertel PV, this modifies gradient Rossby and Richardson numbers permitted for stable flow. This forms the basis of a nondimensional expression that is valid for inviscid, curved fronts on the f plane, which can be used to classify frontal instabilities. In conclusion, the classical criterion fq < 0 should be replaced by the more general criterion for studies involving gravitational, centrifugal, and symmetric instabilities at curved density fronts. In Part II of the study, we examine interesting outcomes of the criterion applied to low-Richardson-number fronts and vortices in GWB.

Accurate prediction of the global properties of wall-bounded turbulence holds significant importance for both fundamental research and engineering applications. In atmospheric boundary layers, the relationship between friction drag and geostrophic wind is described by the geostrophic drag law (GDL). We use carefully designed large-eddy simulations to study nocturnal stable atmospheric boundary layers (NSBLs), which are characterized by a negative potential temperature flux at the surface and neutral stratification higher up. Our simulations explore a wider range of the Kazanski–Monin parameter, $\\mu = L_f / L_s = [16.7, 193.3]$, with $L_f$ the Ekman length scale and $L_s$ the surface Obukhov length. We show collapse of the GDL coefficients onto single curves as functions of $\\mu$, thereby validating the GDL's applicability to NSBLs over a very wide $\\mu$ range. We show that the boundary-layer height $h$ scales with $\\sqrt {L_f L_s}$, while both the streamwise and spanwise wind gradients scale with $u_*^2 / (h^2 f)$, where $u_*$ represents the friction velocity and $f$ the Coriolis parameter. Leveraging these insights, we developed new analytical expressions for the GDL coefficients, significantly enhancing our understanding of the GDL for turbulent boundary layers. These formulations facilitate the analytical prediction of the geostrophic drag coefficient and cross-isobaric angle.

Ocean microstructure, current, and hydrography observations from June 2016 are used to characterize the turbulence structure of the Lofoten Basin eddy (LBE), a long-lived anticyclone in the Norwegian Sea. The LBE had an azimuthal peak velocity of 0.8 m s −1 at 950-m depth and 22-km radial distance from its center and a core relative vorticity reaching −0.7 f ( f is the local Coriolis parameter). When contrasted to a reference station in a relatively quiescent part of the basin, the LBE was significantly turbulent between 750 and 2000 m, exceeding the dissipation rates ε in the reference station by up to two orders of magnitude. Dissipation rates were elevated particularly in the core and at the rim below the swirl velocity maximum, reaching 10 −8 W kg −1 . The sources of energy for the observed turbulence are the background shear (gradient Richardson number less than unity) and the subinertial energy trapped by the negative vorticity of the eddy. Idealized ray-tracing calculations show that the vertical and lateral changes in stratification, shear, and vorticity allow subinertial waves to be trapped within the LBE. Spectral analysis shows increased high-wavenumber clockwise-polarized shear variance in the core and rim regions, consistent with downward-propagating near-inertial waves (vertical wavelengths of order 100 m and energy levels 3 to 10 times the canonical open-ocean level). The energetic packets with a distinct downward energy propagation are typically accompanied with an increase in dissipation levels. Based on these summer observations, the time scale to drain the volume-integrated total energy of the LBE is 14 years.