Tropical Cyclone Response to Time-Dependent Heating and Theory of Tropical Cyclone Motion

热带气旋（TC）的路径和强度的预测仍然是重大的业务挑战。 在过去的50年里，路径预报逐渐得到改善，这主要是因为对控制TC运动的环境转向流的观测和建模得到了改善。 相比之下，强度方面的进展缓慢，统计技术仍然提供最好的预测指导。 热带气旋加强的基本过程是将海洋中的潜热转化为风的有效位能和动能。 该奖项的研究内容包括两个方面：1）TC涡旋对外加热源的响应分析; 2）两层斜压类TC涡旋线性和非线性运动的理论研究。 这些研究所使用的轴对称斜压平均涡结构分析，将是从大量现场观测数据中获得的实际TC的真实代表。首席研究员将通过研究对强加热源的响应来探索TC增强过程，这些热源被表示为时间和方位的截断傅立叶级数。 只有热源的轴对称的、时间恒定的分量提供净加热。 它的影响很容易从经典的Sawyer-Eliassen方程计算。 下一级复杂性使用随时间正弦变化的轴对称热源。 在流体静力平衡和梯度平衡条件下，从平均涡线性化的Navier-Stokes方程导出了一个控制方程。 扰动流可以是非流体静力学的和亚梯度或超梯度的。 如果热源变化的频率足够低，则该模式计算应类似于定常强迫的结果。 在更高的频率下，由于时间变化或投影到重力波模式而导致的有效局部变形半径的变化等影响可能成为因素。 下一级的复杂性考虑了一个类似的推导方程的非对称加热与给定的方位角波数和频率。 要研究的现象包括作为强迫频率的函数的涡旋响应的变化、浮力和动压的作用、非绝热引起的超梯度风和次梯度风、由于扰动引起的热或动量的涡旋通量所导致的平均涡旋的演变以及为模拟真实的飓风而构造的平均流涡旋的流体动力学稳定性。涡动研究将使用两层半谱涡动跟踪模型来研究弹性和重新排列。 要解决的问题包括共振阻尼理论的重新审查，非线性和对称涡的演变的作用的评估，环境位涡和行星涡度梯度的研究，以及现实的初始平均涡结构的影响。这项研究的更广泛的影响包括：基本的新的物理理解至关重要的准确跟踪，特别是强度预报和支持佛罗里达国际大学（FIU）的新生气象学计划。

Forecasts of tropical cyclone (TC) track and intensity remain significant operational challenges. Track forecasts have improved gradually over the last five decades, largely in response to improved observation and modeling of the environmental steering currents that control TC motion. By contrast, progress on intensity has been slow and statistical techniques still provide the best forecast guidance. The fundamental process in TC intensification is conversion of latent heat extracted from the sea into available potential energy and kinetic energy of the wind. The research to be undertaken under this award has two aspects 1) analysis of the TC vortex response to imposed heat sources and 2) theoretical studies of linear and nonlinear motion of a two-layer baroclinic TC-like vortex. The analytical axially symmetric, baroclinic mean-vortex structures used in these studies will be realistic representations of actual TCs derived from a large sample of in situ observations.The Principal Investigator will explore TC intensification processes by studying the responses to imposed heat sources with these sources being represented as truncated Fourier series in both time and azimuth. Only the axially symmetric, temporally constant component of the heat source supplies net heating. Its effect is readily computed from the classical Sawyer-Eliassen equation. The next level of complexity uses an axially symmetric heat source that varies sinusoidally in time. A single governing equation is derived from the Navier-Stokes equations linearized on a mean vortex in hydrostatic and gradient balance. The perturbation flow may be nonhydrostatic and sub- or super-gradient. If the frequency with which the heat source changes is low enough, this model calculation should resemble the results from steady forcing. At higher frequencies, effects such as changes in the effective local deformation radius due to time variation or projection onto gravity-wave modes can become factors. The next level of complexity considers a similarly derived equation for asymmetric heating with a given azimuthal wavenumber and frequency. Phenomena to be studied include changes in vortex response as a function of forcing frequency, the roles buoyancy and dynamic pressure, diabatically induced super- and sub-gradient winds, evolution of the mean vortex as a result of eddy fluxes of heat or momentum due to the perturbations, and hydrodynamic stability of mean-flow vortices constructed to model real hurricanes. The vortex-motion studies will use a two-layer semi spectral, vortex-tracking model to study the resiliency and realignment. Questions to be addressed include re-examination of resonant-damping theory, assessment of the roles of nonlinearity and evolution of the symmetric vortex, study of environmental potential vorticity and planetary vorticity gradients, and the effects of realistic initial mean-vortex structures. Broader impacts of this study include: fundamental new physical understanding essential to accurate track and especially intensity forecasts and support of Florida International University's (FIU) nascent meteorology program.