A Survey of Unbalanced Flow Diagnostics and Their Application

This paper presents an extensive survey of the most commonly used tools for diagnosing unbalanced flow in the atmosphere, namely the Lagrangian Rossby number, Psi vector, divergence equation, nonlinear balance equation, generalized omega-equation, and departure from fields obtained by potential vorticity (PV) inversion. The basic thoery, assumptions as well as implementation and limitations for each of the tools are all discussed. These tools are applied to high—resolution mesoscale model data to assess the role of unbalanced dynamics in the generation of a mesoscale gravity wave event over the East Coast of the United States. Comparison of these tools in this case study shows that these various methods agree to a large extent with each other though they differ in details. Key words Unbalanced flow - Geostrophic adjustment - Gravity waves - Nonlinear balance equation - Potential vorticity inversion - Omega equations - Rossby number This research was conducted under support from NSF grant ATM-9700626 of the United States. The numerical computations described herein were performed on the Cray T90 at the North Carolina Supercomputing Center and the Cray supercomputer at the NCAR Scientific Computing Division, which also provided the initialization fields for the MM5. Thanks are extended to Mark Stoelinga at University of Washington for the RIP post-processing package.

Application of Nonlinear Balance Scheme in Three-Dimensional Variational Data Assimilation

The dynamical constrains in three-dimensional variational data assimilation are discussed when considering the impact of stream divergence and convergence on the pressure and wind fields. For the analysis of severe tropical cyclone, frontal structures, and other rapidly changing structures, the geostrophic balance and linear balance cannot properly represent the relationship between wind and pressure fields. However, the nonlinear balance incremental equation takes into account the information of flow-dependent background, and makes response to the flow-dependent background covariance in the 3D-Var system. Results indicate that the application of the nonlinear balance equation to 3D-Var system improves the quality of severe tropical cyclone assimilation system, which has some positive effects on intensity prediction of tropical cyclones.

TRAVELING WAVE SOLUTIONS AND THEIR STABILITY OF NONLINEAR SCHRDINGER EQUATION WITH WEAK DISSIPATION

In this paper,several new constant-amplitude and variable-amplitude wave solutions（namely,traveling wave solutions） of a generalized nonlinear Schrdinger equation are investigated by using the extended homogeneous balance method,where the balance method is applied to solve the Riccati equation and the reduced nonlinear ordinary differential equation,respectively.In addition,stability analysis of those solutions are also conducted by regular phase plane technique.

Characteristics for the sources and sinks of gravity waves in an orographic heavy snowfall event

The characteristics of the mesoscale gravity waves during a snowfall event on November 30,2018 over the Ili Valley and the northern slope of the Tianshan Mountains are analyzed based on the Weather Research and Forecasting model simulation.The vertical distribution of Ro is similar to that of the residual of the nonlinear balance equation(△NBE),with their high-value areas located over the leeward slope and the fluctuations extending upwardly with time,indicating the characteristics of strong ageostrophy and non-equilibrium of atmospheric motions.In addition,the Ro and(△NBE)are first developed in the lower layers over the leeward slope,revealing that the generation of the gravity waves is closely related to the topography.Thus,the topographic uplifting greatly affects this snowfall,and the ageostrophic motion in the whole troposphere and the lower stratosphere,as well as the unbalanced motions between convergence and divergence over the peak and the leeward slope are conductive to the development of the inertia-gravity waves.In terms of the horizontal scale of the gravity waves,the Barnes’bandpass filter is applied to separate the mesoscale waves and the synoptic-scale basic flow.The vertical distributions of the vorticity and divergence perturbations have a phase difference ofπ/2,indicating the polarization state of gravity waves.The analyses on the sources and sinks of gravity waves by the non-hydrostatic wave equation show that the main forcing term for orographic gravity waves is the second-order nonlinear term,whose magnitude mainly depends on the nonlinear thermal forcing.This term is mainly related to the vertical transport of potential temperature perturbations.During the snowfall,the potential temperature perturbations are mainly caused by the topographic relief and the release of condensation latent heat.Therefore,the gravity waves in this snowfall are caused by the topographic forcing and condensation latent heating.