Refinement of the Ground Forest Fire Model Taking into Account Convective Turbulence
Authors: Andreeva E. S. , Sergeeva G. A. , Bogdanova I. V. 
Published: February 2025

Introduction. The scientific literature is actively discussing the topic of mathematical modeling of forest fires development to predict the speed of spread and area covered. From the perspective of turbulent processes, the height and deflection of fire, smoke, and hot air columns, as well as the spread of combustion particles and rational directions for extinguishing the fire, are evaluated. However, existing models do not provide a clear understanding of how turbulence occurs during the transition of a fire from a near-surface to an unsteady surface layer and higher. In other words, calculating the transition from ground fire to its more intense form remains a challenge. Addressing this gap is an urgent scientific and practical task. The aim of this study is to refine the equations of mathematical models for predicting the spread of forest fires, in order to better control these incidents, which will ultimately help reduce risks and damage from them.

Materials and Methods. To achieve this goal, we studied works covering different approaches, both theoretical and practical, devoted to the problem of predicting the development of fires. The works of D.L. Laikhtman, A.S. Gavrilov, and P.M. Matveev were accepted as the main ones. In addition to analyzing these literary sources, the authors applied statistical methods of information processing and used the possibilities of mathematical modeling.

Results. The generally accepted elliptical shape of the contour of a ground forest fire in the R. Rothermel model has been interpreted. Its disadvantages for predicting spot and intense crown fires have been demonstrated. The introduction of parameters such as relative humidity, terrain slope, surface roughness or viscosity, and features of the burning substance into the equation has been evaluated. The types of convection typical of spot and intense crown fires have been indicated: internal (thermal) and external (mechanical). The decision not to consider near-surface turbulence has been justified. To account for surface air layer turbulence, the authors have relied on the concepts of instability and corresponding physical laws. As a result, the basic formula of the R. Rothermel model was supplemented with a second layer so that it was possible to predict the development of a fire from a ground one to an intense crown fire. The dimensionless parameter of 0.397 was replaced by turbulence coefficient kz. This indicator was introduced into the corrected R. Rothermel equation and supplemented with the average Richardson number, which showed the relationship between temperature and the diffusion rate in neighboring layers. From these components, an updated formula has been developed. The results of simulations for typical cases of convective turbulence and fires, with and without turbulence, were presented in tables. Based on the summary data, we could conclude that the model developed within the scope of this work was adequate.

Discussion and Conclusion. When refining the semi-empirical R. Rothermel model for an unsteady surface layer, the introduction of a turbulence coefficient is justified. In addition, it is shown that it is necessary to supplement the single-layer model with second-level formulas characterizing the development of a fire in an unsteady surface layer. The adjusted model should more effectively predict the parameters of spot and intense crown fires. Further refinements of equations for semi-empirical forest fire models are promising, and it is advisable to continue research in this area.