Physics Research International

Volume 2016 (2016), Article ID 3274147, 8 pages

http://dx.doi.org/10.1155/2016/3274147

## The Investigation of EM Scattering from the Time-Varying Overturning Wave Crest Model by the IEM

^{1}School of Physics and Optoelectronic Engineering, Xidian University, Xi’an 710071, China^{2}State Key Laboratory of Integrated Services Networks, Xidian University, Xi’an 710071, China

Received 30 December 2015; Revised 6 April 2016; Accepted 12 April 2016

Academic Editor: Jianhui Zhong

Copyright © 2016 Xiao Meng et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

Investigation of the electromagnetic (EM) scattering of time-varying overturning wave crests is a worthwhile endeavor. Overturning wave crest is one of the reasons of sea spike generation, which increases the probability of false radar alarms and reduces the performance of multitarget detection in the environment. A three-dimensional (3D) time-varying overturning wave crest model is presented in this paper; this 3D model is an improvement of the traditional two-dimensional (2D) time-varying overturning wave crest model. The integral equation method (IEM) was employed to investigate backward scattering radar cross sections (RCS) at various incident angles of the 3D overturning wave crest model. The super phenomenon, where the intensity of horizontal polarization scattering is greater than that of vertical polarization scattering, is an important feature of sea spikes. Simulation results demonstrate that super phenomena may occur in some time samples as variations in the overturning wave crest.

#### 1. Introduction

A considerable amount of research has recently focused on sea spikes, which are a matter of great importance. Sea spikes have been found to cause false target detections and are typically characterized by horizontal polarization (HH) signals that exceed vertical polarization (VV) signals by as much as 10 dB or more [1, 2]. Breaking waves are believed to be responsible for strong sea spikes [3] and occur in areas of the overturning wave crest where nonlinear sea surfaces are generated. Therefore, knowledge of the EM scattering characteristics of the overturning wave crest model is critical for analyzing sea spikes and represents a special area of interest in the detection of sea spike generation.

LONGTANK waves [4] have been widely used in studies of breaking waves [5]. Holliday [6] studied the backscattering of LONGTANK waves at incident angles of and found that strong sea spikes are generated at the incident wave frequency of 10 GHz. Yang et al. [3] employed MLFMA with higher-order hierarchical Legendre basis functions to conduct a preliminary study on the scattering of 3D breaking water wave crests at LGA and analyzed the VV and HH polarized scattering of profiles of LONGTANK breaking waves. Guan et al. [7] also introduced an algebraic fractal model-Paretian Poisson process to sea spike modeling and target detection. In this work, an improved 3D time-varying overturning wave crest model is described and investigated. This model is based on the 2D time-varying overturning wave crest model in [8], which, in turn, is based on the sea wave of the virtual reality scene in computer graphics; the influences of wind speed on the size and height of the overturning wave were considered in the model.

Numerical techniques have been widely used in recent research on sea surface scattering. However, these techniques involve long computational time and large memory requirements; thus, numerical techniques have become research bottlenecks, especially when considering high-frequency 3D scattering problems. Although several integral equation-based techniques [9, 10] are proposed to improve the efficiency of the classic numerical techniques, it is still difficult to deal with the high-frequency 3D scattering problems. High-frequency techniques, such as geometric optics (GO) and physical optics (PO) [11–13], are fast but they present relatively low accuracy. Therefore, IEM [14] is preliminarily employed to address the EM scattering problems of the improved time-varying overturning wave crest model. IEM was developed by Fung based on an approximate solution of a pair of integral equations for tangential surface fields and was later improved by several groups [15–17]. In this paper, an improved time-varying overturning wave crest model was generated and meshed into a large number of triangles. According to the direction of the incident wave, a triangle which is lighted can be determined, after which the scattered far field is calculated. The total far-field is the sum of the scattered far-fields of all lighted triangles. According to the simulation results, the phenomenon of backscattering RCS of HH polarization exceeding that of VV polarization is observed. Therefore, this phenomenon demonstrated that the overturning wave crest is a reason of the sea spikes. In addition, the backscattering RCS of HH polarization exceeding that of VV polarization by as much as 10 dB or more is more likely to occur for the upwind incidence, which is because the multiple scattering is more obvious when the incident wave is along with the upwind direction compared with the downwind direction.

The remainder of this paper is organized as follows. Section 2 presents the improved time-varying overturning wave crest model and the theoretical IEM formulas used to calculate the EM scattering of this model. The backscattering RCS of HH and VV polarization at different time points is discussed in Section 3. Concluding remarks are addressed and further investigations are proposed in Section 4.

#### 2. Theoretical Analysis

The improved time-varying overturning wave crest was modeled according to [8], where the influences of wind speed on the size and height of overturning wave crest model were considered during modeling. The overturning wave crest model in [8] is a 2D model; the 3D model was obtained by stretching the traditional 2D overturning wave crest model in the -axis. IEM was then used to calculate the backscattering of the 3D model.

##### 2.1. Improved Time-Varying Overturning Wave Crest Model

The construction of the 2D time-varying overturning wave crest model will be described in detail at first. As is known, the Beaufort wind scale is always used to describe the sea condition, which includes the wind speed and the wave height. The sea condition for the different Beaufort wind scales and the relationship between the Beaufort wind scale and wind speed have been presented in [8].

Furthermore, the relationship between the wave height and the wind speed can be obtained by the Gaussian function fitting method and can be approximately written as [18]where , , , is the height of the sea wave and is the wind speed, and is the length of sea wave.

For the 2D time-varying overturning wave crest model, the length and height of the wave crest are varying with the time stepping. Therefore, the time factor was included to control the profile of the overturning wave crest model; the 2D time-varying overturning wave crest model can be expressed aswhere , the period of overturning wave crest is , , , and can be obtained from Table 1. is an arithmetic progress between 0 and 1, and each term of contributes to the calculation of the location of the sampling point of the overturning wave crest. For the th sampling point, and are calculated according to and , . The dimensional information can be achieved by and according to (2). ~ vary with the parameter and are employed to calculate the location of the sampling point.