Objective  At present, most of the calculation methods for thermal wake detection by MRTD analysis consider the water body as uniformly distributed seawater. The stratified nature of seawater temperature and density has great influence on the inversion accuracy of submarine thermal wake on the surface temperature distribution, rise time and wake rise distance. However, the research at home and abroad mainly focuses on the improvement of MRTD algorithm of infrared system or derivation of the detection ability of infrared detector based on other parameters of the system, as well as the influence of weather and other factors on wake detection, and has not analyzed the influence of seawater stratification on wake detection and inversion. Therefore, the research on infrared radiation detection of thermal wake under the conditions of stratified seawater temperature and density is of great significance to the infrared detection of submarines.

  Methods  For the lack of infrared detection of submarine thermal wake under the condition of stratified sea water temperature and density, the calculation error of detection distance and inversion accuracy error of submarine are large. Based on the finite element analysis method, the research on submarine infrared radiation characteristics under the condition of seawater stratification is carried out in this paper. Firstly, the finite element analysis method is used to simulate the floating process of submarine thermal wake in stratified seawater by a full-size submarine model with propeller and bridge characteristics. Then, according to the sea surface infrared radiation model and atmospheric transmission model, the full-link mathematical and physical model of the wake from floating diffusion, atmospheric transmission atmospheric attenuation to sensor detection is built, and the detection distance of the infrared detector to the submarine thermal wake under the condition of layered seawater is calculated according to the specific infrared detector performance parameters.

  Results and Discussions   The comparison shows that the stratification condition of seawater has a great influence on the detection of wake. With 95% detection probability, the detection distance of the wake increases by 10.61%, the identification distance of the wake increases by 9.32%, and the recognition distance of the wake increases by 8.28% (Tab.2). In the case of stratified water, the wake is presented as a cold wake on the water surface. The temperature difference between the cold wake and the sea surface is 0.152 K larger than that between the hot wake and the sea surface in the case of non-stratified water. The submarine travels 340 m forward without stratified seawater and 101.8 m under stratified seawater temperature and density. Compared with seawater stratification, the inversion error of submarine without stratification reaches 238.2 m, and the wake temperature difference on the surface is not only 0.152 K, but also cold wake phenomenon. It can be seen that the seawater stratification condition has a great influence on the submarine's inversion accuracy, and even directly leads to incorrect results.

  Conclusions  The mathematical and physical model of the wake from floating diffusion, atmospheric decay to full link of sensor detection under the condition of seawater temperature and density stratification is established. The influence of seawater temperature and density stratification on the wake floating speed, the detection distance of the infrared detection system to the wake and the inversion error of the wake are obtained by simulation calculation. That is, it takes 101.8 s for the wake to rise to the surface at 50 m under the condition of stratified seawater temperature and density. Under the same conditions, when the seawater is not stratified, the time taken for the wake to rise to the surface is 340 s, which is much longer than that for the stratified seawater. This is due to the lower underwater temperature of the stratified seawater and the large density difference conducive to the floating of the hot wake. The discovery distance of the delaminated water body wake is 6.451 km, the identification distance of the wake is 1.631 km, and the recognition distance of the wake is 0.824 km. The unclassified detection distance, identification distance and recognition distance are 5.832 km, 1.492 km and 0.761 km, respectively. Compared with seawater delamination, the inversion error of submarine wake is 238.2 m without delamination, the temperature difference of wake on water surface is 0.152 K, and the cold and hot wakes on sea surface are different.