To evaluate the effect of wind on corona discharges occurring on the tip of a grounded rod during a negative charging process of thundercloud, a two‐dimensional numerical model has been improved by considering the wind velocity as a driving force for the movement of the corona charges. It was found that not only wind speed but also wind direction have a significant effect on the distribution of corona charges, the local electric field around the rod, and the corona current. (1) Under the same wind speed, a larger horizontal wind can result in less accumulation of corona charges, a larger electric field, and a larger corona current. However, when the speed is less than 5 m s⁻¹, the effect of wind direction on the corona current was weak. (2) Under the same wind direction, a larger wind speed can cause a larger corona current. However, when the horizontal wind component is smaller than the vertical, the larger wind speed would cause a smaller electric field. Thus, it is necessary to take the effects of the wind direction into consideration, rather than to consider its speed only, when studying the corona discharge and its effects on the upward leader.

The study of the ground tip corona discharge is an important part of the lightning strike mechanism and lightning warning research. Because the characteristics of the corona charge distribution are difficult to observe directly, simulation research is indispensable. However, most of the previous models have been unipolar models, which cannot reflect the characteristics of the tip corona discharge under electric field reversal during real thunderstorms. Therefore, the development of three-dimensional positive and negative corona discharge models is of great significance. In this study, a three-dimensional corona discharge numerical model considering the polarity reversal process of the electric field was developed with or without a wind field and simulated the tip corona discharge characteristics under this reversal. The reliability of the model was verified by comparing the observed results. Compared with the unipolar corona discharge model, this model could effectively evaluate the impact of the first half-cycle corona discharge on the second half-cycle opposite-polarity corona discharge and invert the spatial separation distribution characteristics of different polar corona charges released in both cycles under the influence of wind and the spatial electric field distribution characteristics generated by the corresponding corona charges. Comparing unipolar corona discharges under the same wave pattern and amplitude of the background electric field, it was assumed that the unipolar corona discharge occurred in the half cycle after the polarity reversal of an electric field, and there was also an opposite-polarity corona discharge process before it. Due to the influence of the first half cycle, the background electric field required for a corona discharge was smaller, and the corona current was generated earlier, but the end time was equivalent. At the same time, due to the neutralization effect of positive and negative corona charges, the peak value of the total corona charge in the second half cycle was significantly smaller than that of the unipolar model. At different building heights, the peak difference in the corona current and the peak difference in the corona charge between the two models increased linearly with an increase in height. It could be seen that this model had better simulation results and wider application value.

The effect of corona discharge from buildings or structures on the surrounding atmospheric electric field is very important in the measurement of urban atmospheric electric fields and the early warning of lightning. However, most previous studies were focused on independent buildings, with little research on three-dimensional building groups. Therefore, based on three-dimensional numerical simulation technology, this paper uses a double-needle system to simulate the characteristics of thunderstorm corona discharge from two equal-height buildings separated by a variable distance. The shielding effect of the double-needle system on the ground electric field is evaluated both with and without corona discharge, and the main conclusions are as follows: (1) The larger the distance between the two needles, the closer the peak corona current from each tip of the double-needle system is to that from an independent lightning rod at the same height. When the peak corona current from each tip of the double-needle system equals the peak corona current from an independent lightning rod at the same height to some level of approximation, the distance between the two needle systems is determined by the needle height at this time. (2) If the distance between the two needles is 0.1 m, the corona charge released by the double-needle system is almost equal to that released by an independent lightning rod. The corona charge released by the double-needle system is approximately twice as much as that released by an independent lightning rod when the distance between the two needles is increased to a certain value that increases with the needle height and the time of corona discharge. (3) The greater the value of the time of corona discharge, the stronger the shielding effect of the corona discharge on the ground electric field and the larger the shielding range, but the greater the value of the needle height, the smaller the shielding range. (4) Compared with the shielding effect with no corona discharge, that with corona discharge is greater, but the greater the value of the needle height, the less the enhancement. For example, for corona discharge with a time of 10 s, the needle height is 20 m, and the shielding range is ca. 70 m, which is 8.8 times that without corona discharge; however, for the needle height of 100 m, the shielding range is ca. 150 m, which is only 1.5 times that without corona discharge.

Corona discharge at the tip of buildings in a thunderstorm environment is an important factor causing changes in the near-ground electric field, but the influence of a quadratic growth law and quantitative research on the parameters is still rare. Therefore, based on the three-dimensional corona discharge model, this paper studies the influence of positive and negative symmetrical triangular wave electric fields with different amplitudes on the corona discharge of an independent lightning rod. Studies have shown that the corona current is synchronized with the peak of the background electric field. Studies have shown that the corona current is synchronized with the peak of the background electric field. When the polarity of the electric field changes from positive to negative, the positive charge accumulated in the positive half-cycle promotes the subsequent negative corona, so the negative corona starts in advance when the polarity reverses. Compared with unipolar discharge, the amplitude of the negative current and the number of negative charges have significantly improved. However, due to the counteraction of neutralization between positive and negative charges, the total corona charge is at a low level, which shows a net negative polarity result. The corona current and the amount of charge increase nonlinearly with an increase in the background electric field amplitude. Under the symmetrical triangular wave electric field, the quantitative fitting relationship between the peak value of the negative corona current in the second half-cycle and the amount of charge is established for the 5 m high independent lightning rod, which is I⁻ = −0.0532 − 0.153$E$ − 0.0682 $E^2$, Q⁻ = −3.18 × 10⁻³ + 7.762 × 10⁻⁴E − 4.671 × 10⁻⁵$E^2$, respectively. The increase in the background electric field amplitude will aggravate the disturbance of the corona discharge to the near-surface electric field. When the direction of the electric field has reverted to zero, the existence of the space charge will lead to a significant change in the strength and polarity of the ground electric field. When the thunderstorm background electric field changes from positive to negative, the corona effect reverses the polarity of the ground electric field in advance, and the larger the peak value of the background electric field, the larger the advance. The corona interference mechanism revealed by this study can provide an important reference for correcting the electric field monitoring data and improving the accuracy of lightning warnings.

This paper concerned with the existence of solutions of anti-periodic boundary value problems for impulsive differential equations with φ-Laplacian operator. Firstly, the definition a pair of coupled lower and upper solutions of the problem is introduced. Then, under the approach of coupled upper and lower solutions together with Nagumo condition, we prove that there exists at least one solution of anti-periodic boundary value problems for impulsive differential equations with φ-Laplacian operator.