Nat. Hazards Earth Syst. Sci., 17, 671–683, 2017 www.nat-hazards-earth-syst-sci.net/17/671/2017/ doi:10.5194/nhess-17-671-2017 © Author(s) 2017. CC Attribution 3.0 License. Numerical modeling of the 2013 meteorite entry in Lake Chebarkul, Russia Andrey Kozelkov1,2, Andrey Kurkin2, Efim Pelinovsky2,3, Vadim Kurulin1, and Elena Tyatyushkina1 1Russian Federal Nuclear Center, All-Russian Research Institute of Experimental Physics, Sarov, 607189, Russia 2Nizhny Novgorod State Technical University n. a. R. E. Alekseev, Nizhny Novgorod, 603950, Russia 3Institute of Applied Physics, Nizhny Novgorod, 603950, Russia Correspondence to: Andrey Kurkin ([email protected]) Received: 4 November 2016 – Discussion started: 4 January 2017 Revised: 1 April 2017 – Accepted: 13 April 2017 – Published: 11 May 2017 Abstract. The results of the numerical simulation of possi- Emel’yanenko et al., 2013; Popova et al., 2013; Berngardt et ble hydrodynamic perturbations in Lake Chebarkul (Russia) al., 2013; Gokhberg et al., 2013; Krasnov et al., 2014; Se- as a consequence of the meteorite fall of 2013 (15 Febru- leznev et al., 2013; De Groot-Hedlin and Hedlin, 2014): ary) are presented. The numerical modeling is based on the – the meteorite with a diameter of 16–19 m flew into the Navier–Stokes equations for a two-phase fluid. The results of ◦ the simulation of a meteorite entering the water at an angle earth’s atmosphere at about 20 to the horizon at a ve- ∼ −1 of 20◦ are given. Numerical experiments are carried out both locity of 17–22 km s . when the lake is covered with ice and when it is not. The – The meteorite was destroyed in several stages, and the estimation of size of the destructed ice cover is made. It is main explosion occurred at an altitude of about 23 km. shown that the size of the observed ice hole at the place of The analysis of the meteorite fall led to the estimation the meteorite fall is in good agreement with the theoretical of the explosion energy from 380 to 1000 kt of TNT. predictions, as well as with other estimates. The heights of tsunami waves generated by a small meteorite entering the – Surviving fragments of the Chelyabinsk meteorite sup- lake are small enough (a few centimeters) according to the posedly flew at velocities up to 150–300 m s−1, and ac- estimations. However, the danger of a tsunami of meteorite cording to the updated data the velocity was 156 m s−1. or asteroid origin should not be underestimated. – The largest meteorite fragment, weighing about 550 kg, was recovered from Lake Chebarkul near the Krutik Peninsula, and it had an irregular oval shape with an 1 Introduction average outer diameter of about 1 m. – The celestial body exploded when it hit the ice and wa- On 15 February 2013 at 09:20 LT (local time), in the vicin- ter. Its fragments flew more than 100 m and formed an ity of the city of Chelyabinsk, Russia (Fig. 1), a meteorite ice hole of a round shape with a diameter of about 8 m exploded and collapsed in the earth’s atmosphere as a result (Fig. 1). of inhibition. Its fall was accompanied by a series of atmo- spheric explosions and propagation of shock waves over the The ground-penetrating radar (GPR) survey of the crash site territory of the Chelyabinsk region. Small fragments of the showed that the crater, which was formed by the meteorite meteorite came down on the region. It is the largest of the impact on the bottom, was observed 30 m away from the ice known celestial bodies which have fallen to the ground after hole (Kopeikin et al., 2013). the Tunguska meteorite in 1908. The following characteris- The results of the numerical modeling of the processes tics of the Chelyabinsk meteorite are given in recent pub- that began in the water after the meteorite entered Lake lications (Zetser, 2014; Ionov, 2013; Kopeikin et al., 2013; Chebarkul are presented in this paper. We consider two cases Published by Copernicus Publications on behalf of the European Geosciences Union. 672 A. Kozelkov et al.: Numerical modeling of the 2013 meteorite entry in Lake Chebarkul, Russia Figure 1. The ice hole that was formed on the surface of Lake Chebarkul. – the occurrence of a meteorite in the ice-covered lake (as it iments. This estimation is in good agreement with the ob- was in February 2013) and in the lake without ice to estimate served data, as well as with the estimates made previously in the amplitude of the wave in the case of a possible fall in Ivanov (2014). The results are summarized in Sect. 7. the summer. First of all, in Sect. 2 a well-known parametric model of the tsunami source of meteoric origin (Ward and Asphaug, 2000) which estimates the disturbances in the wa- 2 Preliminary estimates of wave heights in the lake ter at the site of the meteorite entry is used. It is shown that with a free surface the size of the source is twice the size of the observed ice To estimate the possible parameters of the water surface dis- hole; that is why this model cannot explain the observed phe- placement when a meteorite falls, we use a simplified model nomenon. In Sect. 3 we describe the hydrodynamic model in which the generation of waves by a meteorite entering of wave generation based on the Navier–Stokes equations the water is parameterized by certain initial conditions (Ward as well as the parameters of its numerical discretization. In and Asphaug, 2000; Mirchina and Pelinovsky, 1988; Kharif Sect. 4 we present the results of numerical experiments on and Pelinovsky, 2005; Levin and Nosov, 2009; Torsvick et the tsunami wave generation in open water. The results of al, 2010). It is suggested that in the initial stage of a crater numerical experiments on disturbance generation in the lake formation a meteorite, vertically entering the water, creates a covered with ice are presented in Sect. 5. The zones of maxi- radially symmetrical cavity on the water surface, which can mum and minimum pressure which could potentially lead to be described by a simple function: the destruction of the ice cover are detected. In Sect. 6 the re- sults of estimations of the ice cover destruction, based on the ηimp.r/ D D 1 − r2=R2 ; r ≤ R ; (1) calculation of the stresses, are shown. The area of ice destruc- C C D imp tion is estimated according to the famous semi-empirical for- η .r/ D 0; r > RD; (2) mulas and pressure values obtained in the numerical exper- Nat. Hazards Earth Syst. Sci., 17, 671–683, 2017 www.nat-hazards-earth-syst-sci.net/17/671/2017/ A. Kozelkov et al.: Numerical modeling of the 2013 meteorite entry in Lake Chebarkul, Russia 673 where DC is the depth of the cavity, and RC and RD are inner andp outer radii of the cavity, respectively. In the case of RD D 2RC the water ejected from the cavity forms the outer splash–ring structure typical of the fall of the object in the water and the volume of which corresponds exactly to the volume of water discharged from the cavity. Considering that the meteorite kinetic energy is converted into the potential energy of the water level displacement, the following simple analytical formulas are derived to calculate the radius and depth of the cavity (see, for instance, Ward and Asphaug, 2000): Figure 2. The initial disturbance of the water surface at the source. s !δ 1 3 2 2 3 2"ρIRI VI VI ρI DC D ;RC D RI 2" ρ gR2 gR ρ w C I w 3 The hydrodynamic model of the tsunami source, 1 −δ !2δ ρ 3 1 based on the Navier–Stokes equations w ; α−1 (3) ρI qR I The models based on the numerical solution of the Navier– Stokes equations (Ferziger and Peric, 2002), which have be- ρ g where w is density of water; is gravitational acceleration; come popular in solving the problems of asteroid tsunami, al- " is the proportion of the kinetic energy of the meteorite, con- low simulating a real meteorite entering the water (Kozelkov ρ R V verted into the tsunami energy; I, I and I are density, ra- et al., 2015, 2016a). In this paper we solve the Navier– q α dius and velocity of the meteorite ; and are the coefficients Stokes equations for a two-component (water and air) in- associated with the properties of the meteorite and the water compressible fluid in a gravitational field, and both air and layer. According to Levin and Nosov (2009) about 16% of water are considered to be incompressible. The incompress- the kinetic energy of the falling body is converted into the ibility/compressibility of air will mainly influence the rate α energy of tsunami waves. The parameter is 1.27, and the of change of the wave parameters in the source during the q δ value of and is calculated as follows: collapse of the cavity. Qualitatively, the process will be de- scribed correctly, but the quantitative difference can be sig- 1 ρ 0:26 1 δ D ; q ≈ 0:39 w : (4) nificant. This is directly related to the Mach number, deter- 2α C 2 ρ 0:27 I RI mined by the characteristic velocity of the meteorite, which in our calculations is 156 m s−1, which is approximately a If the diameter of a meteorite is 1 m, the density is 3.3 g cm−3 −1 Mach number of 0.5.