Modeling of the Adriatic Bora on the Croatian Coast

The article considers the Adriatic bora as a phenomenon of flow around real mountains using a nonlinear analytical two-dimensional model. The atmosphere is presented as three layers: the lower layer represents the troposphere, and the other two represent the influence of the upper atmosphere. The shape of the relief is taken into account accurately, the interaction of the flows in the studied layers is approximate. It has been deduced that disturbances over the main ridge and in the leeward zone over the mountains are often characterized by the presence of a zone with rotors in the form of closed vortices and extended sections of vertical movements. The energy of the disturbances beyond the mountains is estimated by the jet stream velocity at the leeward slope. It has been deduced that its value lies in the range of 19–40 m/s. It’s been deduced that the characteristic cold snap during the bora is determined by the arrival of a colder air mass in the region, and not by the flow process itself. The height and the steepness of the leeward slope of the mountains, as well as the effects of turbulization of movements in the leeward zone are determining factors in increasing the velocity in the surface layer over the mountains.


Introduction
The eastern coast of the Adriatic Sea is characterized by a warm climate all the year round.The wind regime is determined mainly by weak local breezes and the northeast winds.In the winter season these winds can change under the influence of short-period strong winds blowing from the northeast (bora).
Bora (Greek: Bóreas -north wind) is the name of a strong cold and gusty wind blowing from mountain ranges towards the warm sea.Classical bora is associated with pouring a cold air mass over a mountain range when the air rises from the windward side, water vapor condensation and cloud formation take place, and an intense downward air flow reaches the hurricane power on the leeward side (Burman, 1969;Stekhnovsky et al., 1971;Shelkovnikov, 1985).
It is believed that the vertical scale of the bora reaches 200-400 m above the sea level, and the horizontal one is only a few kilometers from the coast (Burman, 1969).Bora is often observed in the cold half-year, from October to April.And it is important to understand that in winter the flow around the ridge weakens the cooling effect, and in summer it strengthens the warming effect.On the Adriatic coast two types of the bora are distinguished.The first type is the the Black Bora; it is a damp warm wind, the second type is Ecologica Montenegrina 23: 87-96 (2019) This journal is available online at: www.biotaxa.org/emthe Clear Bora ; it is a dry cold wind.We are interested in the second type of bora, which is called the Adriatic Bora.
The nature of this natural phenomenon has been studied for a long time, but no consensus has been reached on the primacy of this or that factor during its formation.The first theoretical attempts to explain the Adriatic Bora were made in the work of (Mohorovicic, 1889), which was descriptive to a greater extent.Further works (Yoshino, 1976;Jurcec, 1981) were analytical models of the bora, which attributed it to the type of katabatic winds, i.e. gravitational currents of cold near-surface air flowing from coastal mountains into a warm atmosphere above the sea.Over time, they began to come to the conclusion that the wind increase during this process was quite small and did not correspond to the observed process (Grisogono and Belusic, 2009;Bedanokov et al., 2019).
Further theoretical studies of the bora are associated with the use of models of the dynamic interaction of the incident flow with the roughness of the land [Smith, 1987;Klemp and Durran, 1987;Kozhevnikov, 1999;Jiang and Doyle, 2005;Belusic et al., 2007;Gohm et al., 2008, Berzegova et al., 2019].
Recently, numerical mesoscale modeling based on the WRF model has been widely used to study and predict bora (Toropov et al., 2013;Efimov and Baranov, 2013;Shestakova et al., 2015) The application of this model allows one to take into account a lot of factors of the phenomenon, but it is necessary to introduce a number of parametric simplifications and, as a result, it is difficult to evaluate the credibility of the results.When using analytical modeling, the solution of the problem can be reduced to obtaining specific formulas and at the same time control the accuracy of the results.This can be achieved by taking into account only the most important factors of the phenomenon.
In our research we have investigated the Adriatic Bora in the region of Rijeka (Croatia) located in the territory of the Risnyak National Park.For the first time a nonlinear analytical two-dimensional stationary three-layer mesoscale model has been used for this purpose; it takes into account the real relief (Kozhevnikov, 1999;Berzegova and Bedanokov, 2018).A similar atmospheric disturbances over the Novorossiysk mountains (the Black Sea coast of Russia) and atmospheric energy in the event of the Novorossiysk Bora have been studied using this model (Berzegova at al., 2019).The presentresearch uses the approaches to the problem developed in the study of the Crimean and Novorossiysk boras.
The aim of the research is to study some general features of disturbances in the atmosphere during the flow around mountains and local features of the disturbances that lead to catastrophic damage during the bora in the region of Rijeka (Croatia).The dependence of the disturbances on the properties of the incident flow is studied for the first time for the Adriatic Bora in a wide range of changes in the incident flow velocity.

The theoretical model
The dynamics of the interaction of a moving atmosphere with the roughness of the land for medium-scale processes is studied using a system of equations of motion, adiabaticity and continuity (Kozhevnikov, 1999).Due to the transition to the specific nature of the incident flow: , it is possible to deduce the solution of the problem to the solution of the linear Helmholtz equation, where U is the incident flow velocity, and  is the temperature gradient.A nonlinearity of the velocity field is taken into account.
The used model is a three-layered one: the lower layer represents the troposphere, and the other two represent the influence of the upper atmosphere.The properties of the flowing stream are taken into account by setting U and  , and, moreover, the U velocity is set the same in all the layers, and the gradients j    3 , 2 , 1  j are set different.Analysis of the works on this model (Kozhevnikov, 1999;Berzegova and Bedanokov, 2018;Bedanokov et al., 2019;Berzegova et. al., 2019) has shown that the disturbances depend primarily on the Lyra scale c  (Lyra, 1943), which in turn depends directly on U velocity and on the gradient to a lesser extent.
According to the measurements in the works on numerical modeling of the Adriatic Bora [Gohm and Mayor, 2004;Grisogono and Belušić, 2009;Prtenjak et al., 2010], wind speed values often lay in the range of 6-10 m/s in the flowing stream, and rarely reach large values.Therefore, in the present studywe have carried out calculations for specific 6 values of Lyra scale c  in the troposphere and for one setup of layer- by-layer values 1).The calculations have been carried out to the height of 30 km.In order to take into account the dependence on the horizontal coordinate in solution (1), the Fourier method is used.The spectral composition of the wave components of the solution depends on all parameters of the problem, but primarily on c  and on the shape of the streamlined mountains.The solution has the form of complex functionals, including integrals over the horizontal coordinate and wave numbers.The steps of the computational grid when calculating the field  are 50 and 250 m at x -axis and z-axis, respectively, which ensures a high quality of spatial resolution.

Obtaining a streamlined relief form
In the area of Rijeka the studies have been carried out for the Mount Risnyak with the height of 1528 m above the sea level.Real mountains are not two-dimensional, therefore, before the simulation, a special processing of the real relief has been carried out in order to highlight its main two-dimensional features.As a result, a profile of the characteristic two-dimensional relief of the region has been obtained (hereinafter it is called an average one and is denoted as "av").
The method used to obtain the theoretical profile of the relief was tested in the previous works dedicated to the comparison of the data of theory and observations (Kozhevnikov, 1999, Kozhevnikov and Bedanokov;1998, Kozhevnikov et al., 2017;;Berzegova and Bedanokov, 2018;Berzegova et. al., 2019).Its advantage is that it allows to study exactly the characteristic features of the disturbances during modeling.The height of the main peak of the obtained average relief is 1528 m, the horizontal length does not exceed 41 km. 10 specific sections have been used when receiving the indicated average relief.To assess the range of changes in the results depending on the displacement of the cross sections in space, one peculiar section has been selected, that is different from the obtained average one.Further it is called specific and is denoted as "sp".The height of the lee ridge is 1425 m.

Disturbances in the atmosphere during the flow around the relief
In the present research, 12 flow options have been calculated in accordance with Table 1.The analysis has been carried out for the heights up to 10 km and the length -20 <x <40 km.(Kozhevnikov, 1999;Kozhevnikov and Bedanokov, 1998) the appearance of the rotors is associated with the value inverse to the internal Froude number, where the maximum height of the mountain m h is used as the scale.This value is determined by the formula: and is called dimensionless mountain height (Lin, 2007).
According to Table 1 these parameters have changed in our research within the given below range:  Berzegova et al. (2019).In other words, the intensity of disturbances depends primarily on the height of the mountains, and secondly, on their shape.

The energy of the atmosphere in event of the Adriatic Bora
The nature of the jet stream at the leeward slope and temperature disturbances In all cases it is easy to find the zone of serious increase in the flow velocity modulus in the area of disturbances.Such kind of zones is associated with an area of abrupt rapprochement of the trajectories.In our previous papers (Berzegova et al., 2019;Bedanokov et al., 2019) this effect was most pronounced in the leeward slope of the streamlined mountains.Here, as we see in Fig. 1 and 2, rapprochement of the trajectories are recorded both in the region of the main ridge at altitudes of about 1400 m and at the leeward slope.
The movement of air particles in each such zone has the form of a jet.The trajectories converge in the upper part of the jet, and divergence in the lower part.The inclination of the jets changes with height, and the convergence of the trajectories decreases.Therefore, the speed in the stream is maximum at the main ridge and the leeward slope of the mountains at a certain average height.In the present research we are interested in the wind increase in the jets over the mountains near the leeward slope (Kozhevnikov, 1999;Gohm et al., 2004;Grisogono and Belušić, 2009;Prtenjak et al., 2010;Kozhevnikov, 2019;Berzegova et al., 2019).This increase is almost proportional to the density of the trajectories.In Fig. 1 and 2 similar jets can also be observed at the altitudes of 4-8 km (Fig. 1) and 5.8-9.5 km (Fig. 2).It's clear that the intensity of the jets increases with the appearance of rotors.
When choosing the leeward slope for assessing the energy, we have taken into account that the model gives good results at height, despite the fact that it does not take into account viscosity.It's been also assumed that it is possible to hope that turbulence is suppressed at the slope due to the initial stability and, therefore, the model can be trusted.This gives us reason to assess the intensity of the bora in the region of Rijeka and the Rijeka Bay at the first approximation according to the calculated flow velocity in the jet at the leeward slope of the mountain.
Investigations of the bora are directly related to the disturbances at the leeward slope of the coastal ridge (Gohm et al., 2004;Grisogono and Belušić, 2009;Prtenjak et al., 2010;Berzegova et al., 2019), therefore, the fields of the flow function  , velocities and disturbances T  for all model variants have been calculated here (Table 1).As the disturbance patterns for all c  are qualitatively close, we illustrate the result for one of them in Fig. 3. Figure 3 shows the contour lines of T  disturbances, which provide a qualitative idea of the trajectories of motion.For example, the isoline of 4  

T
degrees practically reproduces the trajectory at 7 , 1 0  z km.Along the slope the jet is almost uniform with a thickness of about 2 km.The motion of air particles acquires a wave character as they move away from the slope (Fig. 2).Fig. 3 shows that there are no T  disturbances directly at the slope; they become positive when distant from it.
It should be noted that the disturbances are only positive and lie in the range of 0-5 degrees in all model calculation options in the air flow near the slope with a thickness of about 0.5 km and in the surface layer over the mountains 300 m thick.Thus, we have obtained conformity with the law of isentropic down gliding.This suggests that sharp drops in temperature during the Adriatic Bora are determined not by the flow process itself, but by the arrival of the air mass of a different, much lower temperature to the city and the bay.

Leeward slope velocity as a measure of the energy of disturbances in event of the bora
The velocity field has been studied at the leeward slope and in the region of the main ridge for the middle relief.Changes in the values of the velocity modulus   x z V , depending on x at the level of 350  z m, which is defined as characteristic (Berzegova et al., 2019) at the level of 1,500 m have been obtained for all values of Lyra scale c  .The jet energy at the indicated heights has been estimated by the average value   x z V , in a layer 200 m thick.This value characterizes the properties of the jet at the selected heights of 300 m and 1400 m.Averaging at the level of maximum speeds has led to the value which now depends only on a specific value of c  and is called the characteristic jet velocity (Berzegova et al., 2019).
It gives an idea of the energy of the flow at the slope, and hence of the intensity of disturbances over the mountains.The calculations have shown that the characteristic jet velocity for a certain value of c  in the area of the main ridge and at the leeward slope differ by 0.7-1 m/s.The velocities in the jet at the altitudes of 1500 -1850 m assume maximum values, then, downstream along the leeward slope, the velocity values gradually decrease.Then, at the altitudes of 300-400 m the velocities in the jet assume maximum values again, but they are by 0.7-1 m/s lower than in the jet in the main ridge area.This effect has also been noted in the paper by (Family, Year).
When we study the atmospheric energy during the bora, we are interested precisely in the jet near the leeward slope.The air particles from the uppermost layers of the jet do not obviously reach the land surface as they descend along the leeward slope.Consequently, a transition layer is formed between the free atmosphere and the surface layer over the mountains.Air particles from the lowest layers of the jet participate in the formation of this layer and its turbulization process.It turns out that the energy of turbulent wind gusts in the surface layer over the mountains is directly proportional to the kinetic energy of the jet, and hence the  b / is more than 1; 2) the curve for the sp relief does not qualitatively differ from the curve for av, so, the results for the middle relief characterize objectively the energy of the atmosphere during the Adriatic Bora; 3) the reliability of the obtained dependencies is confirmed by the smallness of dV .
As is obvious, the velocity in the jet in the first approximation is in the range of 19 -40 m/s for incident flow velocities not exceeding 15 m/s (Fig. 4b).
The model used in the research allows to estimate the kinetic energy of the disturbances, which is determined by the magnitude b V .We can assume that the average wind speed is close to b V , which is confirmed by the research results (Bedanokov et al., 2019;Berzegova at el., 2019).In Gohm et al. (2004), Grisogono andBelušić (2009) andPrtenjak et al. (2010) instrument measurement data are available.The measurements show that the maximum speeds in the area of the City of Rijeka and the Gulf of Rijeka during the bora are more than average values by 5 m/s, and with wind gusts it increases by 10-15 m/s.Despite the fact that there is no information on direct measurements of turbulence characteristics, the results of these studies confirm the turbulent nature of the disturbances in the surface layer.This indicates the reliability of the obtained estimates of b V magnitude, which characterizes the wind strength during the bora on the leeward side of the mountains.

Conclusions
1.The wind in event of the Adriatic Bora has a catastrophic force, primarily due to the fact that the leeward slope of the streamlined mountain has a noticeable slope and the air flow here is jet-like.
2. Theoretically the velocity in the jet depends on the Lyra wave scale in the incident flow in front of the mountains, so, first of all, on its speed.
3. For incident flow velocities not exceeding 15 m/s the velocity in the jet is in the range of 19 -40 m/s at the first approximation.
4. According to calculations, the temperature of the air entering the city and the gulf after pouring over the mountains is heated by no more than 2-3 degrees due to adiabatic compression.So, a significant decrease in temperature during the Adriatic Bora is determined not by the flow effect, but by the arrival of a colder air mass in the considered region.This is a preliminary study which will be followed by a more thorough study of the problem in the area.
Fig. 1 illustrates the result of modeling the field of trajectories of air particles at 5  c  km.The trajectories are identified by the values of their heights in the incident flow 0 z (in km).The flow is directed from left to right.The streamlined relief is painted over.

Figure 1 .z
Figure 1.Trajectories of air particles flowing around the middle relief for 5  c 

Figure 2 ..
Figure 2. Trajectories of air particles flowing around the middle relief for 7 .6  c  km, 4 , 13  U m/s,

Figure 3 .
Figure 3. Temperature disturbances at the leeward slope at coordinate has been carried out at two height levels at which they have maximum values.For these two values the average value of b V and the range of its scatter dV have been found.The values of dV have been not more than 0.18 m/s.Fig. 4 shows the obtained dependences on the values of c  in the incident flow.

Figure 4 .
Figure 4.The dependence of the characteristic velocity on

Table 1 .
Model parameters for the presented model calculations