Ovo istraživanje bavilo se meteorološkim tsunamijima – oscilacijama morske razine čiji se periodi mjere u minutama i meteorološkog su porijekla – i sastojalo se od tri dijela: u prvom je dijelu provedeno testiranje numeričkih modela kako bi se odredila njihova sposobnost reprodukcije Proudmanove rezonancije, a u drugom i trećem je odabrani model korišten za reprodukciju povijesnih događaja meteotsunamija u Jadranu. Testiranje je provedeno koristeći tri modela, od kojih su dva bili modeli konačnih elemenata (ADCIRC i SCHISM), a jedan model konačnih razlika (ROMS). Modeli su testirani na idealiziranom bazenu uniformne dubine iznad kojeg su numerički nametnuti putujući poremećaji tlaka zraka oblika sinusa ili „boxcar” funkcije, različitih valnih duljina i brzina. Rezultati su pokazali da sinusni poremećaj tlaka zraka višestruko većih horizontalnih dimenzija od dimenzija bazena uzrokuje pojavu Chrystalove rezonancije, odnosno seša u bazenu, dok manji sinusi i „boxcar” funkcije bilo kojih dimenzija uzrokuju pojavu Proudmanove rezonancije, odnosno rezonantno pojačanih dugih valova („long period waves”). Rezultati najbliži analitičkim rješenjima dobiveni su korištenjem modela ROMS. Za daljnja istraživanja ipak je odabran model ADCIRC zbog metode diskretizacije pomoću konačnih elemenata kako bi se u zaljevima od interesa mogla koristiti čim ﬁnija rezolucija bez ugnježđivanja domena. SCHISM nije odabran zbog kompliciranijeg CFL uvjeta u odnosu na ADCIRC. Nakon što je odabran model za daljnji rad, provedene su simulacije četiri povijesna događaja meteotsunamija u Jadranu (Vela Luka 1978., Široka 2007., Mali Lošinj 2008. i Stari Grad 2010.), uz korištenje deﬁnirane minimalne dubine u modelu. Za sva četiri slučaja model je pokazao povećane valne visine u zaljevima od interesa, ali ni u jednom nije uspješno reproducirana ekstremna valna visina. Za dva od četiri slučaja (Vela Luka i Stari Grad) zatim su napravljene simulacije koje su uključivale poplavljivanje i osušivanje čvorova mreže. Novi set simulacija za Velu Luku povećao je modeliranu valnu visinu u području gdje je iznosila 2,1 m na 3,7–4,1 m, a u području gdje je iznosila 5,5 m na 7,5 m (opažena je iznosila oko 6 m). Uključivanje poplavljivanja i osušivanja u model dodaje procese koji se odvijaju na granici mora i kopna i u svim je simulacijama dovelo do povećane valne visine; ovakav rezultat implicira da je za modeliranje ekstremnih oscilacija poželjno u modelu omogućiti poplavljivanje i osušivanje. Simulacije za Stari Grad također su dale veće valne visine uključivanjem poplavljivanja i osušivanja čvorova mreže, ali nije uspješno reproducirana opažena valna visina od oko 2 m. U literaturi je prethodno pretpostavljeno da je Stari Grad tada bio potopljen jer se meteotsunami superponirao na olujni uspor koji je već bio podigao razinu mora – ovaj rezultat to potvrđuje.
|Abstract (english)|| |
This study was focused on meteotsunamis – sea level oscillations with periods similar to those of tsunamis, but caused by meteorological phenomena – and consisted of three parts: ﬁrst, three numerical models were tested on an idealised basin with synthetic atmospheric forcing and, then, one model was chosen to reproduce several historical meteotsunami events in the Adriatic in two diﬀerent ways. Models were tested using an idealised rectangular basin of uniform depth. An air pressure disturbance shaped like a sine wave or a boxcar function travelling over the basin was the only external forcing present in the simulations. Three numerical models were used – two ﬁnite element models, ADCIRC and SCHISM, and one ﬁnite diﬀerence model, ROMS. Two parameters were used to quantify results, wave height and energy. Results show that for a sinusoidal disturbance with a wavelength twice the size of the basin or larger, Chrystal resonance develops in the basin causing seiches. The periods of the modelled seiches at the left and right sides of the basin are close to the basin’s eigen period, especially when considering results obtained through maximum wave heights. All model results obtained through maximum energy tend to overestimate the periods. In the central part of the basin where the second mode is expected to be dominant, all the models overestimate the period regardless of the parameter used for calculation. That diﬀerence is explained by considering the analytical solution for sea surface elevation obtained from a 1D system of equations for a basin forced by a travelling sinusoidal air pressure disturbance. A sine wave with a wavelength shorter than the basin length causes Proudman resonance to occur. Although all the models give resonant speed close to the speed of free waves in the basin, none of the results is a complete match to the analytical solution. When the wavelength is the same as the basin length or only slightly larger, neither resonance can be seen clearly as a change in regime occurs. These simulations were then repeated for sine waves with the same wavelengths but doubled lengths (that is, two consecutive sine waves travelling over the basin). Results show that these air pressure disturbances transfer more energy into the sea and the seiche periods are closer to theoretical values but Proudman resonance is clearly visible for smaller wavelengths than it was before. While both sets of simulations have similar results, the double sine wave simulations have a more pronounced transition from one resonance to the other as well as a better representation of Chrystal resonance whereas the single sine wave simulations represent Proudman resonance more clearly. Boxcarshaped air pressure disturbances always cause Proudman resonance in the basin regardless of disturbance size,however,not all themodels give resonance at the same speed. The best results are obtained with ROMS which gives resonance at the speed of free waves for every simulation. ADCIRC and SCHISM tend to slightly underestimate the results, especially when considering results obtained through maximum energy. Based on these results, ADCIRC was chosen as the model for further work as it is a ﬁnite element model which allows for a very ﬁne resolution inside the bays of interest without using nested domains. SCHISM was rejected because it uses a semi-implicit time scheme which makes choosing an adequate time step slightly more complicated and an inadequate time step can aﬀect Proudman resonance in the model. After the testing phase,modelling off our historical meteotsunami events in the Adriatic was conducted. The simulations used a cut-oﬀ depth of 4 m. Results for Vela Luka (21 June 1978), Široka (22 August 2007) and Mali Lošinj (15 August 2008) show that there are signiﬁcant sea level oscillations in the bays but the amplitudes are, at best, 50% of the observed ones. In the case of Stari Grad (19 February 2010) the modelled oscillations were much smaller, up to 30% of the observed ones. The situation in Stari Grad was very speciﬁc that day – sea level was already elevated due to a storm surge and it is assumed that without the storm surge the meteotsunami that hit the bay would not have caused ﬂooding on its own. The next step were simulations that included ﬂooding and drying of grid nodes and they were conducted for the events in Vela Luka and Stari Grad. Grid resolution was enhanced in the entire Adriatic but especially in the two bays where the spatial step was several tens of meters and topography was included in order to allow for wave runup. Results for Vela Luka show a signiﬁcant improvement from the simulations that used a cut-oﬀ depth. The wave amplitude and energy at the mouth of the bay are larger than in cut-oﬀ depth simulations, and better resolution inside the bay coupled with ﬂooding and drying caused the modelled wave heights to be twice as large as in previous simulations and closer to the observations. All modelled wave heights were larger than in cut-oﬀ depth simulations and this result is an indication that modelling extreme wave heights of destructive meteotsunamis can beneﬁt from a ﬂooding and drying module incorporated into the model. Simulations for the event in Stari Grad were not as successful in reproducing extreme wave heights. Although including the ﬂooding and drying module enlarged the wave height, it was not a signiﬁcant improvement and there was no ﬂooding in the bay. Since it is assumed that the meteotsunami that hit that day only caused ﬂooding because the sea level was already extremely high due to a storm surge, these results conﬁrm that assumption. This study shows that in order to model meteotsunamis, it is necessary to understand how the model works and how well it reproduces resonant eﬀects connected to such waves. Further improvements could be made with more accurate modelling of atmospheric pressure disturbances, as well as including a ﬂooding and drying module that enables the reproduction of processes that take place once the waves reach the shore.