20.500.12556/RUL-138863 Analiza meritev turbulence v Bazenu II Luke Koper Analysis of turbulence measurements in Basin II of Port of Koper V magistrskem delu obravnavamo turbulenco v morju. V teoretičnem delu z Reynoldsovo dekompozicijo Navier-Stokesove enačbe izpeljemo hitrost spreminjanja kinetične energije povprečnega in turbulentnega dela toka. Turbulentno kinetično energijo kvalitativno povežemo z njeno viskozno izgubo $\varepsilon$, ki jo zato želimo čim natančneje oceniti. Po razpravi o spektru fluktuacije hitrosti in striženja uvedemo Nasmythov spekter, po razpravi o spektru fluktuacije temperature in njenega vertikalnega odvoda pa Batchelorjev spekter. Pri tem se sklicujemo na predpostavki o izotropni in zamrznjeni turbulenci. Oba spektra sta odvisna od $\varepsilon$, zato poiščemo najboljšo metodo za prileganje teoretičnega spektra spektru fluktuacije striženja in spektru vertikalnega odvoda fluktuacije temperature. Vse metode prilagodimo tako, da z njimi prilegamo teoretični spekter na območju uporabnih valovnih števil iz senzorjev sonde $\texttt{MSS90}$ proizvajalca Sea\&Sun. Kvaliteto metod, ki smo jih spisali sami, ugotavljamo s simulacijami po metodi Monte Carlo. Z njimi ugotovimo, da je najprimernejša metoda za ugotavljanje $\varepsilon$ iz spektra fluktuacije striženja metoda največjega verjetja, medtem ko so vse metode za ugotavljanje $\varepsilon$ iz spektra vertikalnega odvoda fluktuacije temperature zaradi prepočasne odzivnosti senzorja nezanesljive pri $\varepsilon > 10^{-8}~\rm{W/kg}$. Rezultati za $\varepsilon$ iz najboljše metode prileganja Nasmythovega spektra se na realnih podatkih iz sonde $\texttt{MSS90}$ dobro ujemajo z rezultati iz programske opreme za sondo. Vrednosti $\varepsilon$ iz senzorjev temperature so pri $\varepsilon < 10^{-8}~\rm{W/kg}$ tipično nekoliko manjše od vrednosti iz senzorjev striženja, pri $\varepsilon > 10^{-8}~\rm{W/kg}$ pa se z njimi sploh ne ujemajo, kar je skladno z rezultati Monte Carlo simulacij. Na koncu rezultate meritev $\varepsilon$ vzdolž Bazena II Luke Koper iz treh 25-urnih terenov leta 2008 in 2009 interpretiramo z meteorološkimi (temperatura zraka, hitrost vetra), hidrološkimi (plimovanje, pretok reke Rižane) in oceanografskimi pogoji (porazdelitve temperature, slanosti in gostote morske vode v Bazenu II Luke Koper ter profil izmerjenega toka pred bazenom in z njim povezanega striženja) ter manevri bližnjih plovil v času meritev. In the master thesis we deal with marine turbulence. In the theoretical part, we derive the rate of change of the mean and turbulent kinetic energy using the Reynolds decomposition of Navier-Stokes equation. The turbulent kinetic energy can be qualitatively represented by its viscous dissipation $\varepsilon$, so we seek the best estimate for the latter. Assuming an isotropic and frozen turbulence, we describe the spectra of the velocity fluctuation and the shear fluctuation and introduce the Nasmyth spectrum. Under the same assumptions, we also describe the spectra of temperature fluctuation and temperature fluctuation gradient and introduce the Batchelor spectrum. Both the Nasmyth and Batchelor spectra depend on $\varepsilon$, so we try to find the best method to assign the data to these spectra. All methods tested were adapted to handle only the data in the range of reliable wavenumbers from the sensors of Sea\&Sun's $\texttt{MSS90}$ probe, but can be adapted to any other probe. We test our methods using Monte Carlo simulations and conclude that the best method for fitting data to the Nasmyth spectrum is maximum likelyhood estimation. Meanwhile, all the methods for fitting data to the Batchelor spectrum are useless if $\varepsilon > 10^{-8}~\rm{W/kg}$ due to too long response time of the temperature sensor. Comparison of the results with real data from $\texttt{MSS90}$ shows good agreement between $\varepsilon$ from the best fit to Nasmyth spectrum and $\varepsilon$ from the probe software. On the other hand, $\varepsilon$ from the Batchelor spectrum is typically somewhat smaller than $\varepsilon$ from the Nasmyth spectrum when $\varepsilon < 10^{-8}~\rm{W/kg}$ and completely disagrees with $\varepsilon$ from the Nasmyth spectrum when $\varepsilon > 10^{-8}~\rm{W/kg}$, as expected from Monte Carlo simulations. Finally, we interpret the results of $\varepsilon$-measurements along the Basin II of Port of Koper, obtained in 2008 and 2009 during three 25-hour field campaigns, using meteorological (air temperature, wind speed), hydrological (tides, water level of the Rižana river), oceanographic conditions (temperature, salinity and density distribution in the basin, vertical shear of the currents near the basin) and also ship maneuvers during the measurements. izotropna turbulenca viskozna izguba turbulentne kinetične energije spekter fluktuacije hitrosti Nasmythov spekter spekter fluktuacije temperature Batchelorjev spekter Monte Carlo simulacije metoda največjega verjetja integralska metoda isotropic turbulence viscous dissipation of turbulent kinetic energy velocity fluctuation spectrum Nasmyth spectrum temperature fluctuation spectrum Batchelor spectrum Monte Cralo simulations maximum likelyhood estimate integral method true false false Slovenski jezik Angleški jezik Magistrsko delo/naloga 2022-08-24 08:15:08 2022-08-24 08:15:21 2022-09-15 04:17:17 0000-00-00 00:00:00 2022 0 0 0000-00-00 NiDoloceno NiDoloceno NiDoloceno 0000-00-00 0000-00-00 0000-00-00 123904 120221443 4826.pdf 4826.pdf 1 EB3886CC5693F647F5CCC4E7992F3400 c78c67a14ad567008120ea5ef886fa736cd47291404a12b4f09ec5184dca1a5c 1e0a1776-2374-11ed-92af-00155dcfd717 https://repozitorij.uni-lj.si/Dokument.php?lang=slv&id=159342 Fakulteta za matematiko in fiziko 0 0 0