Goseberg, Nils

Horstmann, N.

Kerpen, Nils B.

Schlurmann, Torsten

Institutionelles Repositorium der Leibniz Universität Hannover

0 0.5 1 1.5 200.511.52Right Channel - Fresh water: max. diagonal wave runup Rd,max*H/d [m]Left Channel - Brine: max. diagonal wave runup Rd,max*H/d [m]H= 0.100mH= 0.150mH= 0.175mH= 0.200mH= 0.225mH= 0.250mH= 0.275mH= 0.300m0 0.1 0.2 0.3 0.400.20.40.60.8Surf similarity parameter ξ [-]Wave run up height Rmax/H0.1[-]Brine 18°CFresh water 18°CBrine 25°CFresh water 25°CBrine 30°CFresh water 30°CBrine 35°CFresh water 35°CHunt formula (Eq.2)EuroTop formula (Eq.3)0 0.5 1 1.5 2 2.5 3 3.5 400.511.522.533.54Right Channel - Fresh water: max. diagonal wave runup Rd,max[m]Left Channel - Brine: max. diagonal wave runup Rd,max[m]H= 0.100mH= 0.150mH= 0.175mH= 0.200mH= 0.225mH= 0.250mH= 0.275mH= 0.300mFit function for x > 2 m:y = -0.092x²+1.272x-0.178Investigation on the evolution and propagationof waves in highly concentrated fluidContact: Franzius-Institute for Hydraulics, Estuarineand Coastal EngineeringLeibniz Universität HannoverNienburger Straße 430167 Hannover / GermanyN. Horstmann, N. Kerpen, N. Goseberg, T. SchlurmannReferencesBattjes & Janssen, 1978. Energy loss and set-up due to breaking of random waves.Coastal Eng., pp. 569-587.Dean & Dalrymple, 1991. Water wave mechanics for engineers and scientists. Advanced Series onOcean Engineering - Volume 2. World Scientific Publishing. Singapore.EurOtop, 2007. Wave overtopping of sea defences and related structures.Assess. Manual. Die Küste. No. 73.Thornten & Guza, (1983). Transformation of wave height distribution. Journal of GeophysicalResearch. Vol. 88, No. C10, pp. 5925-5938Corresp. author: Dipl.-Ing. Nannina Horstmannhorstmann@fi.uni-hannover.de2 Physical model descriptionFig. 2 shows the model set-up in the twin flume. Both channels havea width of 2 m, a length of 28 m and a maximum water depth of 1 m.Waves in both channels are generated by only one wave paddleoperated in piston-type mode. One channel has been filled withbrine and the parallel channel with fresh water. A smooth,impermeable slope of 1:20 was installed to investigate wave run-up.Wave heights have been measured with six wired wave gauges inthe fresh water and with ultra sonic sensors in the brine.Orbital velocities were measured by means of 3D velocity sensor infront of the slope and currents due to wave run-up were recorded by2D velocity sensor mounted on the slope.In the beginning of the experimental phase, 24 referencetests with regular waves with fresh water have been performed inorder to calibrate and verify equivalent test conditions in bothchannels of the flume.The run-up height ofwaveswas documentedwith image records and the thickness of therun-up tongue was measured with pressure sensors installed in theslope.Fig. 2: Plan view (top) and cross section (bottom) of the physical modelDue to constructional limitations of the flume, the accuracy of theconcrete slope construction as well as due to the accuracy of themeasurement devices a relative deviation between run-up of left toright channel has been determined to 6.3%. Therefore, the run-upresults of brine hasbeen reducedwith this percentagedeviation.After the preliminary tests, regular waves have been generated toobtain closer insight of the physical effects and processes. In thetest matrix,he surf similarity parameterfor the regular waves ranges between 0.16 and 0.63.wave heights varied from 0.1 to 0.3 m and wave periodsfrom 0.8 to 3.2 s.With these conditions, tTherefore, that the viscosity depends on the temperature the wholetest matrix was repeated for different temperatures at 18, 25, 30 and35°C. Additionally, selected tests of the test matrix were alsorepeated in order to prove reproducibility. Altogether, 1116 tests forregularwaveshavebeenperformed.1 IntroductionIn the framework of an industry-funded research project in theDead Sea, Israel, the evolution and propagation of waves in a fluidwith high density (brine) was investigated. In general, the density aswell as the viscosity of water is neglected in wave theories and run-up formulas due to the fact that fresh water at 20 °C exhibits adensity of 1 t/m³ and a dynamic viscosity of 1x10 ³ kg/(m s). Yet, it isunknown how significant changes of these parameters influence thesensitivity of wave propagation and wave run-up on slopingbeaches. Hence, this project follows the scientific approach to studythe behaviour of a fluid, i.e. brine, stemming from the Dead Sea(Israel) with a density of 1.23 t/m³ and a dynamic viscosity at 20 °C of3.4x10 ³ kg/(m s). In a newly constructed wave (twin) flume with twoseparated channels (see pictures in Fig. 1) wave kinematics andrun-up of brine have been compared directly with fresh water wavekinematics and run-up.--3 Test resultsThe correlation of the wave heights measured at the toeof the slope in the right channel (x-axis) and brine wave heights inthe left channel (y-axis) that small wave heights ofbrine and freshwater generated in the flume are similar. In case oflarger amplitudes, wave heights in brine seem to be higher inrelation to fresh water. Analyzing the corresponding wavesteepness as given in Fig. 3bfresh waterin Fig. 3a showsfreshwater and brinewaves correlateandno clear tendency towards brinewaves canbe seen.4 OutlookFig. 3: Correlation of wave heights inthe right channel (fresh water) and in the left channel (brine) (a.)and correlation of wave steepness of measured wave heights (b.)measured at the toe of the slopeIn Fig. 4, results of maximum diagonal run-up of the totalnumber of tests are given. It can be seen thatRhigher than0.2md,maxthe scattered datacloud shifts towards freshwater run-up forwave heightsdue to increasing ratio ofH/d and increasing bottom influence.The for alltesting temperatures 18°C to 35°C are given in Fig. 6 together withthe formula for regular wave run-up (Eq. 2) developed byHunt (1959) andEurOtop formula (2007) forwave spectra (Eq. 3):results of maximum vertical run-up height R of brinemaxFig. 4: Correlation of maximum fresh water wave run-up R in the rightchannel and brine wave run-upmaxR in the left channel of the flumemaxFig. 6: Normalized max. wave run-up height of brine (dots) andfresh water (crosses) depending on the surf similarity parameterfor different testing temperaturesR /Hmax 0.1ξ[Eq. 2][Eq. 3]where and are the deepwater wave height andwave length,H L,0 0bβξ γisthe beach slope, is the surf similarity parameter, are factorsfor berm, slope roughness and oblique wave attack.γ γf , βFrom these results in Fig. 6, brine and fresh water run-up differ onlyslightly for all testing temperatures. It can be seen that the Huntformula (Eq. 2) underestimates both brine and fresh water run-up.EurOtop formulaEurOtop formula(Eq. 3) seems to bea linear fit for the brine run-up.With these results, the conclusion can be drawn that the applicationof (Eq. 3) is suitable for brinewith the given densityand viscosity and for the testedwaveparameter.In the next research steps, the slope in the twin flume will beincreased and the run-up results will be compared with the resultspresented in this poster. Furthermore, a detailed analysisconsidering energy transport and losses due to the high density andviscosity as well as an analysis of wave kinematics and wavepropagation, shoaling effect andwavebreakingwill be done.From this figure, the conclusion can be drawn that on the basis ofconcise experimental means and under the consideration of itsphysical model uncertainties nearly no clear difference in brine andfresh water wave run-up could be determined for small waveheights(i.e.H<0.2m) anda linear relationship canbeadopted.In case of higher wave heights (i.e. H > 0.2m) the relationshipbetween brine and fresh water run-up can be described by a fitfunction:[Eq. 1]Fig. 1: Wave flume construction as a twin flume with one wave paddleIn general, internal friction due to viscosity as well as energydissipation due to wave breaking and bottom friction changes whenbrine is considered instead of fresh or regular sea water. Thedensity and viscosity of brine yet differ by magnitudes fromliquid properties of fresh or sea water. Most of the formulas at handgiven e.g. in EurOtop (2007) base on an empirical fit of experimentalresults obtained for fresh or sea water. Here, the results of brinewave heights in contrast with fresh water wave heights are shownand finally brine wave run-up will be compared with formulas ofHunt (1959) and EurOtop (2007) .Fig. 5: Correlation of maximum wave run-up R multiplied with H/d forfresh water (Right channel) and brine (Left channel)maxConsidering the increasing bottom influence in case of larger waveheights, Fig. 5 shows the results for the multiplication of maximumdiagonal run-up with H/d which gives a linear relationshipbetweenbrine and freshwaterwave run-up.Rd,max

Investigation on the evolution and propagation of waves in highly concentrated fluid

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Institutionelles Repositorium der Leibniz Universität Hannover