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2-D Characteristics of Wave Deformation Due to Wave-Current Interactions with Density Currents in an Estuary

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water Article 2-D Characteristics of Wave Deformation Due to Wave-Current Interactions with Density Currents in an Estuary Woo-Dong Lee 1 , Norimi Mizutani 2 and Dong-Soo Hur 1,* 1 Department of Ocean Civil Engineering, Gyeongsang National University, Tongyeong 53064, Korea; [email protected] 2 Department of Civil and Environmental Engineering, Nagoya University, Nagoya 464-8603, Japan; [email protected] * Correspondence: [email protected]; Tel.: +82-55-772-9122 Received: 15 October 2019; Accepted: 2 January 2020; Published: 9 January 2020 Abstract: In this study, numerical simulations were conducted in order to understand the role of wave-current interactions in wave deformation. The wave-current interaction mechanisms, wave reflection and energy loss due to currents, the effect of incident conditions on wave-current interactions, the advection-diffusion characteristics of saltwater, and the effect of density currents on wave-current interactions were discussed. In addition, the effect of saltwater–freshwater density on wave-current interactions was investigated under a hypopycnal flow field via numerical model testing. Turbulence was stronger under the influence of wave-current interactions than under the influence of waves alone, as wave-current interactions reduced wave energy, which led to decreases in wave height. This phenomenon was more prominent under shorter wave periods and higher current velocities. These results increase our understanding of hydrodynamic phenomena in estuaries in which saltwater–freshwater and wave-current pairs coexist. Keywords: wave-current interaction; hypopycnal flow; estuarine hydraulics; estuarine currents; Navier–Stokes solver 1. Introduction In the ocean, various continually interacting physical external forces. In particular, estuaries are characterized by freshwater flows from land and saltwater flows from the ocean, which meet and form a major pathway for material transportation. Estuaries are complex, therefore it is difficult to investigate their hydrodynamic characteristics. Thus, it is critical to analyze the dynamic interactions between complex estuary features, including wave-current interaction mechanisms. Furthermore, it is necessary to understand the effect of a density current, which is generated by density differences between saltwater and freshwater, on wave-current interactions. In the estuary that exhibits highly complex hydraulic characteristics, the circulation type varies significantly according to vertical salinity distribution, tide, and wave [1,2]. However, if two fluids differing in density meet at the estuary, three types of flow and material transport patterns are largely exhibited [3,4]. As shown in Figure1, homopycnal flow occurs in the case of no density di fference, hypopycnal flow occurs when the influx flow has a lower density, and hyperpycnal flow occurs when the influx flow has a higher density. Hypopycnal flow generally occurs in the estuary when fresh river water flows in to ocean and interacts with ocean waves. However, most studies that attempted to analyze the wave-current interaction mechanism at the estuary region did not consider the density discrepancy between freshwater and saltwater, and were performed under homopycnal flow conditions. Meanwhile, due to the developments of measurement equipment, wave transformation, wave set-up, Water 2020, 12, 183; doi:10.3390/w12010183 www.mdpi.com/journal/water Water 2020, 12, 183 2 of 30 Water 2020, 12, x FOR PEER REVIEW 2 of 30 waveflow rate, set-up, salinity, flow andrate, temperature salinity, and at temperature the estuary are at beingthe estuary observed are [being5–9]. Inobserved some studies, [5–9]. In a modelsome studies,of the estuary a model was of composedthe estuary in was a three-dimensional composed in a three-dimensional experimental tank experi to measuremental tank wave to variationmeasure wavebased variation on wave-current based on interaction wave-current and interaction vertical salinity and vertical distribution salinity influenced distribution by density influenced current by densitybehavior current at the estuary behavior [10 ,11at]. the Onsite estuary investigations [10,11]. orOnsite transport investigations of three-dimensional or transport experiment of three- to dimensionalthe estuary requires experiment significant to the time estuary and money requires and significant only allows time for limitedand money information and only to beallows recorded for limitedat measurement information points. to be recorded at measurement points. (a) (b) (c) Figure 1. ThreeThree types types of of estuarine estuarine hydrodynamics hydrodynamics based based on on the the density density differences differences between river and sea/lakesea/lake water (Modified (Modified from Bates [3] [3] and Boggs [4]). [4]). ( (aa)) Homopycnal Homopycnal flow; flow; ( (bb)) hypopycnal hypopycnal flow; flow; (c) hyperpycnal flow.flow. Therefore, numericalnumerical simulations simulations are frequentlyare freque performedntly performed to analyze to the analyze hydraulic the characteristics hydraulic characteristicsof the estuary. of Most the ofestuary. studies Most have of used studies the model have basedused the on themodel depth-averaged based on the modeldepth-averaged [12–14] or modelthe 3-D [12–14] model or based the 3-D on σ model-coordinate based system on σ-coordinate [15,16]. This system numerical [15,16]. model This numerical cannot directly model simulate cannot directlywave behavior simulate due wave to a largebehavior discrepancy due to a between large discrepancy the calculation between grid andthe time.calculation To consider grid and the wavetime. Toreaction, consider the wavethe wave radiation reaction, stress estimatedthe wave from radi Simulatingation stress WAves estimated Nearshore from (SWAN Simulating [17]) orWAves WAve NearshoreModel (WAM (SWAN [18]) are[17]) substituted or WAve Model into the (WAM momentum [18]) are equations substituted [14, 19into,20 ].the momentum equations [14,19,20].Various theoretical, experimental and observational studies on waves propagating with currents haveVarious previously theoretical, been conducted experimental in the and field observational of coastal and studies ocean on engineering waves propagating [21–25]. with In particular, currents havethere previously have been manybeen conducted studies on in the the e fffieldects of co waveastal kinematics and ocean (changesengineering in the [21–25]. wave In number particular, and therefrequency have duebeen to many shoaling studies and refraction)on the effects and of dynamics wave kinematics (changes in(changes wave steepness in the wave and number wave-action and frequencyconservation) due accordingto shoaling to and wave-current refraction) and interaction dynamics [26 (changes–29]. Wave in wave kinematics steepness include and thewave-action effects of conservation)depth and current according in wavelength to wave-current variation interactio and dispersionn [26–29]. (Doppler Wave kinematics shift) according include to the opposing effects orof depthfollowing and current.current Wavein wavelength dynamics variation include energy and disper and actionsion (Doppler conservation shift) andaccording the variations to opposing in wave or followingheight and current. water levelWave [ 24dynamics,30]. Umeyama include energy [31] and an Leed action et al. conservation [32] explored and the the vertical variations distribution in wave heightof flow and and water turbulence level [24,30]. structures Umeyama under wave-current [31] and Lee et interactions al. [32] expl inored order the to vertical analyze distribution wave-current of flowinteraction and turbulence mechanisms. structures Smith et under al. [10 wave-current] investigated waveinteractions deformation in order by wave-currentto analyze wave-current interactions interaction mechanisms. Smith et al. [10] investigated wave deformation by wave-current interactions in a 3-D experimental basin with an estuary model. However, these experimental studies were not able to define the mechanisms of wave deformation and energy loss due to wave-current interactions. Water 2020, 12, 183 3 of 30 in a 3-D experimental basin with an estuary model. However, these experimental studies were not able to define the mechanisms of wave deformation and energy loss due to wave-current interactions. Numerical studies have reproduced past experimental results, but have focused mostly on wave deformation, neglecting to analyze the mechanisms behind wave-current interactions. In addition, Umeyama [33] measured and analyzed the flow velocity and trace of water particles by combining them with the particle image velocimetry (PIV) and particle tracking velocimetry (PTV) when the wave and current have the same direction. Chen et al. [34] studied the trace of water particles using the electronic hydrometer when the wave and current have opposite directions. However, none of the experimental studies conducted so far describe the wave deformation phenomenon and the mechanism of energy decrease clearly. The abovementioned studies focus on the motion of water particles from the wave-current interaction instead of the characteristics of wave deformation. Fernando et al. [35] discussed the topographic change resulting from the wave-current crossing angle, and the characteristics of local and vertical distribution of flow velocity. However, it is difficult to extend this study to analyze the effect of the hydraulic pattern. Lim and Madsen [36] analyzed the vertical flow velocity structure and shear velocity for wave-current
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