Alec Torres-Freyermuth

On the dynamics of wave-mud interaction: A numerical study

[1] Many previous studies consider wave attenuation over muddy seabeds and bottom boundary layer fluid-mud transport as two distinct research topics. Hence, various processes related to the physics of wave-mud interaction, such as turbulence-sediment interactions, rheological stresses, and nonlinear wave-wave interactions are incorporated rather artificially. The aim of this work is to present a new modeling approach which allows for the resolution of nonlinear wave propagation and bottom boundary layer mud transport with a single set of governing equations and closures. By adopting a fluid-mud modeling framework, a well-validated depth/phase-resolving wave propagation model, based on the Reynolds-Averaged Navier-Stokes (RANS) equations, is extended to model cohesive sediment transport. The numerical model consists of a set of governing equations based on the equilibrium Eulerian approach accurate for the fine sediment limit. The numerical model reduces to the clear fluid RANS equations when the sediment concentration approaches zero. Hence, the model is able to calculate continuously and consistently the nonlinear wave propagation, wave boundary layer processes, and fluid-mud transport without the need to prescribe the mud layer characteristics. Numerical simulations reveal several important physical processes that are critical for understanding the water-wave dynamics over muddy seabeds: (i) an enhancement of the wave boundary layer thickness due to the presence of the fluid-mud and rheological stress, which leads to a scaling relation between the enhanced wave boundary-layer and the fluid-mud layer and (ii) a direct wave amplitude dissipation due to rheological effects and clear evidences of low- and high-frequency wave attenuation via nonlinear energy transfer.

Wave Climate and Trends for the Gulf of Mexico: A 30-Yr Wave Hindcast

AbstractThis paper describes wave climate and variability in the Gulf of Mexico based on a 30-yr wave hindcast. The North American Regional Reanalysis wind fields are employed to drive a third-generation spectral wave model with high spatial (0.005°–0.06°) and temporal (3 hourly) resolution from 1979 through 2008. The wave hindcast information is validated using National Data Buoy Center (NDBC) data and altimeter wave information (GlobWave). The model performance is satisfactory (r2 ~ 0.90) in the Gulf of Mexico and to a lesser extent in the Caribbean Sea (r2 ~ 0.87) where only locally generated waves are considered. However, the waves generated by the Caribbean low-level jet (CLLJ) are discussed in this work. Subsequently, the yearly/monthly mean and extreme wave climates are characterized based on the (30 yr) wave hindcast information. The model results show that the mean wave climate is mainly modulated by winter cold fronts (nortes) in the Gulf of Mexico, whereas extreme wave climate is modulated by b...

Longshore Sediment Transport on the Northern Coast of the Yucatan Peninsula

Abstract Appendini, C.M.; Salles, P.; Mendoza, E.T.; López, J., and Torres-Freyermuth, A., 2012. Longshore sediment transport on the northern coast of the Yucatan Peninsula. This paper presents a qualitative assessment of coastal processes along the northern coast of the Yucatan Peninsula based on a method used to estimate the potential longshore sediment transport. Despite the deep-water low-energy wave conditions (Hs  =  1 m) in the study area, erosion is critical in many locations, including the urbanized stretches of coast. The waves were characterized using a 12 y (1997–2009) deep-water wave hindcast data (WAVEWATCH III) as forcing for a spectral wind-wave numerical model (MIKE 21 SW) used to propagate the waves to the coast. Simulated time series of significant wave height, peak period, and direction are compared against in situ measurements at 10 m water depth. Numerical results are further employed for estimation of the nearshore wave climate along the coast. Wave conditions are strongly affected by the wide continental shelf in front of the northern Yucatan Peninsula, with an increase in wave energy at the eastern part of the peninsula where the shelf narrows. The nearshore wave climate is employed for the qualitative assessment of potential longshore sediment transport (LITDRIFT model) in the study area. The sediment transport calculations are consistent with both volume impoundment estimations at a groin and dredging estimates at a harbor (−35,000 m3/y). A net westward potential longshore sediment transport is found along the entire coast, ranging between −20,000 and −80,000 m3/y, except west of Holbox, where longshore transport direction is inverted. Based on sediment transport gradients, potential erosion and deposition areas are identified. Erosion/accretion patterns at nonurbanized areas are consistent with field observations. This dominant westward longshore transport suggests an extremely sensitive shoreline to littoral barriers, as supported by observations in the most urbanized areas. These areas show no gradients on longshore sediment transport, whereas beach erosion is a common feature enhanced by littoral barriers. Shore protection should then be oriented toward sediment management strategies. Resumen En este trabajo se presenta una evaluación cualitativa de los procesos costeros a lo largo de la costa norte de Yucatán, en base a una metodología para la estimación del transporte potencial de sedimentos. A pesar de las condiciones de baja energía de oleaje (Hs  =  1 m) en la zona, los problemas de erosión costera son críticos en varias localidades, incluyendo zonas urbanizadas. Se utilizaron 12 años de datos (1979–2009) de un retroanálisis de oleaje (WAVEWATCH III) como condiciones de frontera para un modelo de oleaje en la zona costera (MIKE 21 SW). Las series de tiempo de altura significante, periodo pico y dirección de oleaje se compararon con mediciones in situ a 10 m de profundidad. Las condiciones de oleaje son muy afectadas por la amplia plataforma continental frente a la costa de Yucatán, mostrando una tendencia a incrementar al acercarnos a la parte este de la península donde la plataforma es reducida. El clima de oleaje determinado a lo largo de la costa fue utilizado para evaluar el transporte potencial de sedimentos (modelo LITDRIFT) en la zona de estudio. Los cálculos de transporte son consistentes con las estimaciones en la zona (−35,000 m3/año). Se determinó una tendencia dominante hacia el oeste para el transporte potencial de sedimentos en prácticamente toda la costa, con valores entre −20,000 y −80,000 m3/año, siendo que únicamente al oeste de Holbox hay una inversión en la dirección del transporte. Los patrones de erosión/acumulación en las zonas no urbanizadas son consistentes con observaciones de campo. La dominancia del transporte de sedimentos con dirección al oeste indica que es una costa muy sensible a las barreras litorales, lo cual es sustentado por las observaciones en las zonas densamente urbanizadas. Estas zonas no muestran gradientes en el transporte de sedimentos, sin embargo la erosión es una característica común como resultado de las barreras litorales. De esta manera, la protección costera deberá orientarse a estrategias de manejo de sedimento.

Effects of reef roughness on wave setup and surf zone currents

ABSTRACT Franklin, G.L., Mariño-Tapia, I. and Torres-Freyermuth, A., 2013. Effects of reef roughness on wave setup and surf zone currents. Circulation in reef systems controls an important number of key processes, such as the transport and dispersion of larvae, nutrients, and sediments. In fringing reef systems, where a shallow lagoon backs onto the reef crest, circulation appears to be dominated by wave breaking. Despite the identified importance of wave driven flows within reef systems, there is a lack of detailed knowledge on these processes within the surf zone of reef crests and the effects reef roughness has on these flows. A numerical study, using two-dimensional (2DV) simulations, was carried out in order to improve the understanding of wave-driven flows in the surf zone of a fringing reef. The model used is Cornell Breaking Wave and Structures (COBRAS), which solves the Reynolds-Averaged Navier-Stokes (RANS) equations with a turbulence closure scheme. The effect of different reef roughness on wave height, wave setup, infragravity waves and mean flows was studied. Model results revealed that wave setup increases significantly (~22%) with increasing bed roughness, consistent with prior studies on sandy beaches. Furthermore, cross-shore velocity structure is heavily affected by bed roughness. The latter implies that the coral reef flattening trend observed world-wide could result in a decrease in the circulation within the lagoon with important implications for reef health.

On the role of infiltration and exfiltration in swash zone boundary layer dynamics

Boundary layer dynamics are investigated using a 2-D numerical model that solves the Volume-Averaged Reynolds-Averaged Navier-Stokes equations, with a VOF-tracking scheme and a k - ϵ turbulence closure. The model is validated with highly resolved data of dam break driven swash flows over gravel impermeable and permeable beds. The spatial gradients of the velocity, bed shear stress, and turbulence intensity terms are investigated with reference to bottom boundary layer (BL) dynamics. Numerical results show that the mean vorticity responds to flow divergence/convergence at the surface that result from accelerating/decelerating portions of the flow, bed shear stress, and sinking/injection of turbulence due to infiltration/exfiltration. Hence, the zero up-crossing of the vorticity is employed as a proxy of the BL thickness inside the shallow swash zone flows. During the uprush phase, the BL develops almost instantaneously with bore arrival and fluctuates below the surface due to flow instabilities and related horizontal straining. In contrast, during the backwash phase, the BL grows quasi-linearly with less influence of surface-induced forces. However, the infiltration produces a reduction of the maximum excursion and duration of the swash event. These effects have important implications for the BL development. The numerical results suggest that the BL growth rate deviates rapidly from a quasi-linear trend if the infiltration is dominant during the initial backwash phase and the flat plate boundary layer theory may no longer be applicable under these conditions.

Storm characterization and coastal hazards in the Yucatan Peninsula

ABSTRACT Mendoza, E.T., Trejo-Rangel., M. A., Salles, P., Appendini, C.M., Lopez-Gonzalez, J. and Torres-Freyermuth, A., 2013. Storm characterization and coastal vulnerability in the Yucatan Peninsula A preliminary coastal hazard potential assessment due to storm impacts in terms of erosion and flooding for the Yucatan coast is presented. Firstly, a 30-year wave hindcast is employed in order to characterize the coastal storms by creating a 5-class storm scale in terms of wave information. Subsequently, the storm classification is converted to one based on the consequences over 26 beach profile sections located along the Yucatan coast. The storm consequences were classified according to their flood and erosion potential by means of parametric and numerical model results which are correlated with key beach characteristics such as beach width and maximum beach height. According to the obtained results, the storms were characterized in five different categories and it was found that the Yucatan coast presents higher threat to flood than to erosion during the impact of storms.

On the Role of Climate Change on Wind Waves Generated by Tropical Cyclones in the Gulf of Mexico

To generate projections of wave climate associated to tropical cyclones is a challenge due to their short historical record of events, their low occurrence, and the poor wind field resolution in General Circulation Models. Hence, synthetic tropical cyclones provide an alternative to overcome such limitations, improving robust statistics under both present and future climates. We use synthetic events to characterize present and future wave climate associated with tropical cyclones in the Gulf of Mexico. The NCEP/NCAR atmospheric reanalysis and the Coupled Model Intercomparison Project Phase 5 models NOAA/GFDL CM3 and UK Met Office HADGEM2-ES, were used to derive present and future wave climate under RCPs 4.5 and 8.5 scenarios. The GFDL model shows less bias in the present climate with respect to NCEP/NCAR results. Furthermore, the numerical results suggest an increase in wave activity for the future climate in the Caribbean Sea and Northern Gulf of Mexico, whereas some areas are expected to decrease the wave energy, as the stretch of the Gulf of Mexico between Yucatan and Southern Texas. The results have practical implications on the design of offshore structures. The 100-year design wave based on the present climate might result in under/over design of structures, owing to the lifespan of a structure that is within the future wave climate period.

On dam-break wave propagation and its implication to sediment erosion

This paper presents experimental and numerical studies of the evolution of dam-break driven wave on a horizontal smooth bed and its implication to sediment transport. Laboratory experiments are carried out using high-speed video images in order to obtain the spatio-temporal evolution of the free surface. Furthermore, a numerical model based on the two-dimensional-vertical Reynolds-averaged Navier–Stokes equations, with a k−ϵ turbulence closure and a volume of fluid method, is validated with the laboratory observations. The numerical model is shown to accurately predict the measured free-surface profiles, the wave-front velocities, as well as the impingement location of the first forward breaking jet. In order to bring more insight on dam-break wave induced erosion, the numerical model is extended for simulating suspended sediment transport. Model results suggest that the maximum bed-erosion occurs at the gate location and it moves farther downstream depending on the ratio between the downstream and the upstream water depth.

On the mechanisms of low‐frequency wave attenuation by muddy seabeds

Low-frequency (LF) wave energy increases as the waves shoal into shallow waters. However, recent field observations reported an unexpected near-shore LF wave energy dissipation on muddy seabeds, which cannot be explained by the classic two-layer formulation. Therefore, this phenomenon has been ascribed to either direct dissipation or nonlinear energy transfer. We investigate, by means of a two-layer nonlinear model, the role of the wave nonlinearity and mud viscosity in controlling these two competing mechanisms of mud-induced LF wave attenuation. Bispectral analysis of the simulated cases reveals the existence of three distinct LF wave attenuation regimes, which determine if the LF wave energy losses are owing to either nonlinear energy transfer or direct dissipation. These regimes can be predicted based on the Ursell number, whereas the mud viscosity controls the amount of energy transfer. The present findings clarify apparent inconsistencies in the literature regarding the mechanisms of LF wave attenuation by mud.

An Engineering Approach for Modeling Hurricane Extreme Waves Using Analytical and Numerical Tools

This work aims to evaluate the ocean wave statistics (i.e., significant height, peak period, mean wave direction, and spectral form) under hurricane events, at any geographical point and coastal location by employing two different approaches. First, by the use of classical fast and mid-accurate analytical engineering tools comparing three classical set of equations (Bretschneider 1990; Young 1988; and the Shore Protection Manual SPM 1984) and their further validation against instrumental data provided by the National Data Buoy Centre (NDBC). On the other hand, by using a high-accurate numerical approach is proposed, using the unstructured-mesh SWAN spectral wave model (Zijlema et al. 2010), comparing the results between the stationary and non stationary approach, and validating the nearshore ocean wave characteristics with measured data at different water depth locations. Both approaches are forced with accurate pressure and wind speed fields obtained with classical and well-known parametric equations (i.e., Holland 1980; Hydromet-Rankin Vortex 1980; and Bretschneider 1990), integrated with the NCEP/NCAP wind fields. Hurricane waves for both approaches are validated with instrumental data from the NDBC measured for hurricanes: Katrina (2005); Gilbert (1998); Mitch (1998); Wilma (2005); and Ike (2008). Comparisons between both approaches have been made. Additionally, user recommendations and a sensitivity analysis about the optimization and design of the numerical mesh are presented, taking into account an efficient design of the numerical finite element mesh of the model, and the optimal spatial distribution of the nodes and elements along the hurricane track. The present study provides an efficient and easy engineering-mathematical tool to evaluate the hurricane induced waves, identifying its application limits and derived recommendations. Moreover, an accurate numeric methodology is here described, which allows to obtain the historical ocean wave data for all the historic events and tracks for North Atlantic and Pacific hurricanes, registered since mid-50’s (lat-lon tracks, and central pressures provided by NOAA and the National Hurricane Centre), by improving the hurricane wind fields of any reanalysis database. Finally providing improved knowledge for coastal and harbor design considerations / construction purposes.