A mathematical model of spit growth and barrier elongation: Application to Fire Island Inlet (USA) and Badreveln Spit (Sweden)

A mathematical model of spit growth and barrier elongation adjacent to an inlet (of arbitrary width), supplied by sediment coming from longshore sediment transport, was developed based on the spit growth model proposed by Kraus (1999). The fundamental governing equation is the conservation equation for sand, where the width of the spit is assumed constant during growth. The portion of the longshore sediment transport feeding the spit has been estimated based on the ratio between the depth of the inlet channel and the depth of active longshore transport. Sediment transport from the channel due to the inlet flow, as well as other sinks of sand (e.g., dredging), are taken into account. Measured data on spit elongation at Fire Island Inlet, United States, and at Badreveln Spit, Sweden, were used to validate the model. The simulated results agree well with the measured data at both study sites, where spit growth at Fire Island was restricted by the inlet flow and the growth at Badreveln Spit was unrestricted. The model calculation for Fire Island Inlet indicates that the dredging to maintain channel navigation is the major reason for the stable period observed from 1954 to 1994 at the Fire Island barrier. The average annual net longshore transport rate at the eastern side of the Fire Island inlet obtained in this study was about 220,000 m³/yr, of which approximately 165,000 m³/yr (75% of the net longshore transport) is deposited in the inlet feeding the spit growth, whereas the remaining portion (25%) is bypassed downdrift through the ebb shoal complex.     

Discussion of “Measurements of sheet flow transport in acceleration-skewed oscillatory flow and comparison with practical formulations” by D.A. van der A,T. O'Donoghue and J.S. Ribberink

The authors present a very interesting data set on the acceleration effects on sheet flow transport and compare their experimental results with different transport practical formulas. However, they omit some previous work by Camenen and Larson (2007) that we would like to bring to the authors' attention. A more extensive discussion on some aspects of the acceleration effects is also lacking in their paper and, thus, additional material is provided here.     

A numerical model of beach morphological evolution due to waves and currents in the vicinity of coastal structures

A numerical model was developed of beach morphological evolution in the vicinity of coastal structures. The model includes five sub-models for random wave transformation, surface roller development, nearshore wave-induced currents, sediment transport, and morphological evolution. The model was validated using high-quality data sets obtained during experiments with a T-head groin and a detached breakwater in the basin of the Large-scale Sediment Transport Facility at the Coastal and Hydraulics Laboratory in Vicksburg, Miss, USA. The simulations showed that the model reproduced well the wave conditions, wave-induced currents, and beach morphological evolution in the vicinity of coastal structures. Both salient and tombolo formation behind a T-head groin and a detached breakwater were simulated with good agreement compared to the measurements.     

A model for underpressure development in a glacial valley,an example from Adventdalen,Svalbard

The underpressure observed in the glacial valley Adventdalen at Svalbard is studied numerically with a basin model and analytically with a compartment model. The pressure equation used in the basin model, which accounts for underpressure generation, is derived from mass conservation of pore fluid and solid, in addition to constitutive equations. The compartment model is derived as a similar pressure equation, which is based on a simplified representation of the basin geometry. It is used to derive analytical expressions for the underpressure (overpressure) from a series of unloading (loading) intervals. The compartment model gives a characteristic time for underpressure generation of each interval, which tells when the pressure state is transient or stationary. The transient pressure is linear in time for short‐time spans compared to the characteristic time, and then it is proportional to the weight removed from the surface. We compare different contributions to the underpressure generation and find that porosity rebound from unloading is more important than the decompression of the pore fluid during unloading and the thermal contraction of the pore fluid during cooling of the subsurface. Our modelling shows that the unloading from the last deglaciation can explain the present day underpressure. The basin model simulates the subsurface pressure resulting from erosion and unloading in addition to the fluid flow driven by the topography. Basin modelling indicates that the mountains surrounding the valley are more important for the topographic‐driven flow in the aquifer than the recharging in the neighbour valley. The compartment model turns out to be useful to estimate the orders of magnitude for system properties like seal and aquifer permeabilities and decompaction coefficients, despite its geometric simplicity. We estimate that the DeGeerdalen aquifer cannot have a permeability that is higher than 1 · 10^?18 m², as otherwise, the fluid flow in the aquifer becomes dominated by topographic‐driven flow. The upper value for the seal permeability is estimated to be 1 · 10^?20 m², as higher values preclude the generation and preservation of underpressure. The porosity rebound is estimated to be <0.1% during the last deglaciation using a decompaction coefficient α_r = 1 · 10^?9 Pa^?1.     

A new formula for the total longshore sediment transport rate

A new predictive formula for the total longshore sediment transport (LST) rate was developed from principles of sediment transport physics assuming that breaking waves mobilize the sediment, which is subsequently moved by a mean current. Six high-quality data sets on hydrodynamics and sediment transport collected during both field and laboratory conditions were employed to evaluate the predictive capability of the new formula. The main parameter of the formula (a transport coefficient), which represents the efficiency of the waves in keeping sand grains in suspension, was expressed through a Dean number based on dimensional analysis. The new formula yields predictions that lie within a factor of 0.5 to 2 of the measured values for 62% of the data points, which is higher than other commonly employed formulas for the LST rate such as the CERC equation or the formulas developed by Inman–Bagnold and Kamphuis, respectively. The new formula is well suited for practical applications in coastal areas, as well as for numerical modeling of sediment transport and shoreline change in the nearshore.