Alexandru Sheremet

Stochastic nonlinear shoaling of directional spectra

We derive a deterministic directional shoaling model and a stochastic directional shoaling model for a gravity surface wave field, valid for a beach with parallel depth contours accounting for refraction and nonlinear quadratic (three wave) interactions. A new phenomenon of non-resonant spectral evolution arises due to the medium inhomogeneity. The kernels of the kinetic equation depend on the bathymetry through an integral operator. Preliminary tests carried out on laboratory data for a unidirectional case indicate that the stochastic model also works rather well beyond the region where the waves may be regarded as nearly Gaussian. The limit of its applicability is decided by the dispersivity of the medium (relative to the nonlinearity). Good agreement with both laboratory data and the underlying deterministic model is found up to a value of about 1.5 for the spectral peak Ursell number. Beyond that only the deterministic model matches the measurements.

New model for the emplacement, bioturbation, and preservation of fine-scaled sedimentary strata

We present a new quantitative model for the formation and preservation of sedimentary fabric based on interacting sedimentation and bioturbation. The model is one-dimensional and is forced by fluctuation of the sedimentation rate, which affects deposition of sediment possessing primary (depositional) fabric. Primary fabric is modified by bioturbation, which is represented as a depth-limited reaction term. Model output includes depth in seabed and preservation quotient, a measure of relative preservation of primary versus biogenic fabric at each depth. The required parameters (sedimentation rate and bioturbation rate) can be derived from studies of seabed processes; model output can be compared directly to observations of both modern and ancient sedimentary strata.

Effects of Cold Fronts on Bayhead Delta Development: Atchafalaya Bay, Louisiana, USA

Delta-building in the Holocene Mississippi River system is characterized by the successive construction and abandonment of delta lobes (Fisk, 1944; Kolb and Van Lopik, 1958; Frazier, 1967). Each major delta-building episode is accompanied by a rather orderly and predictable set of events starting with stream capture followed by filling of an interdistributary basin with lacustrine deltas and swamp deposits, building of a bayhead delta at the coast, and finally construction of a major shelf delta. The process of “delta switching” involves the initiation of a new major delta while the previously active delta is systematically abandoned. These changes associated with shifting fluvial input are commonly referred to as the “delta cycle” (Roberts, 1997). Each major delta lobe in the Mississippi River system is active for about 1000–1500 years.

A weakly dispersive edge wave model

Abstract We derive a general linear, weakly dispersive, Boussinesq-type equation that can be used to study edge waves on beaches with slow cross-shore variation of the depth and the alongshore current. The equation is more accurate than the non-dispersive shallow water equations and simpler than the fully dispersive elliptic mild slope equation (especially for a non-zero alongshore current). The improved performance of the new Boussinesq-type model is demonstrated using analytic solutions for edge waves on a plane beach with zero alongshore current.

Disintegration of Cnoidal Waves over Smooth Topography

The transformation of cnoidal waves in a basin with smooth topography is studied in the frame of the variable-coefficient Korteweg–de Vries equation and the generalized Zakharovs system. It is shown that the cnoidal structure of the propagating nonlinear wave is destroyed if the topography contains a periodic component with a characteristic scale close to the nonlinearity length. Focusing on waves in intermediate depth, a simple analytical model based on a two-harmonic representation of the cnoidal wave demonstrates the main features of the process of disintegration of the cnoidal structure of the nonlinear wave. Numerical simulations of the interaction of several harmonics confirm the analytical conclusions.

Complex Morpho-Hydrodynamic Response of Estuaries and Bays to Winter Storms: North-Central Gulf of Mexico, USA

Concepts pertaining to our understanding of estuarine dynamics have been heavily influenced by work carried out on the east and west coasts of the United States and western Europe (Pritchard, 1967). Antecedent geological controls have played an important role in predetermining the dominant type of estuaries along these coasts, namely drowned river valleys on coastal plains and fjord type systems tuned to moderate/high tidal regimes. Along the northern Gulf of Mexico (Fig. 1), however, estuaries are predominantly bar-built where the latest Holocene “stillstand” in sea level has permitted waves to build barrier islands/spits/beaches supplied by sediment from updrift and offshore sand sources (Stone et al., 1992; Stapor and Stone, 2004). Tides in the Gulf of Mexico are microtidal (0–0.3 m), predominantly diurnal and mixed (Marmer, 1954). Characteristically broad regions of low bathymetric relief result in minimal bathymetric steering of the otherwise low-frequency flow (Schroeder and Wiseman, 1999). Due to a high incidence of tropical cyclones in the northern Gulf (Stone et al., 1997; Muller and Stone, 2001), low profile barriers are susceptible to multiple breaches and inlet development. Such occurrences play an important role in estuarine circulation patterns due to phase lags in tidally driven waves. These interlinkages have, however, yet to be fully explored (Schroeder and Wiseman, 1999).

Dissipation of Wave Energy by Cohesive Sediments

Abstract : Wave energy dissipation by bottom muds is studied. A dissipation mechanism which contains explicit expressions of wavenumber modification due to a viscous bottom fluid is incorporated into a nonlinear wave shoaling model. This formulation allows a preliminary look at mud-induced energy decay without cumbersome root-finding numerics. Several cases of linear and nonlinear wave transformation over sloping and flat bottoms are run with the modified model. It is found that nonlinear energy exchange between spectral components, and a general trending toward spectral whiteness, is exacerbated in the presence of the mud layer. Strongest dissipation occurs only in the lower frequencies, contradicting field measurements of mud-induced decay which show dissipation over the entire frequency range. Thus, the need for a more comprehensive formulation of the interfacial dynamics between the water and the underlying mud layer is apparent.