Publisher Correction: Impact of wave whitecapping on land falling tropical cyclones
A correction to this article has been published and is linked from the HTML and PDF versions of this paper. The error has not been fixed in the paper.
Wave-Current Interaction in an Oceanic Circulation Model with a Vortex-Force Formalism: Application to the Surf Zone
Abstract A vortex-force formalism for the interaction of surface gravity waves and currents is implemented in a three-dimensional (3D), terrain-following, hydrostatic, oceanic circulation model (Regional Oceanic Modeling System: ROMS; Shchepetkin and McWilliams, 2005 ). Eulerian wave-averaged current equations for mass, momentum, and tracers are included in ROMS based on an asymptotic theory by McWilliams et al. (2004) plus non-conservative wave effects due to wave breaking, associated surface roller waves, bottom streaming, and wave-enhanced vertical mixing and bottom drag especially for coastal and nearshore applications. The currents are coupled with a spectrum-peak WKB wave-refraction model that includes the effect of currents on waves, or, alternatively, a spectrum-resolving wave model (e.g., SWAN) is used. The coupled system is applied to the nearshore surf zone during the DUCK94 field measurement campaign. Model results are compared to the observations and effects of parameter choices are investigated with emphasis on simulating and interpreting the vertical profiles for alongshore and cross-shore currents. The model is further compared to another ROMS-based 3D coupled model by Warner et al. (2008) with depth-dependent radiation stresses on a plane beach. In both tests the present model manifests an onshore surface flow and compensating offshore near-bed undertow near the shoreline and around the breaking point. In contrast, the radiation-stress prescription yields significantly weaker vertical shear. The currents’ cross-shore and vertical structure is significantly shaped by the wave effects of near-surface breaker acceleration, vertical component of vortex force, and wave-enhanced pressure force and bottom drag.
Inhomogeneous Boundary Value Problems for Compressible Navier-Stokes Equations: Well-Posedness and Sensitivity Analysis
In this paper compressible, stationary Navier–Stokes equations are considered. A framework for analysis of such equations is established. In particular, the well-posedness for inhomogeneous boundary value problems of elliptic-hyperbolic type is shown. Analysis is performed for small perturbations of the so-called approximate solutions that take form (1.12). The approximate solutions are determined from Stokes problem (1.11). The small perturbations are given by solutions to (1.13). The uniqueness of solutions for problem (1.13) is proved, and, in addition, the differentiability of solutions with respect to the coefficients of differential operators is shown. The results on the well-posedness of nonlinear problems are interesting on their own and are used to obtain the shape differentiability of the drag functional for incompressible Navier–Stokes equations. The shape gradient of the drag functional is derived in the classical and useful for computations form; an appropriate adjoint state is introduced to ...