Session H1: Geophysical: Ocean II

Large-eddy simulation of open channel flow with surface cooling

Results are presented from large-eddy simulations of unstably stratified open channel flow driven by a pressure gradient with zero surface shear stress and a no-slip bottom. Unstable stratification is imposed by a constant cooling flux at the surface and an adiabatic bottom wall. Under neutrally stratified conditions, the flow is characterized by weak full-depth streamwise cells similar to, but less coherent than Couette cells in plane Couette flow. Surface cooling leads to full-depth convection cells characterized by greater coherency than Couette cells. The structure of the turbulence and turbulence statistics are analyzed with respect to the Rayleigh number (Ra) representative of the surface buoyancy relative to shear. Increased surface cooling and thus increased Ra leads to full-depth convection cells of greater spanwise size than Couette cells. Impact of the convection cells on mean velocity, root mean square of velocity, and budgets of resolved turbulent kinetic energy and Reynolds shear stress will be investigated as a function of Rayleigh number. These results motivate further studies of the effect of surface cooling on tidal boundary layers simulated via an oscillating pressure gradient.   

Evaluation of turbulence models in RANSS of wind-driven flow with full-depth Langmuir circulation

Large-eddy simulations of full-depth Langmuir circulation (LC) in a wind-driven shear current in neutrally-stratified shallow water have revealed modified bottom log-layer dynamics. For example, mixing due to LC induces a large wake region eroding the classical log-law velocity profile within the range 90 $<$ z+ $<$ 200. This has important implications on Reynolds-averaged Navier-Stokes simulations (RANSS) of the coastal ocean circulation. Turbulence models in RANSS are typically calibrated under the assumption of log-layer dynamics, which could potentially be invalid during occurrence of full-depth LC, often observed in shallow coastal shelf regions. Motivated by this, we perform RANSS of wind-driven flows with LC with a 1-D water column model in order to assess the performance of various turbulence parameterizations such as the k-epsilon model in capturing the disruption of log-layer dynamics induced by LC. Modifications to these models will be described in order to account for the presence of LC.   

Scalar transport in large-eddy simulation of Langmuir turbulence in shallow water

Large-eddy simulations (LES) of wind-driven shallow water flows with Langmuir turbulence have been conducted and associated passive scalar transport analyzed. In these flows, the largest scales of the Langmuir turbulence consist of full-depth Langmuir circulation (LC), parallel downwind-elongated, counter-rotating vortices acting as a secondary structure to the mean flow. Langmuir turbulence is generated by the interaction of the wind-driven shear current with the Stokes drift velocity induced by surface gravity waves. LES shows that Langmuir turbulence plays a major role in determining scalar transport throughout the entire water column and scalar transfer at the surface. Langmuir turbulence affects scalar transport and its surface transfer through 1. the full-depth homogenizing action of the large-scale LC and 2. the near-surface vertical turbulence intensity induced by the Stokes drift velocity shear. Results from simulations are analyzed in order to understand the effect of wind and wave forcing parameters on these two mechanisms.   

Numerical Simulations of an Asymptotically Reduced Model of Anisotropic Langmuir Turbulence

The Craik--Leibovich (CL) model of Langmuir circulation (LC), a prominent form of shear turbulence in the ocean surface boundary layer (BL), is a variant of the Navier--Stokes equations in which high-frequency surface wave dynamics are filtered. Various investigators have performed large-eddy simulations of the CL equations in moderate-sized domains. Extension of these simulations to wide domains, several hundred times the BL depth, is computationally intensive, yet is necessary for investigating the impact of LC on submesoscale upper ocean phenomena. To facilitate such simulations, Chini et al. (GAFD, 2009) derived asymptotically exact, reduced CL equations by exploiting the strongly anisotropic character of LC in the strong CL vortex-force limit using multiscale analysis. The reduced equations go beyond strictly 2D (downwind invariant) formulations by consistently incorporating the dominant 3D physical processes while averaging or filtering certain fast, fine-scale flow features. Here, secondary stability analysis and pseudospectral numerical simulations are performed to explore the dynamics of the reduced model. The simulations suggest a possible dynamical explanation for the commonly observed Y-junctions in LC surface signatures.   

Numerical Simulations of a Multiscale Model of Stratified Langmuir Circulation

Langmuir circulation (LC), a prominent form of wind and surface-wave driven shear turbulence in the ocean surface boundary layer (BL), is commonly modeled using the Craik--Leibovich (CL) equations, a phase-averaged variant of the Navier--Stokes (NS) equations. Although surface-wave filtering renders the CL equations more amenable to simulation than are the instantaneous NS equations, simulations in wide domains, hundreds of times the BL depth, currently earn the ``grand challenge" designation. To facilitate simulations of LC in such spatially-extended domains, we have derived multiscale CL equations by exploiting the scale separation between submesoscale and BL flows in the upper ocean. The numerical algorithm for simulating this multiscale model resembles super-parameterization schemes used in meteorology, but retains a firm mathematical basis. We have validated our algorithm and here use it to perform multiscale simulations of the interaction between LC and upper ocean density stratification.   

POD analysis of Langmuir circulation interacting with a crossed pressure gradient driven flow

The interaction between surface gravity wave and a wind driven shear current can lead to the generation of longitudinal counter-rotating pairs of vortices. This phenomenon is known as Langmuir Circulation and can extend to the full depth of the water column in coastal shallow waters. In cases of full depth Langmuir circulation, the cells are subjected to interactions with tidal currents of comparable magnitude as the current generated by wind shear and the intensity of the cells may be affected. The intent of this study is to apply proper orthogonal decomposition on results obtained through large eddy simulation, in order to evaluate the influence of a cross tidal current on the energy contained in Langmuir cells with a wave forcing varying in amplitude and wavelength. The stress Reynolds numbers considered will allow an equal stress for the pressure gradient driven flow and the wind driven flow and the total Reynolds number is set at 395.   

Langmuir circulation in sheared shallow waters

The instability of shallow water waves on a moderate shear to Langmuir circulation is considered. In such instances, specifically at the shallow end of the inner coastal region, the shear can significantly affect the drift giving rise to profiles markedly different from the simple Stokes drift. Since drift and shear are instrumental in the instability to Langmuir circulation, of key interest is how that variation in turn affects onset to Langmuir circulation. Also of interest is the effect to onset of various boundary conditions, viz Neumann and Cauchy. Two typical flow fields are considered, namely shear driven and current driven flow. Relative to the reference case, shear driven flow is found to be destabilizing and current driven stabilizing to Langmuir circulation. In current driven flow it is further found that multiple layers, as opposed to a single layer, of Langmuir circulation can form. Moreover the layers can extend into a region of flow beyond that in which the instability applies. Finally, while Neumann-Neumann are known to ensure the least stable spanwise wavenumber is zero and Cauchy-Neumann boundary conditions non zero, we find the latter further act to realize the long observed but unexplained large aspect-ratio shallow water Langmuir circulation.   

Interfacial flux in wetlands predicted using surface divergence measurements

Surface divergence has been shown to be a robust predictor of the air-water gas transfer velocity, $k$. We used this surface divergence model to investigate the effects of wind on $k$ in wetlands with emergent vegetation. We used fluoropolymer tubes to represent plant stems in a laboratory tank equipped with a wind tunnel. The fluoropolymer material provided optical access to the water flows directly around the ``stems'' for PIV. The $k$ values predicted by the surface divergence model from PIV-derived near surface divergence fields in the tank matched directly-measured $k$ values in the tank. The surface divergence fields also illustrated a mechanism for wind-induced gas transfer in wetlands with emergent vegetation. We observed an area of high surface divergence surrounding each stem and order of magnitude lower surface divergence in areas away from any stems. Thus we expect a nearly linear relationship between stem density and $k$ (if average wind speed in the emergent canopy is held constant). The agreement between modeled and measured $k$ values in this low-Reynolds-number, obstructed flow provides further support for the universality of the surface divergence model for $k$. The results also permit improved prediction of $k$ in wetlands.   

On similarity of wind-waves spectral shapes in laboratory and in ocean

Wind-wave field evolving in a compact laboratory facility that consists of a wind tunnel capable of generating wind speed that may exceed 15 m/s atop of a 5 m long wave tank is studied. Surface elevation measurements were carried out at numerous positions along the test section and at different mean wind flow rates. For each experimental condition, the accumulated records were long enough to contain at least $O$(10$^{4})$ dominant waves; the wave power spectra computed from the recorded time series cover up to 5 decades. Similarity of the spectral shapes in the vicinity of the peak frequency $f_{p}$ obtained at various fetches and wind conditions was observed. This similarity manifests itself when normalized frequency deviation from the peak value is introduced. Detailed comparison is carried out of spectra obtained in the present measurements at all fetches and wind conditions, to the similarly normalized JONSWAP spectrum that represents field experiments. When estimating spectral tail behavior, care was taken to consider frequencies exceeding about 3.5$f_{p}$ to alleviate the effect of bound waves. The spectral tails dependence on frequency follows the power law $f^{-n}$; the values of $n $being in the range $3 < n < 4$, depending on wave age. It thus can be concluded that the spectra of wind-waves in a small facility exhibit significant similarities to those obtained in field studies at much larger scales, as well as to theoretical estimates.