White
Brian L.
White
Brian L.
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ArticleA vortexbased model of velocity and shear stress in a partially vegetated shallow channel(American Geophysical Union, 20080108) White, Brian L. ; Nepf, Heidi M.This paper presents a method for predicting the distributions of velocity and shear stress in shallow channels with a boundary of emergent vegetation. Experiments in a laboratory channel with model vegetation show that the velocity profile exhibits a distinct twolayer structure, consisting of a rapidly varying shear layer across the vegetation interface and a more gradual boundary layer in the main channel. In addition, coherent vortices are observed which span both layers, and are the dominant contributors to lateral momentum fluxes. From these observations, we propose a model for the vortexinduced exchange and find expressions for the width of momentum penetration into the vegetation, the velocity and shear stress at the vegetation edge, and the width of the boundary layer in the main channel. These variables, along with a momentum balance in the main channel, comprise a modeling framework which accurately reproduces the observed velocity and shear stress distributions. The predictions for the velocity and shear stress can provide a basis for modeling flood conveyance, overbank sediment transport, and scalar residence time in the vegetated layer.

ArticleA model for largeamplitude internal solitary waves with trapped cores(Copernicus Publications on behalf of the European Geosciences Union and the American Geophysical Union, 20100715) Helfrich, Karl R. ; White, Brian L.Largeamplitude internal solitary waves in continuously stratified systems can be found by solution of the DubreilJacotinLong (DJL) equation. For finite ambient density gradients at the surface (bottom) for waves of depression (elevation) these solutions may develop recirculating cores for wave speeds above a critical value. As typically modeled, these recirculating cores contain densities outside the ambient range, may be statically unstable, and thus are physically questionable. To address these issues the problem for trappedcore solitary waves is reformulated. A finite core of homogeneous density and velocity, but unknown shape, is assumed. The core density is arbitrary, but generally set equal to the ambient density on the streamline bounding the core. The flow outside the core satisfies the DJL equation. The flow in the core is given by a vorticitystreamfunction relation that may be arbitrarily specified. For simplicity, the simplest choice of a stagnant, zero vorticity core in the frame of the wave is assumed. A pressure matching condition is imposed along the core boundary. Simultaneous numerical solution of the DJL equation and the core condition gives the exterior flow and the core shape. Numerical solutions of timedependent nonhydrostatic equations initiated with the new stagnantcore DJL solutions show that for the ambient stratification considered, the waves are stable up to a critical amplitude above which shear instability destroys the initial wave. Steadily propagating trappedcore waves formed by lockrelease initial conditions also agree well with the theoretical wave properties despite the presence of a "leaky" core region that contains vorticity of opposite sign from the ambient flow.

PreprintOptimal transient growth in thininterface internal solitary waves( 20180110) Passaggia, PierreYves ; Helfrich, Karl R. ; White, Brian L.The dynamics of perturbations to largeamplitude Internal Solitary Waves (ISW) in twolayered ows with thin interfaces is analyzed by means of linear optimal transient growth methods. Optimal perturbations are computed through directadjoint iterations of the NavierStokes equations linearized around inviscid, steady ISWs obtained from the DubreilJacotinLong (DJL) equation. Optimal perturbations are found as a function of the ISW phase velocity c (alternatively amplitude) for one representative stratification. These disturbances are found to be localized wavelike packets that originate just upstream of the ISW selfinduced zone (for large enough c) of potentially unstable Richardson number, Ri < 0:25. They propagate through the base wave as coherent packets whose total energy gain increases rapidly with c. The optimal disturbances are also shown to be relevant to DJL solitary waves that have been modi ed by viscosity representative of laboratory experiments. The optimal disturbances are compared to the local WKB approximation for spatially growing KelvinHelmholtz (KH) waves through the Ri < 0:25 zone. The WKB approach is able to capture properties (e.g., carrier frequency, wavenumber and energy gain) of the optimal disturbances except for an initial phase of nonnormal growth due to the Orr mechanism. The nonnormal growth can be a substantial portion of the total gain, especially for ISWs that are weakly unstable to KH waves. The linear evolution of Gaussian packets of linear free waves with the same carrier frequency as the optimal disturbances is shown to result in less energy gain than found for either the optimal perturbations or the WKB approximation due to nonnormal effects that cause absorption of disturbance energy into the leading face of the wave. Twodimensional numerical calculations of the nonlinear evolution of optimal disturbance packets leads to the generation of largeamplitude KH billows that can emerge on the leading face of the wave and that break down into turbulence in the lee of the wave. The nonlinear calculations are used to derive a slowly varying model of ISW decay due to repeated encounters with optimal or free wave packets. Field observations of unstable ISW by Moum et al. (2003) are consistent with excitation by optimal disturbances.

ArticleShear instability and coherent structures in shallow flow adjacent to a porous layer(Cambridge University Press, 20071123) White, Brian L. ; Nepf, Heidi M.Results are presented from an experimental study of shallow flow in a channel partially obstructed by an array of circular cylinders. The cylinder array is a model for emergent vegetation in an open channel, but also represents a simple sparse porous medium. A shear layer with regular vortex structures forms at the edge of the array, evolving downstream to an equilibrium width and vortex size. The vortices induce nearly periodic oscillations with a frequency that matches the most unstable linear mode for a parallel shear flow. The shear layer is asymmetric about the array interface and has a twolayer structure. An inner region of maximum shear near the interface contains a velocity inflection point and establishes the penetration of momentum into the array. An outer region, resembling a boundary layer, forms in the main channel, and establishes the scale of the vortices. The vortex structure, educed by conditional sampling, shows strong crossflows with sweeps from the main channel and ejections from the array, which create significant momentum and mass fluxes across the interface. The sweeps maintain the coherent structures by enhancing shear and energy production at the interface. A linear stability analysis is consistent with the experimental results and demonstrates that the instability is excited by the differential drag between the channel and the array.

ArticleRetention time and dispersion associated with submerged aquatic canopies(American Geophysical Union, 20070418) Nepf, Heidi M. ; Ghisalberti, Marco ; White, Brian L. ; Murphy, E.The shear layer at the top of a submerged canopy generates coherent vortices that control exchange between the canopy and the overflowing water. Unlike free shear layers, the vortices in a canopy shear layer do not grow continuously downstream but reach and maintain a finite scale determined by a balance between shear production and canopy dissipation. This balance defines the length scale of vortex penetration into the canopy, δ e , and the region of rapid exchange between the canopy and overflow. Deeper within the canopy, transport is constrained by smaller turbulence scales. A twobox canopy model is proposed on the basis of the length scale δ e . Using diffusivity and exchange rates defined in previous studies, the model predicts the timescale required to flush the canopy through vertical exchange over a range of canopy density and height. The predicted canopy retention times, which range from minutes to an hour, are consistent with canopy retention inferred from tracer observations in the field and comparable to retention times for some hyporheic regions. The timescale for vertical exchange, along with the incanopy velocity, determines the minimum canopy length for which vertical exchange dominates water renewal. Shorter canopies renew interior water through longitudinal advection. Finally, canopy water retention influences longitudinal dispersion through a transient storage process. When vertical exchange controls canopy retention, the transient storage dispersion increases with canopy height. When longitudinal advection controls water renewal, dispersion increases with canopy patch length.

ArticleGravity currents and internal waves in a stratified fluid(Cambridge University Press, 20081114) White, Brian L. ; Helfrich, Karl R.A steady theory is presented for gravity currents propagating with constant speed into a stratified fluid with a general density profile. Solution curves for front speed versus height have an energyconserving upper bound (the conjugate state) and a lower bound marked by the onset of upstream influence. The conjugate state is the largestamplitude nonlinear internal wave supported by the ambient stratification, and in the limit of weak stratification approaches Benjamin's energyconserving gravity current solution. When the front speed becomes critical with respect to linear long waves generated above the current, steady solutions cannot be calculated, implying upstream influence. For nonuniform stratification, the critical longwave speed exceeds the ambient longwave speed, and the criticalFroudenumber condition appropriate for uniform stratification must be generalized. The theoretical results demonstrate a clear connection between internal waves and gravity currents. The steady theory is also compared with nonhydrostatic numerical solutions of the full lock release initialvalue problem. Some solutions resemble classic gravity currents with no upstream disturbance, but others show long internal waves propagating ahead of the gravity current. Wave generation generally occurs when the stratification and current speed are such that the steady gravity current theory fails. Thus the steady theory is consistent with the occurrence of either wavegenerating or steady gravity solutions to the dambreak problem. When the available potential energy of the dam is large enough, the numerical simulations approach the energyconserving conjugate state. Existing laboratory experiments for intrusions and gravity currents produced by fulldepth lock exchange flows over a range of stratification profiles show excellent agreement with the conjugate state solutions.