Peter Diamessis

Similarity scaling and vorticity structure in high-Reynolds-number stably stratified turbulent wakes

The mean velocity profile scaling and the vorticity structure of a stably stratified, initially turbulent wake of a towed sphere are studied numerically using a high-accuracy spectral multi-domain penalty method model. A detailed initialization procedure allows a smooth, minimum-transient transition into the non-equilibrium (NEQ) regime of wake evolution. A broad range of Reynolds numbers, Re = UD/ν ∈ [5 × 10 3 , 10 5 ] and internal Froude numbers, Fr = 2 U /( ND ) ∈ [4, 64] ( U , D are characteristic velocity and length scales, and N is the buoyancy frequency) is examined. The maximum value of Re and the range of Fr values considered allow extrapolation of the results to geophysical and naval applications. At higher Re , the NEQ regime, where three-dimensional turbulence adjusts towards a quasi-two-dimensional, buoyancy-dominated flow, lasts significantly longer than at lower Re . At Re = 5 × 10 3 , vertical fluid motions are rapidly suppressed, but at Re = 10 5 , secondary Kelvin–Helmholtz instabilities and ensuing turbulence are clearly observed up to Nt ≈ 100. The secondary motions intensify with increasing stratification strength and have significant vertical kinetic energy. These results agree with existing scaling of buoyancy-driven shear on Re / Fr 2 and suggest that, in the field, the NEQ regime may last up to Nt ≈ 1000. At a given high Re value, during the NEQ regime, the scale separation between Ozmidov and Kolmogorov scale is independent of Fr . This first systematic numerical investigation of stratified turbulence (as defined by Lilly, J. Atmos. Sci. vol. 40, 1983, p. 749), in a controlled localized flow with turbulent initial conditions suggests that a reconsideration of the commonly perceived life cycle of a stratified turbulent event may be in order for the correct turbulence parametrizations of such flows in both geophysical and operational contexts.

Interaction of vorticity, rate-of-strain, and scalar gradient in stratified homogeneous sheared turbulence

The structure and dynamics of stably stratified homogeneous sheared turbulence is investigated in terms of the triadic interaction of vorticity ω, rate-of-strain S, and scalar (density fluctuation) gradient G≡∇ρ′. Results of direct numerical simulations are presented. Due to the presence of the mean velocity and scalar gradients, distinct directional preferences develop which affect the dynamics of the flow. The triadic interaction is described in terms of the direct coupling of primary mechanism pairs and influential secondary effects. Interaction of ω and S is characterized by the coupling of vortex stretching and locally-induced rotation of the S axes. Due to the intrinsic directionality of baroclinic torque, the generated ω acts to impede S axes rotation. Interaction of ω and G involves an inherent negative feedback between baroclinic torque and reorientation of G by ω. This causes baroclinic torque to act as a sink which promotes decay of ω2. Interaction of S and G is characterized by a positive feed...

Self-preservation in stratified momentum wakes

A general model is described for drag wakes in a linearly stratified fluid, based on the self-preservation of the flow. It is assumed that the buoyancy-controlled self-similar wake expands in the horizontal direction due to turbulent diffusion and in the vertical direction due to viscous diffusion. The mean characteristics of the wake (height, width and velocity defect) are analytically derived and show good agreement with existing data from experimental and numerical results. Moreover, the three regimes previously found in the literature that characterize different dynamical phases of the wake evolution are recovered, and two new regimes are found. The model allows for prediction of characteristic length and velocity scales at the high Reynolds numbers of large-scale applications of geophysical and naval origin.

Reflection of an internal gravity wave beam off a horizontal free-slip surface

The reflection of a planar finite-amplitude internal gravity wave beam off a free-slip flat horizontal surface is investigated numerically in a uniformly stratified Boussinesq fluid. Nonlinear effects such as mean currents and harmonics are observed in the wave reflection zone. Mean currents form a stationary, vertically oscillatory, layered structure under the free-slip reflecting surface. The vertical wavelength of the mean-flow layers equals half of the vertical wavelength of the reflecting wave. An empirical predictive model for the steady-state mean flow strength, based on the degree of wave nonlinearity and hydrostaticity, is proposed and subsequently compared to the weakly nonlinear theory by Tabaei et al. [J. Fluid Mech. 526, 217–243 (2005)10.1017/S0022112004002769]. Very strong agreement between simulation results and theory is observed for all waves considered, suggesting although weakly nonlinear in its formulation, the Tabaei et al. theory is valid for the full range of finite amplitudes for w...

The interaction of vorticity and rate-of-strain in homogeneous sheared turbulence

The coupled interaction of vorticity ω and rate-of-strain S in homogeneous sheared turbulence is investigated using direct numerical simulation. Conditional sampling and comparison with linear simulations reveal various aspects of the structure and dynamics. Due to the influence of the imposed ω and S, distinct directional features develop. Initial stretching of fluctuating ω by mean extensional strain and the presence of mean vorticity establish a predominant misalignment of ω with respect to the principal axes of S. The associated locally induced rotation of the S axes results in preferred orientations in ω and S. In high amplitude rotation-dominated regions of the flow, distinct characteristics are exhibited by the pressure Hessian Π due to the presence of small-scale spatial structure. Nonlocally induced S axes rotation through Π tends to counteract locally induced rotation in these regions. These features are absent in the linear flow which suggests a lack of spatial coherence in the corresponding in...

High-order discontinuous element-based schemes for the inviscid shallow water equations: spectral multidomain penalty and discontinuous Galerkin methods

Two commonly used types of high-order-accuracyelement-based schemes, collocationbased spectral multidomain penalty methods (SMPM) and nodal discontinuous Galerkin methods (DGM), are compared in the framework of the inviscid shallow water equations. Differences and similarities in formulation are identified, with the primary difference being the dissipative term in the Rusanov form of the numerical flux for the DGM that provides additional numerical stability; however, it should be emphasized that to arrive at this equivalence between SMPM and DGM requires making specific choices in the construction of both methods; these choices are addressed. In general, both methods offer a multitude of choices in the penalty terms used to introduce boundary conditions and stabilize the numerical solution. The resulting specialized class of SMPM and DGM are then applied to a suite of six commonly considered geophysical flow test cases, three linear and three non-linear; we also include results for a classical continuous Galerkin (i.e., spectral element) method for comparison. Both the analysis and numerical experiments show that the SMPM and DGM are essentially identical; both methods can be shown to be equivalent for very special choices of quadrature rules and Riemann solvers in the DGM along with special choices in the type of penalty term in the SMPM. Although we only focus our studies on the inviscid shallow water equations the results presented should be applicable to other systems of nonlinear hyperbolic equations (such as the compressible Euler equations) and extendable to the compressible and incompressible Navier-Stokes equations, where viscous terms are included.

Spatial characterization of vortical structures and internal waves in a stratified turbulent wake using proper orthogonal decomposition

Proper orthogonal decomposition (POD) has been applied to two-dimensional transects of vorticity obtained from numerical simulations of the stratified turbulent wake of a towed sphere at a Reynolds number Re=(UD)/ν=5×103 and Froude number Fr=2U/(ND)=4 (U and D are characteristic velocity and length scales and N is the stratification frequency). At 231 times during the interval 12<Nt<35, the streamwise and spanwise vorticity components are sampled on span-depth (yz) and stream-depth (xz) planes, respectively, at select streamwise and spanwise locations. POD appears to provide a natural decomposition of the vorticity field inside the wake core in terms of the relative influence of buoyancy on flow dynamics. The geometry of the individual eigenmodes shows a vorticity structure that is buoyancy-controlled at the lowest modes and is increasingly more actively turbulent as modal index is increased. In the wake ambient, i.e., the initially quiescent region outside the turbulent wake, the geometry of the POD mode...

Mass transfer model of nanoparticle-facilitated contaminant transport in saturated porous media

A one-dimensional model has been evaluated for transport of hydrophobic contaminants, such as polycyclic aromatic hydrocarbon (PAH) compounds, facilitated by synthetic amphiphilic polyurethane (APU) nanoparticles in porous media. APU particles synthesized from poly(ethylene glycol)-modified urethane acrylate (PMUA) precursor chains have been shown to enhance the desorption rate and mobility of phenanthrene (PHEN) in soil. A reversible process governed by attachment and detachment rates was considered to describe the PMUA binding in soil in addition to PMUA transport through advection and dispersion. Ultimately, an irreversible second-order PMUA attachment rate in which the fractional soil saturation capacity with PMUA was a rate control was found to be adequate to describe the retention of PMUA particles. A gamma-distributed site model (GS) was used to describe the spectrum of physical/chemical constraints for PHEN transfer from solid to aqueous phases. Instantaneous equilibrium was assumed for PMUA-PHEN interactions. The coupled model for PMUA and PHEN behavior successfully described the enhanced elution profile of PHEN by PMUA. Sensitivity analysis was performed to analyze the significance of model parameters on model predictions. The adjustable parameter alpha in the gamma-distribution shapes the contaminant desorption distribution profile as well as elution and breakthrough curves. Model simulations show the use of PMUA can be also expected to improve the release rate of PHEN in soils with higher organic carbon content. The percentage removal of PHEN mass over time is shown to be influenced by the concentration of PMUA added and this information can be used to optimize cost and time require to accomplish a desired remediation goal.

Two-dimensional instability of the bottom boundary layer under a solitary wave

The objective of this paper is to establish a detailed map for the temporal instability of the bottom boundary layer (BBL) flow driven by a soliton-like wave induced pressure gradient in a U-tube-shaped tunnel, which serves as an approximation to the BBL under surface solitary waves. Both linear stability analysis and fully nonlinear two-dimensional simulations using high-order numerical methods have been carried out. The process of delineation of the stability regions as a function of boundary layer thickness-based Reynolds number of the temporally evolving base flow, Reδ, consists of two parts. In the first part, we assess the lower limit of the Reδ range within which the standard, quasi-steady, linear stability analysis is applicable when considering individual base flow profiles sampled during its transient evolution. Below this limit, transient linear stability analysis serves as a more accurate predictor of the stability properties of the base flow. In the second step, above the Reδ limit where the ...

Deflation-accelerated preconditioning of the Poisson-Neumann Schur problem on long domains with a high-order discontinuous element-based collocation method

A combination of block-Jacobi and deflation preconditioning is used to solve a high-order discontinuous element-based collocation discretization of the Schur complement of the Poisson-Neumann system as arises in the operator splitting of the incompressible Navier-Stokes equations. The preconditioners and deflation vectors are chosen to mitigate the effects of ill-conditioning due to highly-elongated domains typical of simulations of strongly non-hydrostatic environmental flows, and to achieve Generalized Minimum RESidual method (GMRES) convergence independent of the size of the number of elements in the long direction. The ill-posedness of the Poisson-Neumann system manifests as an inconsistency of the Schur complement problem, but it is shown that this can be accounted for with appropriate projections out of the null space of the Schur complement matrix without affecting the accuracy of the solution. The block-Jacobi preconditioner is shown to yield GMRES convergence independent of the polynomial order and only weakly dependent on the number of elements within a subdomain in the decomposition. The combined deflation and block-Jacobi preconditioning is compared with two-level non-overlapping block-Jacobi preconditioning of the Schur problem, and while both methods achieve convergence independent of the grid size, deflation is shown to require half as many GMRES iterations and 25 % less wall-clock time for a variety of grid sizes and domain aspect ratios. The deflation methods shown to be effective for the two-dimensional Poisson-Neumann problem are extensible to the three-dimensional problem assuming a Fourier discretization in the third dimension. A Fourier discretization results in a two-dimensional Helmholtz problem for each Fourier component that is solved using deflated block-Jacobi preconditioning on its Schur complement. Here again deflation is shown to be superior to two-level non-overlapping block-Jacobi preconditioning, requiring about half as many GMRES iterations and 15 % less time.