Mean Shear Flow Research Articles

Incorporating Wind Information in the Inversion of Co‐Located Pressure and Seismic Data for Shallow Elastic Structure

AbstractWhen surface pressure is large, seismic noise between about 0.01 and 0.05 Hz is mostly generated by wind‐related surface pressure changes. By analyzing this phenomenon using co‐located pressure and seismic data, we can derive shallow elastic structure in the uppermost 50–100 m. However, there still remains a difficult question on seismic excitation by wind‐related surface pressure because of complexity in wind behaviors. Roughly speaking, it consists of the mean shear flow and turbulence. The mean flow should act like a moving pressure source on the surface while turbulent parts act like a stochastic source as the surface pressure field becomes heterogeneous. We point out that this complexity may be reduced by selecting time intervals of stable wind direction. During such time intervals, pressure changes occur in the direction of winds, which justifies us to use a relatively simple, moving pressure source model. We quantify the stability of wind direction by the standard deviation of wind direction data (ΔΨ). For stations with co‐located wind, pressure, and seismic data, we propose to select time intervals with small ΔΨ first and apply our inversion method based on the moving pressure model. In the absence of wind data at a station with co‐located pressure and seismic data, we propose to analyze the high‐pressure end of data, as this selection partially satisfies the stable wind condition.

Wave trapping and E × B staircases

A model of E × B staircases is proposed based on a wave kinetic equation coupled to a poloidal momentum equation. A staircase pattern is idealized as a periodic radial structure of zonal shear layers that bound regions of propagating wave packets, viewed as avalanches. Wave packets are trapped in shear flow layers due to refraction. In this model, an E × B staircase motif emerges due to the interaction between propagating wave packets (avalanches) and trapped waves in the presence of an instability drive. Amplitude, shape, and spatial period of the staircase E × B flow are predicted as functions of the background fluctuation spectrum and the growth rate of drift waves. The zonal flow velocity radial profile is found to peak near its maxima and to flatten near its minima. The optimum configuration for staircase formation is a growth rate, that is, maximum at zero radial wave number. A mean shear flow is responsible for a preferential propagation speed of avalanches. It is not a mandatory condition for the existence of staircase solutions, but has an impact on their spatial period.

A global linearized framework for modelling shear dispersion and turbulent diffusion of passive scalar fluctuations

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Dynamical evolution of cross phase of edge fluctuations and transport bifurcation

The dynamical evolution of edge turbulence during a transport bifurcation is explored using a flux-driven nonlinear fluid model with a geometry relevant to the plasma edge region. The simulations show that the self-generated mean shear flows can dramatically modify the phase angle between turbulent fluctuations. The changes in phase differences and amplitudes of edge fluctuations give rise to the modifications of turbulent edge transport. The statistical properties of flux and fluctuations are also investigated before and after edge shear flow generation.

Prediction of shear thickening of particle suspensions in viscoelastic fluids by direct numerical simulation

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Roles of Shear and Convection in Driving Mixing in the Ocean

AbstractUsing field, numerical, and laboratory studies, we consider the roles of both shear and convection in driving mixing in the interior of the density‐stratified ocean. Shear mixing dominates when the Richardson number Ri < 0.25, convective mixing dominates when Ri > 1.0, and in the intermediate regime when 0.25 < Ri < 1.0 both shear and convection can contribute to mixing. For pure shear mixing the mixing efficiency Rif approaches 0.5, while for pure convective mixing the mixing efficiency Rif approaches 0.75. The diapycnal diffusivities for the two mechanisms are given by very different expressions. Despite these complexities, a simple mixing length model using the mean flow shear S provides robust estimates of diffusivity across the range 0 < Ri < 2. To account for the roles of both shear and convection over this range of Ri, we also formulate a modified version of the empirical KPP model for parameterizing ocean mixing in numerical models.

On a new formulation for energy transfer between convection and fast tides with application to giant planets and solar type stars

ABSTRACT All the studies of the interaction between tides and a convective flow assume that the large-scale tides can be described as a mean shear flow that is damped by small-scale fluctuating convective eddies. The convective Reynolds stress is calculated using mixing length theory, accounting for a sharp suppression of dissipation when the turnover time-scale is larger than the tidal period. This yields tidal dissipation rates several orders of magnitude too small to account for the circularization periods of late-type binaries or the tidal dissipation factor of giant planets. Here, we argue that the above description is inconsistent, because fluctuations and mean flow should be identified based on the time-scale, not on the spatial scale, on which they vary. Therefore, the standard picture should be reversed, with the fluctuations being the tidal oscillations and the mean shear flow provided by the largest convective eddies. We assume that energy is locally transferred from the tides to the convective flow. Using this assumption, we obtain values for the tidal Q factor of Jupiter and Saturn and for the circularization periods of pre-main-sequence binaries in good agreement with observations. The time-scales obtained with the equilibrium tide approximation are however still 40 times too large to account for the circularization periods of late-type binaries. For these systems, shear in the tachocline or at the base of the convective zone may be the main cause of tidal dissipation.

An application of WKBJ theory for triad interactions of internal gravity waves in varying background flows

AbstractMotivated by the question of whether and how wave–wave interactions should be implemented into atmospheric gravity‐wave parametrizations, the modulation of triadic gravity‐wave interactions by a slowly varying and vertically sheared mean flow is considered for a non‐rotating Boussinesq fluid with constant stratification. An analysis using a multiple‐scale WKBJ (Wentzel–Kramers–Brillouin–Jeffreys) expansion identifies two distinct scaling regimes, a linear off‐resonance regime, and a nonlinear near‐resonance regime. Simplifying the near‐resonance interaction equations allows for the construction of a parametrization for the triadic energy exchange which has been implemented into a one‐dimensional WKBJ ray‐tracing code. Theory and numerical implementation are validated for test cases where two wave trains generate a third wave train while spectrally passing through resonance. In various settings, of interacting vertical wavenumbers, mean‐flow shear, and initial wave amplitudes, the WKBJ simulations are generally in good agreement with wave‐resolving simulations. Both stronger mean‐flow shear and smaller wave amplitudes suppress the energy exchange among a resonantly interacting triad. Experiments with mean‐flow shear as strong as in the vicinity of atmospheric jets suggest that internal gravity‐wave dynamics are dominated in such regions by wave modulation. However, triadic gravity‐wave interactions are likely to be relevant in weakly sheared regions of the atmosphere.

Slowly varying modes in a two-dimensional duct with shear flow and lined walls

Abstract

Measuring Basal Force Fluctuations of Debris Flows Using Seismic Recordings and Empirical Green's Functions

AbstractWe present a novel method for measuring the fluctuating basal normal and shear stresses of debris flows by using along‐channel seismic recordings. Our method couples a simple parameterization of a debris flow as a seismic source with direct measurements of seismic path effects using empirical Green's functions generated with a force hammer. We test this method using two large‐scale (8 and 10 m3) experimental flows at the U.S. Geological Survey debris‐flow flume that were recorded by dozens of three‐component seismic sensors. The seismically derived basal stress fluctuations compare well in amplitude and timing to independent force plate measurements within the valid frequency range (15–50 Hz). We show that although the high‐frequency seismic signals provide band‐limited forcing information, there are systematic relations between the fluctuating stresses and independently measured flow properties, especially mean basal shear stress and flow thickness. However, none of the relationships are simple, and since the flow properties also correlate with one another, we cannot isolate a single factor that relates in a simple way to the fluctuating forces. Nevertheless, our observations, most notably the gradually declining ratio of fluctuating to mean basal stresses during flow passage and the distinctive behavior of the coarse, unsaturated flow front, imply that flow style may be a primary control on the conversion of translational to vibrational kinetic energy. This conversion ultimately controls the radiation of high‐frequency seismic waves. Thus, flow style may provide the key to revealing the nature of the relationship between fluctuating forces and other flow properties.

Rotation of anisotropic particles in Rayleigh–Bénard turbulence

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Effect of Couette component on the stability of Poiseuille flow of a Bingham fluid–porous system: Modal and non-modal approaches

In this study, both modal and non-modal stability analyses are attempted in case of Couette–Poiseuille flow of a Bingham fluid overlying a porous layer. Such a flow configuration is widely encountered in the geophysical context in case of oil drilling. The solution of the modal problem yields no unstable eigenvalue, similar to the flow of a viscoplastic fluid in a non-porous channel configuration. Thus, non-modal analysis is performed to throw light on the short-time characteristics. The primary goal is to unveil the complex interplay between the upper plate velocity (Couette component) and the parameters characterizing the porous layer in dictating the flow transition characteristics. The current study is possibly the first attempt at investigating the effect of the Couette flow on the stability of a fluid–porous system for any kind of non-Newtonian fluid and reveals marked departure from the results reported in the literature for a similar flow configuration involving Newtonian rheology. The reason for the deviation is attributed to the role of yield stress, quantified by the Bingham number, and its complex interaction with the Couette number and porous layer parameters (depth, permeability, anisotropy, inhomogeneity, etc.). The relative interaction between fluid and porous modes in an environment of non-linear viscosity variation (owing to the rheology of the viscoplastic fluid), coupled with enhanced shearing (imparted by the Couette component), is found to demonstrate unique, non-monotonic flow transition characteristics. The possible physical mechanism governing short-time (non-modal) amplifications via interaction between the mean shear flow and the perturbation waves is also explored in detail.

Theoretical Foundation of Rapid Distortion Theory on Transversely Sheared Mean Flows

The focus of this paper is on Rapid Distortion Theory on transversely sheared mean flows, which is often used to investigate turbulence-solid surface interactions. The main purpose of the paper is to bring together and present in a consistent fashion a general theory that has been developed in several different papers that have been published in the Journal of Fluid Mechanics. The equations for the unsteady pressure and velocity flections (which decouple from the entropy fluctuations) are rewritten in terms of a gauge function in order to obtain expressions that involve two arbitrarily convected quantities. A pair of very general conservation laws are used to derive upstream boundary conditions that relate these quantities to the actual physical variables. The entropy fluctuations can be determined after the fact once the solutions for the pressure and velocity fluctuations are known. The result involves a third arbitrary convected quantity that is equal to the entropy fluctuations at upstream infinity and can, therefore, be specified as an additional upstream boundary condition. A secondary purpose of the paper is to summarize a number of applications of the theory that have also appeared in the literature and show how they compare with an experiment.

Perfectly matched layer absorbing boundary conditions for Euler equations with oblique mean flows modeled with smoothed particle hydrodynamics.

Absorbing boundary conditions (ABCs) play a critical role in the simulation of sound or wave propagation problems. This paper proposes a technique of space-time transformed perfectly matched layer (PML) boundary condition implemented in a widely used mesh-free method called smoothed particle hydrodynamic (SPH) method, to absorb the outgoing sound waves with oblique shear mean flow. Special consideration is given to the particle features of the SPH, and the PMLs are formulated to correct the truncation error of SPH and absorb the outgoing wave at the same time, aiming to reduce the storage and computational cost in the infinite computational domain. Because the group velocity and phase velocity of the outgoing sound waves in the PMLs may be in different directions, exponentially growing pseudo reflections can result. The authors thus employ space-time transformation to eliminate the reflections effectively in PML boundaries for stable solutions. Moreover, a uniform framework of PML absorbing boundary conditions for Euler equations in the cases of arbitrary oblique mean flow and static media is derived. Finally, the present PML-SPH method with this stable absorbing boundary is applied to simulate sound waves propagating with mean flow. The obtained numerical results agree very well with the reference results.

Observations of mean and wave orbital flows in the ocean’s upper centimetres

Sophisticated measurements of fluid velocity near to an undulating air–water boundary have traditionally been confined to the laboratory setting. Developments in camera technology and the opening of novel modes of analysis have allowed for sensitive measurements of the current profile in the ocean’s uppermost layer. Taking advantage of the Research Platform R/P FLIP as a ‘laboratory at sea’, here we present first-of-their-kind thermal and polarimetric camera-based observations of wave orbital velocities and mean shear flows in the upper centimetres of the ocean surface layer. Measurements reveal a well-defined logarithmic layer as seen in laboratory measurements and described by classical surface layer theory; however, substantial spread of observations is found at low levels of wind forcing, where the Stokes drift of swell may have a substantial impact on the near-surface current profile. A novel application of short time window Fourier transforms allows for the estimation of near-surface wave orbital velocity magnitudes. These are found to be in general agreement with the prescriptions of linear wave theory, although observations diverge from theory at high levels of wind forcing where the interface is subject to surface wave breaking. Finally, the surface gravity wave phase-coherent short wave growth is presented and discussed in the context of hydrodynamic wave and airflow modulation.

Influence of Rigid Emerged Vegetation in a Channel Bend on Bed Topography and Flow Velocity Field: Laboratory Experiments

Trees have been used extensively by river managers for improving the river environment and ecology. The link between flow hydraulics, bed topography, habitat availability, and organic matters is influenced by vegetation. In this study, the effect of trees on the mean flow, bed topography, and bed shear stress were tested under different flow conditions. It was found that each configuration of trees produced particular flow characteristics and bed topography patterns. The SR (single row of trees) model appeared to deflect the maximum velocity downstream of the bend apex toward the inner bank, while leading the velocity to be more uniformly distributed throughout the bend. The entrainment of sediment particles occurred toward the area with higher values of turbulent kinetic energy (TKE). The results showed that both SR and DR (double rows of trees) models are effective in relieving bed erosion in sharp ingoing bends. The volume of the scoured bed was reduced up to 70.4% for tests with trees. This study shows the effectiveness of the SR model in reducing the maximum erosion depth.

Rapid distortion theory on transversely sheared mean flows of arbitrary cross-section

This paper is concerned with rapid distortion theory on transversely sheared mean flows that (among other things) can be used to analyse the unsteady motion resulting from the interaction of a turbulent shear flow with a solid surface. It expands on a previous analysis of Goldsteinet al. (J. Fluid Mech., vol. 824, 2017, pp. 477–512) that uses a pair of conservation laws to derive upstream boundary conditions for planar mean flows and extends these findings to transversely sheared flows of arbitrary cross-section. The results, which turn out to be quite general, are applied to the specific case of a round jet interacting with the trailing edge of a flat plate and are used to calculate the radiated sound field, which is then compared with experimental data taken at the NASA Glenn Research Center.

A Geometric Interpretation of Southern Ocean Eddy Form Stress

AbstractAn interpretation of eddy form stress via the geometry described by the Eliassen–Palm flux tensor is explored. Complimentary to previous works on eddy Reynolds stress geometry, this study shows that eddy form stress is fully described by a vertical ellipse, whose size, shape, and orientation with respect to the mean flow shear determine the strength and direction of vertical momentum transfers. Following a recent proposal, this geometric framework is here used to form a Gent–McWilliams eddy transfer coefficient that depends on eddy energy and a nondimensional geometric parameter α, bounded in magnitude by unity. The parameter α expresses the efficiency by which eddies exchange energy with baroclinic mean flow via along-gradient eddy buoyancy flux—a flux equivalent to eddy form stress along mean buoyancy contours. An eddy-resolving ocean general circulation model is used to estimate the spatial structure of α in the Southern Ocean and assess its potential to form a basis for parameterization. The eddy efficiency α averages to a low but positive value of 0.043 within the Antarctic Circumpolar Current, consistent with an inefficient eddy field extracting energy from the mean flow. It is found that the low eddy efficiency is mainly the result of that eddy buoyancy fluxes are weakly anisotropic on average. The eddy efficiency is subject to pronounced vertical structure and is maximum at ~3-km depth, where eddy buoyancy fluxes tend to be directed most downgradient. Since α partly sets the eddy form stress in the Southern Ocean, a parameterization for α must reproduce its vertical structure to provide a faithful representation of vertical stress divergence and eddy forcing.

Hybrid numerical model for acoustic propagation through sheared flows

Simulating the propagation of sound in non-uniform flows remains challenging, especially for large, three-dimensional problems. To account for the sound refraction due to gradients of velocity and temperature, one has to solve the Linearised Euler Equations (LEE) which can be computationally expensive in three dimensions. Alternatively, one can use the Linearised Potential Equation (LPE) which is much cheaper but is limited to potential, isentropic flows. In this paper, a hybrid model combining the LEE and the LPE is proposed in order to simulate the sound propagation in sheared flows at a reasonable computational cost. The LEE are applied only in regions with strong sheared mean flows, the LPE is used everywhere else. The coupling between the LEE and the LPE consists in imposing relations for the characteristic waves propagating at the interface between the LEE and the LPE regions. In this study, the hybrid model is implemented in a high-order finite element solver in the frequency domain. Its performance is first assessed by simulating the propagation of planes waves in a uniform mean flow and the acoustic radiation from a semi-infinite duct in a strongly sheared non-isothermal jet flow. No significant spurious noise is produced at the LEE-LPE interfaces. The applicability of the hybrid model to industrial problems is then demonstrated by simulating the propagation of fan noise through the jet flow exiting from a turbofan exhaust. The use of the proposed hybrid model does not affect the propagation of the sound field while reducing the memory footprint by more than one order of magnitude compared to a full three-dimensional LEE simulation.

Approximation of wave action conservation in vertically sheared mean flows

We develop asymptotic expressions for wave action density and action flux, using an extension of Kirby & Chen (1989)’s perturbation solution for weakly-sheared currents allowing for a basic flow with Froude number F=U∕gh=O(1) but with weak vertical shear. The accuracy of the expressions for action density and flux is established by comparison to analytic results for a current with constant shear, and to numerical results for a field case involving a buoyant ebb-tidal plume with strong vertical shear and for a case involving a numerically determined profile for a wind-driven current. We compare our results to those from recent work of Quinn et al. (2017), and find unresolved discrepancies in that prior work. We provide additional suggestions for efficiently implementing the required extensions in coupled wave/circulation models using a Taylor series expansion based on conditions at peak frequency and direction. These results generalize the previous work of Banihashemi et al. (2017) to motions in two horizontal dimensions, and cover the determination of the wave action.