6 results
Direct numerical simulation of wind-wave generation processes
- MEI-YING LIN, CHIN-HOH MOENG, WU-TING TSAI, PETER P. SULLIVAN, STEPHEN E. BELCHER
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- Journal:
- Journal of Fluid Mechanics / Volume 616 / 10 December 2008
- Published online by Cambridge University Press:
- 10 December 2008, pp. 1-30
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An air–water coupled model is developed to investigate wind-wave generation processes at low wind speed where the surface wind stress is about 0.089 dyn cm−2 and the associated surface friction velocities of the air and the water are u*a~8.6 cms−1 and u*w~0.3 cms−1, respectively. The air–water coupled model satisfies continuity of velocity and stress at the interface simultaneously, and hence can capture the interaction between air and water motions. Our simulations show that the wavelength of the fastest growing waves agrees with laboratory measurements (λ~8–12 cm) and the wave growth consists of linear and exponential growth stages as suggested by theoretical and experimental studies. Constrained by the linearization of the interfacial boundary conditions, we perform simulations only for a short time period, about 70s; the maximum wave slope of our simulated waves is ak~0.01 and the associated wave age is c/u*a~5, which is a slow-moving wave. The effects of waves on turbulence statistics above and below the interface are examined. Sensitivity tests are carried out to investigate the effects of turbulence in the water, surface tension, and the numerical depth of the air domain. The growth rates of the simulated waves are compared to a previous theory for linear growth and to experimental data and previous simulations that used a prescribed wavy surface for exponential growth. In the exponential growth stage, some of the simulated wave growth rates are comparable to previous studies, but some are about 2–3 times larger than previous studies. In the linear growth stage, the simulated wave growth rates for these four simulation runs are about 1–2 times larger than previously predicted. In qualitative agreement with previous theories for slow-moving waves, the mechanisms for the energy transfer from wind to waves in our simulations are mainly from turbulence-induced pressure fluctuations in the linear growth stage and due to the in-phase relationship between wave slope and wave-induced pressure fluctuations in the exponential growth stage.
A numerical study on the evolution and structure of a stress-driven free-surface turbulent shear flow
- WU-TING TSAI, SHI-MING CHEN, CHIN-HOH MOENG
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- Journal:
- Journal of Fluid Mechanics / Volume 545 / 25 December 2005
- Published online by Cambridge University Press:
- 02 December 2005, pp. 163-192
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Turbulent shear flow beneath a flat free surface driven by a surface stress is simulated numerically to gain a better understanding of the hydrodynamic processes governing the scalar transfer across the air-water interface. The simulation is posed to mimic the subsequent development of a wind-driven shear layer as in a previous experiment except that the initiation of the surface waves is inhibited, thus focusing on the boundary effect of the stress-imposed surface on the underlying turbulent flow and vice versa. Despite the idealizations inherent in conducting the simulation, the computed flow exhibits the major surface features, qualitatively similar to those that appear in the laboratory and field experiments. Two distinct surface signatures, namely elongated high-speed streaks and localized low-speed spots, are observed in the simulated flow. Including temperature as a passive tracer and describing an upward heat flux at the surface, we obtain high-speed streaks that are colder and low-speed spots that are warmer than the surrounding regions. The high-speed streaks, arranged with somewhat equal cross-spacing of centimetres scale, are formed by an array of streamwise jets within the viscous sublayer immediately next to the surface. Beneath the streaks, counter-rotating streamwise vortex pairs are observed among other prevailing elongated vortices. However, they are significantly shorter in length and more irregular than their corresponding high-speed streaks at the surface. Accompanying the more organized high-speed streaks, localized regions of low streamwise velocity emerge randomly on the surface. These low-speed spots are attributed to strong upwelling flows which disrupt the viscous sublayer and also bring up the submerged fluids of low streamwise velocity. The occasional interruptions of the streamwise high-speed jets by the upwelling flows account for bifurcation or dislocation of the surface streaks. Statistics of the turbulence are presented and their implications for the formation of the flow structures are discussed.
5 - Large-eddy simulations of cloud-topped mixed layers
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- By Chin-Hoh Moeng, Peter P. Sullivan, National Center for Atmospheric Research, Boulder, USA, Bjorn Stevens, Department of Atmospheric and Oceanic Sciences, University of California, Los Angeles, USA
- Edited by Evgeni Fedorovich, University of Oklahoma, Richard Rotunno, National Center for Atmospheric Research, Boulder, Colorado, Bjorn Stevens, University of California, Los Angeles
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- Book:
- Atmospheric Turbulence and Mesoscale Meteorology
- Published online:
- 04 August 2010
- Print publication:
- 21 October 2004, pp 95-114
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Summary
Introduction
With the advent of computers, scientists in the 1950s and 1960s began to explore the possibility of using numerical simulation to generate virtual laboratories for exploring specific geophysical processes in a controlled manner. Doug Lilly helped pioneer this emerging science of numerical simulation. As pointed out by Wyngaard (Chapter 1), Lilly presented a “bold, three-phase plan of attack” in which well-behaved numerical models would be developed; their fidelity would be benchmarked against known solutions; and as confidence builds they would be used to explore conditions not adequately reproducible by experiment. In the subsequent decades this strategy has become a staple of theoretical studies of turbulence. In particular, a class of numerical simulations Doug helped develop in the early 1960s has come to be known as large-eddy simulation (LES) and is now widely used in the field of planetary boundary layer (PBL) turbulence and clouds.
We begin in Section 5.2 by giving an example of the second element of Doug's plan of attack, and what we call “benchmarking.” This is by no means trivial, because for turbulent flows there are no known solutions. To better appreciate this point we consider LES of the cloud-topped boundary layer which couples turbulence, radiation, and cloud processes. As cloudy boundary layers cannot be created in the laboratory, one must invariably turn to field data to construct meaningful benchmarks. Historically, field data have been collected to explore phenomenology, and thus few datasets exist to benchmark computations. The second field study of the Dynamics and Chemistry of Marine Stratocumulus (DYCOMS-II) is unique in that it was designed from the outset with the purpose of testing LES.
Structure of subfilter-scale fluxes in the atmospheric surface layer with application to large-eddy simulation modelling
- PETER P. SULLIVAN, THOMAS W. HORST, DONALD H. LENSCHOW, CHIN-HOH MOENG, JEFFREY C. WEIL
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- Journal:
- Journal of Fluid Mechanics / Volume 482 / 10 May 2003
- Published online by Cambridge University Press:
- 13 May 2003, pp. 101-139
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In the atmospheric surface layer, the wavelength of the peak in the vertical velocity spectrum $\Lambda_w$ decreases with increasing stable stratification and proximity to the surface and this dependence constrains our ability to perform high-Reynolds-number large-eddy simulation (LES). Near the ground, the LES filter cutoff $\Delta_f$ is comparable to or larger than $\Lambda_w$ and as a result the subfilter-scale (SFS) fluxes in LES are always significant and their contribution to the total flux grows with increasing stability.
We use the three-dimensional turbulence data collected during the Horizontal Array Turbulence Study (HATS) field program to construct SFS fluxes and variances that are modelled in LES codes. Detailed analysis of the measured SFS motions shows that the ratio $\Lambda_w/\Delta_f$ contains the essential information about stratification, vertical distance above the surface, and filter size, and this ratio allows us to connect measurements of SFS variables with LES applications. We find that the SFS fluxes and variances collapse reasonably well for atmospheric conditions and filter widths in the range $\Lambda_w/\Delta_f = [0.2,15]$. The SFS variances are anisotropic and the SFS energy is non-inertial, exhibiting a strong dependence on the stratification, large-scale shear, and proximity to the surface. SFS flux decomposition into modified-Leonard, cross-, and Reynolds terms illustrates that these terms are of comparable magnitude and scale content at large $\Lambda_w/\Delta_f$. As $\Lambda_w/\Delta_f \rightarrow 0$, the SFS flux approaches the-ensemble-average flux and is dominated by the Reynolds term. Backscatter of energy from the SFS motions to the resolved fields is small in the bulk of the surface layer, less than 20% for $\Lambda_w/\Delta_{f} < 2$.
A priori testing of typical SFS models using the HATS dataset shows that the turbulent kinetic energy and Smagorinsky model coefficients $C_k$ and $C_s$ depend on $\Lambda_w/\Delta_f$ and are smaller than theoretical estimates based on the assumption of a sharp spectral cutoff filter in the inertial range. $C_k$ and $C_s$ approach zero for small $\Lambda_w/\Delta_f$. Much higher correlations between measured and modelled SFS fluxes are obtained with a mixed SFS model that explicitly includes the modified-Leonard term. The eddy-viscosity model coefficients still retain a significant dependence on $\Lambda_w/\Delta_f$ with the mixed model. A dissipation model of the form $\epsilon = C_\epsilon E_s^{3/2}/\Delta_f$ is not universal across the range of $\Lambda_w/\Delta_f$ typical of atmospheric LES applications. The inclusion of a shear-stability-dependent length scale (Canuto & Cheng 1997) captures a large fraction of the variation in the eddy-viscosity and dissipation model coefficients.
Simulation of turbulent flow over idealized water waves
- PETER P. SULLIVAN, JAMES C. McWILLIAMS, CHIN-HOH MOENG
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- Journal:
- Journal of Fluid Mechanics / Volume 404 / 10 February 2000
- Published online by Cambridge University Press:
- 10 February 2000, pp. 47-85
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Turbulent flow over idealized water waves with varying wave slope ak and wave age c/u∗ is investigated using direct numerical simulations at a bulk Reynolds number Re = 8000. In the present idealization, the shape of the water wave and the associated orbital velocities are prescribed and do not evolve dynamically under the action of the wind. The results show that the imposed waves significantly influence the mean flow, vertical momentum fluxes, velocity variances, pressure, and form stress (drag). Compared to a stationary wave, slow (fast) moving waves increase (decrease) the form stress. At small c/u∗, waves act similarly to increasing surface roughness zo resulting in mean vertical velocity profiles with shorter buffer and longer logarithmic regions. With increasing wave age, zo decreases so that the wavy lower surface is nearly as smooth as a flat lower boundary. Vertical profiles of turbulence statistics show that the wave effects depend on wave age and wave slope but are confined to a region kz < 1 (where k is the wavenumber of the surface undulation and z is the vertical coordinate). The turbulent momentum flux can be altered by as much as 40% by the waves. A region of closed streamlines (or cat's-eye pattern) centred about the critical layer height was found to be dynamically important at low to moderate values of c/u∗. The wave-correlated velocity and flux fields are strongly dependent on the variation of the critical layer height and to a lesser extent the surface orbital velocities. Above the critical layer zcr the positions of the maximum and minimum wave-correlated vertical velocity ww occur upwind and downwind of the peak in zcr, like a stationary surface. The wave-correlated flux uwww is positive (negative) above (below) the critical layer height.
Langmuir turbulence in the ocean
- JAMES C. McWILLIAMS, PETER P. SULLIVAN, CHIN-HOH MOENG
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- Journal:
- Journal of Fluid Mechanics / Volume 334 / 10 March 1997
- Published online by Cambridge University Press:
- 10 March 1997, pp. 1-30
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Solutions are analysed from large-eddy simulations of the phase-averaged equations for oceanic currents in the surface planetary boundary layer (PBL), where the averaging is over high-frequency surface gravity waves. These equations have additional terms proportional to the Lagrangian Stokes drift of the waves, including vortex and Coriolis forces and tracer advection. For the wind-driven PBL, the turbulent Langmuir number, Latur = (U∗/Us)1/2, measures the relative influences of directly wind-driven shear (with friction velocity U∗) and the Stokes drift Us. We focus on equilibrium solutions with steady, aligned wind and waves and a realistic Latur = 0.3. The mean current has an Eulerian volume transport to the right of the wind and against the Stokes drift. The turbulent vertical fluxes of momentum and tracers are enhanced by the presence of the Stokes drift, as are the turbulent kinetic energy and its dissipation and the skewness of vertical velocity. The dominant coherent structure in the turbulence is a Langmuir cell, which has its strongest vorticity aligned longitudinally (with the wind and waves) and intensified near the surface on the scale of the Stokes drift profile. Associated with this are down-wind surface convergence zones connected to interior circulations whose horizontal divergence axis is rotated about 45° to the right of the wind. The horizontal scale of the Langmuir cells expands with depth, and there are also intense motions on a scale finer than the dominant cells very near the surface. In a turbulent PBL, Langmuir cells have irregular patterns with finite correlation scales in space and time, and they undergo occasional mergers in the vicinity of Y-junctions between convergence zones.