A Simple Eddy Viscosity Model of Rough Turbulent Wave Boundary Layer

A one-layer time-invariant eddy viscosity model is specified to develop a mathematical model for describing the essential features of the turbulent wave boundary layer over a rough bed. The functional form of the eddy viscosity is evaluated based on computational results from a two-equation turbulence model in which the eddy viscosity varies with time and space. The present eddy viscosity model simplifies much of the mathematical complexity in many existing models. Predictions from the present model have been compared with a wide range of experimental data. It is found that the eddy viscosity model adopted in the present study is physically reasonable.

Proof of Six-Wave Resonance Conditions of Ocean Surface Gravity Waves in Deep Water

A necessary big step up in the modern water wave theories and their widespread application in ocean engineering is how to obtain 6-wave resonance conditions and to prove it. In the light of the existing forms and characteristics of 3-wave, 4-wave and 5-wave resonance conditions, the 6-wave resonance conditions are proposed and proved for currently a maximum wave-wave resonance interactions of the ocean surface gravity waves in deep water, which will be indispensable to both the Kolmogorov spectrum of the corresponding universal wave turbulence and a synthetic 4-5-6-wave resonant model for the ocean surface gravity waves.

NATURE OF THE SURFACE HEAT TRANSFER FLUCTUATION IN A HYPERSONIC SEPARATED TURBULENT FLOW

This paper presents the results of an experimental study of the unsteady nature of a hypersonic sepa- rated turbulent flow.The nominal test conditions were a freestream Mach number of 7.8 and a unit Reynolds number of 3.5x10^7/m.The separated flow was generated using finite span forward facing steps.An array of flush mounted high spatial resolution and fast response platinum film resistance thermometers was used to make mul- ti-channel measurements of the fluctuating surface heat trtansfer within the separated flow.Conditional sampling ana- lysis of the signals shows that the root of separation shock wave consists of a series of compression wave extending over a streamwise length about one half of the incoming boundary layer thickness.The compression waves con- verge into a single leading shock beyond the boundary layer.The shock structure is unsteady and undergoes large-scale motion in the streamwise direction.The length scale of the motion is about 22 percent of the upstream influence length of the separation shock wave.There exists a wide band of frequency of oscillations of the shock system.Most of the frequencies are in the range of 1-3 kHz.The heat transfer fluctuates intermittently between the undisturbed level and the disturbed level within the range of motion of the separation shock wave.This inter mittent phenomenon is considered as the consequence of the large-scale shock system oscillations.Downstream of the range of shock wave motion there is a separated region where the flow experiences continuous compression and no intermittency phenomenon is observed.

Correlation dimension analysis and capillary wave turbulence in Dragon-Wash phenomena

This paper describes the evolution of surface capillary waves of deep water excited by gradually increasing the lateral external force at a single frequency. The vertical velocities of the water surface are measured by using a Polytec Laser Vibrometer with a thin layer of aluminium powder scattering on the surface to reflect the laser beam. Nonlinear interaction processes result in a stationary Fourier spectrum of the vertical surface velocities （the same as the surface elevation）, i.e. Iω -ω^-3-5. The observed spectrum can be interpreted as a wave-turbulent Kolmogorov spectrum for the case of ‘narrowband pumping＇ for a direct cascade of energy. Correlation dimension analysis of the whole development process reveals four distinct stages during the wave structure development and identifies the wave turbulence stage.

液晶流动可视化方法研究拟似冲击波的内部超声速流动(英文)

The flow visualization technique using shear-sensitive liquid crystal is applied to the investigation of a Mach 2 internal supersonic flow with pseudo-shock wave （PSW） in a pressure-vacuum supersonic wind tunnel. It provides qualitative information mainly concerning the overall flow structure, such as the turbulent boundary layer separation, reattachment locations and the dimensionalities of the flow. Besides, it can also give understanding of the surface streamlines, vortices in separation region and the corner effect of duct flow. Two kinds of crystals with different viscosities are used in experiments to analyze the viscosity effect. Results are compared with schlieren picture, confirming the effectiveness of liquid crystal in flow-visualization.

Impact of Cyclone Nilam on Tropical Lower Atmospheric Dynamics

A deep depression formed over the Bay of Bengal on 28 October 2012, and developed into a cyclonic storm. After landfall near the south coast of Chennai, cyclone Nilam moved north-northwestwards. Coordinated experiments were conducted from the Indian stations of Gadanki（13.5？N, 79.2？E） and Hyderabad（17.4？N, 78.5？E） to study the modification of gravity-wave activity and turbulence by cyclone Nilam, using GPS radiosonde and mesosphere–stratosphere–troposphere radar data. The horizontal velocities underwent large changes during the closest approach of the storm to the experimental sites. Hodograph analysis revealed that inertia gravity waves（IGWs） associated with the cyclone changed their directions from northeast（control time） to northwest following the path of the cyclone. The momentum flux of IGWs and short-period gravity waves（1–8 h） enhanced prior to, and during, the passage of the storm（±0.05 m2s-2and ±0.3 m2s-2, respectively）, compared to the flux after its passage. The corresponding body forces underwent similar changes, with values ranging between ±2–4m s-1d-1and ±12–15 m s-1d-1. The turbulence refractivity structure constant（C2n） showed large values below 10 km before the passage of the cyclone when humidity in the region was very high. Turbulence and humidity reduced during the passage of the storm when a turbulent layer at ～17 km became more intense. Turbulence in the lower troposphere and near the tropopause became weak after the passage of the cyclone.

Damping and power spectra of quasi-periodic intensity disturbances above a solar polar coronal hole

We study intensity disturbances above a solar polar coronal hole that can be seen in the AIA 171 and 193 ＆ passbands, aiming to provide more insights into their physical nature. The damping and power spectra of the intensity disturbances with frequencies from 0.07 mHz to 10.5 mHz are investigated. The damping of the intensity disturbances tends to be stronger at lower frequencies, and their damping behavior below 980＂ （for comparison, the limb is at 945＂） is different from what happens above. No significant difference is found between the damping of the intensity disturbances in the AIA 171 ~ and that in the AIA 193 ]k. The indices of the power spectra of the intensity disturbances are found to be slightly smaller in the AIA 171/~ than in the AIA 193 ~, but the difference is within one standard deviation. An additional enhanced component is present in the power spectra in a period range of 8-40 min at lower heights. The power spectra of a spicule is highly correlated with its associated intensity disturbance, which suggests that the power spectra of the intensity disturbances might be a mixture of spicules and wave activities. We suggest that each intensity disturbance in the polar coronal hole is possibly a series of independent slow magnetoacoustic waves triggered by spicular activities.

Steady-state probability density function in wave turbulence under large volume limit

We investigate the possibility for two-mode probability density function （PDF） to have a non-zero flux steady state solution. We take the large volume limit so that the space of modes becomes continuous. It is shown that in this limit all the steady-state twoor higher-mode PDFs are the product of one-mode PDFs. The flux of this steady-state solution turns out to be zero for any finite mode PDF.

MEASUREMENTS AND THEORETICAL STUDY ON GROWTH RATES OF TURBULENT WIND WAVES

The spatial growth of turbulent wind waves is investigated theoretically and experimentally. Introduction of wave induced turbulent Reynolds stress, in particu- lar at the average interface, makes great improvement in the prediction of wind wave properties.

Scaling of interaction lengths for hypersonic shock wave/turbulent boundary layer interactions

The interaction length induced by Shock Wave/Turbulent Boundary-Layer Interactions(SWTBLIs)in the hypersonic flow was investigated using a scaling analysis,in which the interaction length normalized by the displacement thickness of boundary layer was correlated with a corrected non-dimensional separation criterion across the interaction after accounting for the wall temperature effects.A large number of hypersonic SWTBLIs were compiled to examine the scaling analysis over a wide range of Mach numbers,Reynolds numbers,and wall temperatures.The results indicate that the hypersonic SWTBLIs with low Reynolds numbers collapse on the supersonic SWTBLIs,while the hypersonic cases with high Reynolds numbers show a more rapid growth of the interaction length than that with low Reynolds numbers.Thus,two scaling relationships are identified according to different Reynolds numbers for the hypersonic SWTBLIs.The scaling analysis provides valuable guidelines for engineering prediction of the interaction length,and thus,enriches the knowledge of hypersonic SWTBLIs.

Zonal Jet Creation from Secondary Instability of Drift Waves for Plasma Edge Turbulence

A new strategy is presented to explain the creation and persistence of zonal flows widely observed in plasma edge turbulence.The core physics in the edge regime of the magnetic-fusion tokamaks can be described qualitatively by the one-state modified Hasegawa-Mima(MHM for short)model,which creates enhanced zonal flows and more physically relevant features in comparison with the familiar Charney-Hasegawa-Mima(CHM for short)model for both plasma and geophysical flows.The generation mechanism of zonal jets is displayed from the secondary instability analysis via nonlinear interactions with a background base state.Strong exponential growth in the zonal modes is induced due to a non-zonal drift wave base state in the MHM model,while stabilizing damping effect is shown with a zonal flow base state.Together with the selective decay effect from the dissipation,the secondary instability offers a complete characterization of the convergence process to the purely zonal structure.Direct numerical simulations with and without dissipation are carried out to confirm the instability theory.It shows clearly the emergence of a dominant zonal flow from pure non-zonal drift waves with small perturbation in the initial configuration.In comparison,the CHM model does not create instability in the zonal modes and usually converges to homogeneous turbulence.

Resonance Clustering in Wave Turbulent Regimes:Integrable Dynamics

Two fundamental facts of the modern wave turbulence theory are 1)existence of power energy spectra in k-space,and 2)existence of“gaps”in this spectra corresponding to the resonance clustering.Accordingly,three wave turbulent regimes are singled out:kinetic,described by wave kinetic equations and power energy spectra;discrete,characterized by resonance clustering;and mesoscopic,where both types of wave field time evolution coexist.In this review paper we present the results on integrable dynamics of resonance clusters appearing in discrete and mesoscopic wave turbulent regimes.Using a novel method based on the notion of dynamical invariant we show that some of the frequently met clusters are integrable in quadratures for arbitrary initial conditions and some others-only for particular initial conditions.We also identify chaotic behaviour in some cases.Physical implications of the results obtained are discussed.

A survey of the Szeg? equation Dedicated to Professor Jean-Yves Chemin on the Occasion of His 60th Birthday

We survey the main properties of the cubic Szeg? equation from the PDE viewpoint, emphasising global existence of smooth solutions, analytic regularity, growth of high Sobolev norms and the effects of weak damping.

Application of phase‑conjugate beams in beam correction and underwater optical wireless communication subject to surface wave turbulence

Water surface wave turbulence is one of the factors afecting the performances of underwater optical wireless communication(UOWC)systems.In our research,a phase-conjugate beam was used to correct the beam distortion and enhance the communication performances when a system is subject to surface wave turbulence.The phase-conjugate beam was generated by a phase-conjugate mirror(PCM),and a turbulence generator was used to generate surface wave turbulence in the experiment.We calculated the beam centroid distribution and the results showed that the phase-conjugate beam had a better propagation performance than the distorted beam at the diferent water depths.The root mean square(RMS)of the beam centroid for the phase-conjugate beam was 11 times less than that for the distorted beam,which meant that the phase-conjugate beam could efectively correct the beam drift.We further investigated the scintillation index and the signal-to-noise ratio(SNR);the results showed that the phase-conjugate beam was able to reduce the scintillation and an obvious improvement in SNR could be obtained.This research has the potential to be applied in UWC.

Laminated Wave Turbulence: Generic Algorithms Ⅱ

The model of laminated wave turbulence puts forth a novel computational problem–construction of fast algorithms for finding exact solutions of Diophantine equations in integers of order 10^(12) and more.The equations to be solved in integers are resonant conditions for nonlinearly interacting waves and their form is defined by the wave dispersion.It is established that for the most common dispersion as an arbitrary function of a wave-vector length two different generic algorithms are necessary:(1)one-class-case algorithm for waves interacting through scales,and(2)two-class-case algorithm for waves interacting through phases.In our previous paper we described the one-class-case generic algorithm and in our present paper we present the two-classcase generic algorithm.