The boundary layer equations for plane, incompressible, and steady flow are 

$$\matrix{ {u{{\partial u} \over {\partial x}} + v{{\partial u} \over {\partial y}} = - {1 \over \varrho }{{\partial p} \over {\partial x}} + v{{{\partial ^2}u} \over {\partial {y^2}}},} \cr {0 = {{\partial p} \over {\partial y}},} \cr {{{\partial u} \over {\partial x}} + {{\partial v} \over {\partial y}} = 0.} \cr }$$

Boundary Layer Theory

Thank you for reading principles of optics electromagnetic theory of propagation interference and diffraction of light. As you may know, people have search hundreds times for their favorite novels like this principles of optics electromagnetic theory of propagation interference and diffraction of light, but end up in harmful downloads. Rather than enjoying a good book with a cup of coffee in the afternoon, instead they are facing with some infectious bugs inside their computer.

Principles Of Optics Electromagnetic Theory Of Propagation Interference And Diffraction Of Light

To improve the performance of particle image velocimetry in measuring instantaneous velocity fields, direct cross-correlation of image fields can be used in place of auto-correlation methods of interrogation of double- or multiple-exposure recordings. With improved speed of photographic recording and increased resolution of video array detectors, cross-correlation methods of interrogation of successive single-exposure frames can be used to measure the separation of pairs of particle images between successive frames. By knowing the extent of image shifting used in a multiple-exposure and by a priori knowledge of the mean flow-field, the cross-correlation of different sized interrogation spots with known separation can be optimized in terms of spatial resolution, detection rate, accuracy and reliability.

Theory of cross-correlation analysis of PIV images : Image analysis as measuring technique in flows

The problem of suspended sediment transport in river and coastal flows is addressed. High-quality field data of river and coastal flows have been selected and clustered into four particle size classes 60-100, 100-200, 200-400, and 400-600 m. The suspended sand transport is found to be strongly dependent on particle size and on current velocity. The suspended sand transport in the coastal zone is found to be strongly dependent on the relative wave height Hs/h, particularly for current velocities in the range 0.2-0.5 m/s. The time-averaged over the wave period advection-diffusion equation is applied to compute the time-averaged sand concentration profile for combined current and wave conditions. Flocculation, hindered settling, and stratification effects are included by fairly simple expressions. The bed-shear stress is based on a new bed roughness predictor. The reference concentration function has been recalibrated using laboratory and field data for combined steady and oscillatory flow. The computed transport rates show reasonably good agreement within a factor of 2 with measured values for velocities in the range of 0.6-1.8 m/s and sediments in the range of 60-600 m. The proposed method underpredicts in the low-velocity range 0.6 m/s. A new simplified transport formula is presented, which can be used to obtain a quick estimate of suspended transport. The modeling of wash load transport in river flow based on the energy concept of Bagnold shows that an extremely large amount of very fine sediment clay and very fine silt can be transported by the flow.

/pdf/unified-view-of-sediment-transport-by-currents-and-waves-ii-rvfxe5e5he.pdf

Unified View of Sediment Transport by Currents and Waves. II: Suspended Transport

Marine plastic debris floating on the ocean surface is a major environmental problem. However, its distribution in the ocean is poorly mapped, and most of the plastic waste estimated to have entered the ocean from land is unaccounted for. Better understanding of how plastic debris is transported from coastal and marine sources is crucial to quantify and close the global inventory of marine plastics, which in turn represents critical information for mitigation or policy strategies. At the same time, plastic is a unique tracer that provides an opportunity to learn more about the physics and dynamics of our ocean across multiple scales, from the Ekman convergence in basin-scale gyres to individual waves in the surfzone. In this review, we comprehensively discuss what is known about the different processes that govern the transport of floating marine plastic debris in both the open ocean and the coastal zones, based on the published literature and referring to insights from neighbouring fields such as oil spill dispersion, marine safety recovery, plankton connectivity, and others. We discuss how measurements of marine plastics (both in situ and in the laboratory), remote sensing, and numerical simulations can elucidate these processes and their interactions across spatio-temporal scales.

/pdf/the-physical-oceanography-of-the-transport-of-floating-32bmq1tv9q.pdf

The physical oceanography of the transport of floating marine debris

Concentrations in oscillatory sheet flow for well sorted and graded sands

Flow tunnel measurements of velocities and sand flux in oscillatory sheet flow for well-sorted and graded sands

The knowledge and modeling of wave-induced sand transport over rippled beds still has significant shortcomings, which is partly related to a lack of measurements of the detailed processes from controlled laboratory experiments. We have carried out new measurements of the detailed time-dependent velocity and suspended sand concentration field around vortex ripples for regular oscillatory flow conditions. The fact that the ripples were mobile and the flow conditions were full-scale makes these measurements unique. We made velocity measurements for 14 different flows and concentration measurements for three of these flows. The velocity and concentration field above ripples are dominated by the generation and ejection of vortices on the ripple flanks around the time of flow reversal. Vortex formation results in near-ripple flow reversals ahead of free-stream reversals and velocity maxima near the ripple crest that are much higher than the free-stream maxima. Asymmetry in the free stream produces steady circulation cells with dominant offshore mean flow up the ripple lee slope, balanced by weaker onshore streaming up the ripple stoss slope as well as higher up in the flow. The time- and bed-averaged horizontal velocity profile comprises an offshore streaming near the bed and an onshore drift higher up in the flow. The vortices are responsible for three main concentration peaks: one just after on-offshore flow reversal associated with the passage of a sand-laden vortex followed by two smaller peaks due to advected suspension clouds generated by vortex action at the neighboring onshore ripples. The sand flux field measured for one typical asymmetric flow condition is dominated by an offshore flux associated with the suspended sand cloud generated by vortex shedding from the ripple's lee slope around the time of on-offshore flow reversal. The net (time-averaged) current-related and wave-related horizontal sand fluxes are generally offshore directed and mostly contained within 1.5 ripple heights above the ripple crest. The wave-related suspended transport component is larger, but the contribution of the current-related suspended sand transport cannot be neglected. In addition to the measured offshore net transport of suspended sand, there is an onshore-directed transport very close to the ripple surface. The total net transport is in the offshore direction for this specific asymmetric flow condition.

/pdf/detailed-measurements-of-velocities-and-suspended-sand-5bs5m7ac19.pdf

Tom O'Donoghue

Papers

Concentrations in oscillatory sheet flow for well sorted and graded sands

Flow tunnel measurements of velocities and sand flux in oscillatory sheet flow for well-sorted and graded sands

Detailed measurements of velocities and suspended sand concentrations over full-scale ripples in regular oscillatory flow

Direct bed shear stress measurements in bore-driven swash

The dimensions of sand ripples in full-scale oscillatory flows