ALBERT

Description: This open access book allows the reader to grasp the main bulk of fluid flow problems at a brisk pace. Starting with the basic concepts of conservation laws developed using continuum mechanics, the incompressibility of a fluid is explained and modeled, leading to the famous Navier-Stokes equation that governs the dynamics of fluids. Some exact solutions for transient and steady-state cases in Cartesian and axisymmetric coordinates are proposed. A particular set of examples is associated with creeping or Stokes flows, where viscosity is the dominant physical phenomenon. Irrotational flows are treated by introducing complex variables. The use of the conformal mapping and the Joukowski transformation allows the treatment of the flow around an airfoil. The boundary layer theory corrects the earlier approach with the Prandtl equations, their solution for the case of a flat plate, and the von Karman integral equation. The instability of fluid flows is studied for parallel flows using the Orr-Sommerfeld equation. The stability of a circular Couette flow is also described. The book ends with the modeling of turbulence by the Reynolds-averaged Navier-Stokes equations and large-eddy simulations. Each chapter includes useful practice problems and their solutions. The book is useful for engineers, physicists, and scientists interested in the fascinating field of fluid mechanics.

Description: Submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy at the Massachusetts Institute of Technology and the Woods Hole Oceanographic Institution February 2003

Description: Oceanic observations indicate that abyssal mixing is localized in regions of rough topography. How locally mixed fluid interacts with the ambient fluid is an open question. Laboratory experiments explore the interaction of mechanically induced boundary mixing and an interior body of linearly stratified rotating fluid. A single oscillating bar produces a small region of turbulence along the wall at middepth. Mixed fluid quickly reaches a steady state height set by a turbulent-buoyant balance, independent of rotation. Initially, the bar is exposed on three sides. Mixed fluid intrudes directly into the interior rather than forming a boundary current. The circulation patterns suggest a model of unmixed fluid being laterally entrained into the turbulent zone. In accord with the model, observed outflux is constant, independent of stratification and restricted by rotation. Later the bar is laterally confines between two walls, which form a channel opening into the basin. A small percentage of mixed fluid enters a boundary current, which exits the channel. The bulk forms a cyclonic circulation in front of the bar, which blocks the channel and restricts horizontal entrainment. In the confined case, the volume flux of mixed fluid decays with time.

Description: This work was supported by the Ocean Ventures Fund, the Westcott Fund and the WHOI Education Office. Financial support was also provided by the National Science Foundation through grant OCE-9616949.

Description: Submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy at the Massachusetts Institute of Technology and the Woods Hole Oceanographic Institution September 2000

Description: This thesis investigates the physical mechanisms of air-water gas transfer through direct measurements of turbulence at the air--water interface. To enable this study, a new approach to the particle image velocimetry (PIV) technique is developed in order to quantify free-surface flows. Two aspects of this work are innovative. First, the use of a three-dimensional laser light cone and optical filtering of the camera allow for the motion of fluorescent flow tracers at the water surface to be isolated and measured. Validation experiments indicate that this measurement reflects the fluid motion within the upper few hundred microns. A key benefit to this approach is the ability to deal with deforming surfaces, provided the amplitudes are not prohibitively large. This feature was used in this thesis to explore the surface flow induced by mechanically generated waves. Second, a new hybrid PIV image processing algorithm was developed that provides high accuracy velocity estimation with improved computational efficiency. This algorithm combines the concepts of dynamic Fourier-domain cross-correlation with a localized direct multiplicative correlation. In order to explore relationships between free-surface hydrodynamics and air-water gas transfer, an oscillating grid-stirred tank was constructed. By its design, this tank can be managed for chemical cleanliness, offers an unobstructed free surface, and is suited for turbulent mixing and air--water gas-exchange studies. A series of acoustic Doppler velocimeter, PIV, and infrared imaging experiments are presented that characterize the flow for the grid forcing conditions studied. Results indicate that the flows are stationary and reasonably repeatable. In addition, the flows exhibit near-isotropic turbulence and are quasi-homogeneous in horizontal planes. Secondary circulations are revealed and investigated. Finally, PIV measurements of free-surface turbulence are performed with concurrent measurements of gas transfer in the grid tank for a range of turbulent mixing and surface conditions. Surface turbulence, vorticity, and divergence are all affected by the presence of a surface film, with significant effects realized for relatively small surface pressures. Results show that while a relationship between surface turbulence and the gas-transfer velocity is an obvious improvement over that found using an estimate of the bulk flow turbulence, this relationship is dependent on the flow regime. This is revealed through additional surface wave studies. However, the data from both the wave experiments and the grid turbulence experiments can be reconciled by a single relationship between the gas-transfer velocity and the 1/2-power of the surface divergence, which agrees with previous conceptual models. These results (1) further our understanding of interfacial transport processes, (2) demonstrate the important role of surface divergence in air-water gas exchange, and (3) relate, in a physically meaningful way, the interactions between surface renewal, surfactants, and gas transfer.

Description: I was supported as an Office of Naval Research Graduate Fellow. This assistance was the impetus for my pursuit of a doctoral degree and is gratefully acknowledged. Very special thanks also to the WHOI Ocean Ventures Fund Program, Mr. F. Thomas Westcott, and the WHOI Education Department for generous financial support over the past several years.

Description: Submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy at the Massachusetts Institute of Technology and the Woods Hole Oceanographic Institution September 1996

Description: This thesis addresses the question of how a highly energetic eddy field could be generated in the interior of the ocean away from the swift boundary currents. The energy radiation due to the temporal growth of non-trapped (radiating) disturbances in such a boundary current is thought to be one of the main sources for the described variability. The problem of stability of an energetic current, such as the Gulf Stream, is formulated. The study then focuses on the ability of the current to support radiating instabilities capable of significant penetration into the far-field and their development with time. The conventional model of the Gulf Stream as a zonal current is extended to allow the jet axis to make an angle to a latitude circle. The linear stability of such a nonzonal flow, uniform in the along-jet direction on a beta-plane, is first studied. The stability computations are performed for piece-wise constant and continuous velocity profiles. New stability properties of nonzonal jets are discussed. In particular, the destabilizing effect of the meridional tilt of the jet axis is demonstrated. The radiating properties of nonzonal currents are found to be very different from those of zonal currents. In particular, purely zonal flows do not support radiating instabilities, whereas flows with a meridional component are capable of radiating long and slowly growing waves. The nonlinear terms are then included in the consideration and the effects of the nonlinear interactions on the radiating properties of the solution are studied in detail. For these purposes, the efficient numerical code for solving equation for the QG potential vorticity with open boundary conditions of Orlanski's type is constructed. The results show that even fast growing linear solutions, which are trapped during the linear stage of developement, can radiate energy in the nonlinear regime if the basic current is nonzonal. The radiation starts as soon as the initial fast exponential growth significantly slows. The initial trapping of those solutions is caused by their fast temporal growth. The new mechanism for radiation is related to the nonzonality of a current.

Description: This work was supported by NSF Grant OCE 9301845.

Description: Author Posting. © American Meteorological Society, 2015. This article is posted here by permission of American Meteorological Society for personal use, not for redistribution. The definitive version was published in Journal of Physical Oceanography 45 (2015): 2006–2024, doi:10.1175/JPO-D-14-0234.1.

Description: The effects of wind-driven whitecapping on the evolution of the ocean surface boundary layer are examined using an idealized one-dimensional Reynolds-averaged Navier–Stokes numerical model. Whitecapping is parameterized as a flux of turbulent kinetic energy through the sea surface and through an adjustment of the turbulent length scale. Simulations begin with a two-layer configuration and use a wind that ramps to a steady stress. This study finds that the boundary layer begins to thicken sooner in simulations with whitecapping than without because whitecapping introduces energy to the base of the boundary layer sooner than shear production does. Even in the presence of whitecapping, shear production becomes important for several hours, but then inertial oscillations cause shear production and whitecapping to alternate as the dominant energy sources for mixing. Details of these results are sensitive to initial and forcing conditions, particularly to the turbulent length scale imposed by breaking waves and the transfer velocity of energy from waves to turbulence. After 1–2 days of steady wind, the boundary layer in whitecapping simulations has thickened more than the boundary layer in simulations without whitecapping by about 10%–50%, depending on the forcing and initial conditions.

Description: We thank Skidmore College for financial and infrastructure support, and Skidmore and the National Science Foundation for funding travel to meetings where early versions of this work were presented. We also thank the National Science Foundation, Oregon State University, Jonathan Nash, and Joe Jurisa for funding and hosting a workshop on River Plume Mixing in October, 2013, where ideas and context for this paper were developed.

Description: 2016-02-01

Description: Author Posting. © American Meteorological Society, 2018. This article is posted here by permission of American Meteorological Society for personal use, not for redistribution. The definitive version was published in Journal of Physical Oceanography 48 (2018): 1555-1566, doi:10.1175/JPO-D-17-0231.1.

Description: A primary challenge in modeling flow over shallow coral reefs is accurately characterizing the bottom drag. Previous studies over continental shelves and sandy beaches suggest surface gravity waves should enhance the drag on the circulation over coral reefs. The influence of surface gravity waves on drag over four platform reefs in the Red Sea is examined using observations from 6-month deployments of current and pressure sensors burst sampling at 1Hz for 4–5min. Depth-average current fluctuations U0 within each burst are dominated by wave orbital velocities uw that account for 80%–90%of the burst variance and have a magnitude of order 10 cm s21, similar to the lower-frequency depth-average current Uavg. Previous studies have shown that the cross-reef bottom stress balances the pressure gradient over these reefs. A bottom stress estimate that neglects the waves (rCdaUavgjUavgj, where r is water density and Cda is a drag coefficient) balances the observed pressure gradient when uw is smaller than Uavg but underestimates the pressure gradient when uw is larger than Uavg (by a factor of 3–5 when uw 5 2Uavg), indicating the neglected waves enhance the bottom stress. In contrast, a bottom stress estimate that includes the waves [rCda(Uavg 1 U0)jUavg 1 U0j)] balances the observed pressure gradient independent of the relative size of uw and Uavg, indicating that this estimate accounts for the wave enhancement of the bottom stress. A parameterization proposed by Wright and Thompson provides a reasonable estimate of the total bottom stress (including the waves) given the burst-averaged current and the wave orbital velocity.

Description: The Red Sea field program was supported by Awards USA 00002 and KSA 00011 made by KAUST. S. Lentz was supported for the analysis by NSF Award OCE-1558343.

Description: 2019-01-13

Description: Submitted in partial fulfillment of the requirements for the degree of Doctor of Science at the Massachusetts Institute of Technology and the Woods Hole Oceanographic Institution August, 1977

Description: Stimulated by new evidence from both "in situ" oceanic observations and results from numerical modelling, a laboratory study of quasigeostrophic flow and turbulence in a rotating homogeneous fluid has been undertaken. Two dimensional turbulence driven by a uniform distribution of sources and sinks which oscillate in time, can be fairly well reproduced in this context. Inertial time scales are about ten times smaller than Ekman spinup time, and typical Reynolds numbers read 2000. The observations emphasize the spectral tendency of the energy containing eddies. The case of no topography is first discussed. In steadily forced turbulence, it is observed that the energy containing scale is significantly larger than the forcing scale. In the decaying stage the red cascade is observed and rates of interaction are measured. Theoretical arguments for both behaviors are presented; the former concerning the forced turbulence case is believed to be new. The forcing is next applied over various large scale topographies, modelling the geophysical beta effect. The polar beta plane geometry preserves the above spectral characteristics but at the same time introduces anisotropy into the flow pattern. A broad westward mean flow develops in the north and is surrounded by a belt of cyclones lying on its southward side. The calculated second-order Eulerian mean flows induced by steadily and uniformly forced Rossby waves in a long zonal channel, exhibit much of the same momentum distribution in the inertial regime. In contrast, the "sliced cylinder" geometry which possesses no closed geostrophic contours drastically modifies the above picture. Both mean flow production and a large scale tendency for the eddies are inhibited. The geographical distribution of the eddy intensities and scales is now wildly inhomogeneous. The second aspect of this work is a study of the interaction of Rossby waves with mean flows. A zonally traveling, forced wave is generated near the southern boundary of a polar beta plane. Due to energy radiation in the free interior and (or) potential vorticity mixing by the finite amplitude waves, a westward zonal flow develops. The effect of the mean flow upon the forced steady waves is to weaken the anticyclones and intensify the cyclones. Pressure time series reveal a growth of harmonics and general spectral broadening as the waves travel freely inwards, suggesting active nonlinear interactions. An experimental test of Rhines' (1977) potential vorticity mixing theory is also presented at free latitudes. The decay period when the driving is suppressed shows that a net transfer from the waves to the mean flow kinetic energy occurs. Connection with hydrodynamic stability theory is discussed. Interaction of Rossby waves with an externally generated westward mean flow allows one to make a controlled study of the critical layer problem. For small amplitude waves, the mean flow is accelerated in the entire region between the forcing and the critical latitude which acts as a wall for mean wave momentum. In nonlinear runs the steady profile of the westward flow indicates that an accelerating force is acting everywhere, revealing the increasing transmission of wave momentum through the critical layer. At the same time, pressure measurements near the critical point show considerable fine structure developing over a long time scale. The third part deals with steady isolated source-sink flows in the sliced cylinder geometry. The response of the fluid to a meridionally oriented steady dipole extends exclusively westward of the forcing. The viscously balanced solutions are discussed and relevance to oceanic abyssal circulation is emphasized. With strong driving, the combination of a cyclone to the north and an anticyclone to the south is absolutely stable although the reverse configuration is not. A connection with a certain class of free, steady, isolated, inertial solutions developed recently by Stern (1976) is made.

Description: The DGRST . (FRACE) and the Joint Program in Oceanography, Massachusetts Institute of Technology and the Woods Hole Oceanographic Institution offered a fellowship for the first two years. The National Science Foundation under Grant OCE75-2l 674 and the Office of Naval Research under Contract N00014-74-C0262-NR-083-004 supported this study for the final two years.

Description: Submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy at the Massachusetts Institute of Technology and the Woods Hole Oceanographic Institution January 1977

Description: Millimeter scale fluctuations in refractive index recorded with a freely sinking shadowgraph system are correlated with finestructure profiles of temperature, salinity and density and compared to models of ocean turbulence. Images with vertically aligned periodic structure, called bands, are identified as salt fingers, while others with chaotic structure are turbulent. Images are found on interfaces that are 1-10m thick and have gradients at least several times the mean. From 6 profiles in the Mediterranean Outflow region of the eastern North Atlantic between 1.0 and 1.9 km depth, 398 interfaces have been identified and a significant fraction (about 1/3) of these have detectable images. High contrast images, including bands, are most often found below warm, saline intrusions and within stepped structure where there is a regular sequence of homogeneous mixed layers separated by interfaces. As the interfacial salinity gradient increases in the sense that allows salt finger convection, the fraction of interfaces with images increases. The horizontal spacing of bands (~5 mm) is consistent with calculated salt finger diameter. The calculated and observed length of ocean salt fingers (10-20 cm) is a small fraction of the interface thickness. High levels of small scale variability in the shadowgraphs is reflected in high levels of variance in the finestructure band of the temperature spectra. The temperature gradient spectra have a slope of -1, indicative of turbulence affected by buoyancy forces, and there is a relative peak at a wavelength near the observed salt finger length. The high contrast images are found at interfaces within the enhanced mean salinity gradient below saline intrusions. For very strong salinity gradients there is a solitary interface with intense images, but for weaker mean gradients the convection takes the form of stepped structure. The steps may evolve from the solitary interface as the salinity gradient is run down by salt finger convection. This study identifies parts of the ocean where salt finger convection is prevalent and includes the first comprehensive description of salt fingers in the ocean. Existing models of salt fingers are evaluated in light of ocean observations, and models of ocean turbulence are compared to measurements.

Description: Support from ONR contract N00014-66-C0241 NR. 083-004 is also acknowledged.

Description: Author Posting. © American Meteorological Society, 2009. This article is posted here by permission of American Meteorological Society for personal use, not for redistribution. The definitive version was published in Journal of Physical Oceanography 39 (2009): 1077–1096, doi:10.1175/2008JPO4044.1.

Description: Observations of turbulent kinetic energy (TKE) dynamics in the ocean surface boundary layer are presented here and compared with results from previous observational, numerical, and analytic studies. As in previous studies, the dissipation rate of TKE is found to be higher in the wavy ocean surface boundary layer than it would be in a flow past a rigid boundary with similar stress and buoyancy forcing. Estimates of the terms in the turbulent kinetic energy equation indicate that, unlike in a flow past a rigid boundary, the dissipation rates cannot be balanced by local production terms, suggesting that the transport of TKE is important in the ocean surface boundary layer. A simple analytic model containing parameterizations of production, dissipation, and transport reproduces key features of the vertical profile of TKE, including enhancement near the surface. The effective turbulent diffusion coefficient for heat is larger than would be expected in a rigid-boundary boundary layer. This diffusion coefficient is predicted reasonably well by a model that contains the effects of shear production, buoyancy forcing, and transport of TKE (thought to be related to wave breaking). Neglect of buoyancy forcing or wave breaking in the parameterization results in poor predictions of turbulent diffusivity. Langmuir turbulence was detected concurrently with a fraction of the turbulence quantities reported here, but these times did not stand out as having significant differences from observations when Langmuir turbulence was not detected.

Description: The Office of Naval Research funded this work as a part of CBLAST-Low.

Description: Author Posting. © American Meteorological Society, 2007. This article is posted here by permission of American Meteorological Society for personal use, not for redistribution. The definitive version was published in Journal of Physical Oceanography 37 (2007): 1764-1777, doi:10.1175/jpo3098.1.

Description: The vertical structure of the dissipation of turbulence kinetic energy was observed in the nearshore region (3.2-m mean water depth) with a tripod of three acoustic Doppler current meters off a sandy ocean beach. Surface and bottom boundary layer dissipation scaling concepts overlap in this region. No depth-limited wave breaking occurred at the tripod, but wind-induced whitecapping wave breaking did occur. Dissipation is maximum near the surface and minimum at middepth, with a secondary maximum near the bed. The observed dissipation does not follow a surfzone scaling, nor does it follow a “log layer” surface or bottom boundary layer scaling. At the upper two current meters, dissipation follows a modified deep-water breaking-wave scaling. Vertical shear in the mean currents is negligible and shear production magnitude is much less than dissipation, implying that the vertical diffusion of turbulence is important. The increased near-bed secondary dissipation maximum results from a decrease in the turbulent length scale.

Description: Funding was provided by NSF and ONR.