We present an overview of the lattice Boltzmann method (LBM), a parallel and efficient algorithm for simulating single-phase and multiphase fluid flows and for incorporating additional physical complexities. The LBM is especially useful for modeling complicated boundary conditions and multiphase interfaces. Recent extensions of this method are described, including simulations of fluid turbulence, suspension flows, and reaction diffusion systems.

Lattice boltzmann method for fluid flows

A fast-Fourier-transform method of topography and interferometry is proposed. By computer processing of a noncontour type of fringe pattern, automatic discrimination is achieved between elevation and depression of the object or wave-front form, which has not been possible by the fringe-contour-generation techniques. The method has advantages over moire topography and conventional fringe-contour interferometry in both accuracy and sensitivity. Unlike fringe-scanning techniques, the method is easy to apply because it uses no moving components.

Fourier-transform method of fringe-pattern analysis for computer-based topography and interferometry

A primary focus of coastal science during the past 3 decades has been the question: How does anthropogenic nutrient enrichment cause change in the structure or function of nearshore coastal ecosystems? This theme of environmental science is recent, so our conceptual model of the coastal eutrophication problem continues to change rapidly In this review, I suggest that the early (Phase I) con- ceptual model was strongly influenced by limnologists, who began intense study of lake eutrophication by the 1960s The Phase I model emphasized changing nutrient input as a signal, and responses to that signal as increased phytoplankton biomass and primary production, decomposition of phytoplankton- derived organic matter, and enhanced depletion of oxygen from bottom waters Coastal research in recent decades has identified key differences in the responses of lakes and coastal-estuarine ecosystems to nutrient enrichment The contemporary (Phase II) conceptual model reflects those differences and includes explicit recognition of (1) system-specific attributes that act as a filter to modulate the responses to enrichment (leading to large differences among estuarine-coastal systems in their sensitivity to nu- trient enrichment); and (2) a complex suite of direct and indirect responses including linked changes in: water transparency, distribution of vascular plants and biomass of macroalgae, sediment biogeochem- istry and nutrient cycling, nutrient ratios and their regulation of phytoplankton community composition, frequency of toxic/harmful algal blooms, habitat quality for metazoans, reproduction/growth/survival of pelagic and benthic invertebrates, and subtle changes such as shifts in the seasonality of ecosystem functions Each aspect of the Phase II model is illustrated here with examples from coastal ecosystems around the world In the last section of this review I present one vision of the next (Phase III) stage in the evolution of our conceptual model, organized around 5 questions that will guide coastal science in the early 21st century: (1) How do system-specific attributes constrain or amplify the responses of coastal ecosystems to nutrient enrichment? (2) How does nutrient enrichment interact with other stressors (toxic contaminants, fishing harvest, aquaculture, nonindigenous species, habitat loss, climate change, hydro- logic manipulations) to change coastal ecosystems? (3) How are responses to multiple stressors linked? (4) How does human-induced change in the coastal zone impact the Earth system as habitat for humanity and other species? (5) How can a deeper scientific understanding of the coastal eutrophication problem be applied to develop tools for building strategies at ecosystem restoration or rehabilitation?

https://www.int-res.com/articles/meps/210/m210p223.pdf

Our evolving conceptual model of the coastal eutrophication problem

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

Communities of microscopic plant life, or phytoplankton, dominate the Earth's aquatic ecosystems. This important new book by Colin Reynolds covers the adaptations, physiology and population dynamics of phytoplankton communities in lakes and rivers and oceans. It provides basic information on composition, morphology and physiology of the main phyletic groups represented in marine and freshwater systems and in addition reviews recent advances in community ecology, developing an appreciation of assembly processes, co-existence and competition, disturbance and diversity. Although focussed on one group of organisms, the book develops many concepts relevant to ecology in the broadest sense, and as such will appeal to graduate students and researchers in ecology, limnology and oceanography.

/pdf/the-ecology-of-phytoplankton-4ev70n3jsq.pdf

The Ecology of Phytoplankton

The dynamic subgrid‐scale eddy viscosity model of Germano et al. [Phys. Fluids A 3, 1760 (1991)] (DSM) is modified by employing the mixed model of Bardina et al. [Ph.D dissertation, Stanford University (1983)] as the base model. The new dynamic mixed model explicitly calculates the modified Leonard term and only models the cross term and the SGS Reynolds stress. It retains the favorable features of DSM and, at the same time, does not require that the principal axes of the stress tensor be aligned with those of the strain rate tensor. The model coefficient is computed using local flow variables. The new model is incorporated in a finite‐volume solution method and large‐eddy simulations of flows in a lid‐driven cavity at Reynolds numbers of 3200, 7500, and 10 000 show excellent agreement with the experimental data. Better agreement is achieved by using the new model compared to the DSM. The magnitude of the dynamically computed model coefficient of the new model is significantly smaller than that from DSM.

A dynamic mixed subgrid‐scale model and its application to turbulent recirculating flows

A non-staggered grid, fractional step method for time-dependent incompressible Navier-Stokes equations in curvilinear coordinates

We examine observations of turbulence in the geophysical environment, primarily from oceans but also from lakes, in light of theory and experimental studies undertaken in the laboratory and with numerical simulation. Our focus is on turbulence in density-stratified environments and on the irreversible fluxes of tracers that actively contribute to the density field. Our understanding to date has come from focusing on physical problems characterized by high Reynolds number flows with no spatial or temporal variability, and we examine the applicability of these results to the natural or geophysical-scale problems. We conclude that our sampling and interpretation of the results remain a first-order issue, and despite decades of ship-based observations we do not begin to approach a reliable sampling of the overall turbulent structure of the ocean interior.

Density Stratification, Turbulence, but How Much Mixing?

Laboratory experiments on stably stratified grid turbulence have suggested that turbulent diffusivity , suggesting that such Reynolds–Richardson number or Reynolds–Froude number aggregates are more descriptive of stratified turbulent flow conditions than the conventional reliance on Richardson number alone.

Jeffrey R. Koseff

Papers

A dynamic mixed subgrid‐scale model and its application to turbulent recirculating flows

A non-staggered grid, fractional step method for time-dependent incompressible Navier-Stokes equations in curvilinear coordinates

Density Stratification, Turbulence, but How Much Mixing?

Parameterization of turbulent fluxes and scales using homogeneous sheared stably stratified turbulence simulations

The Lid-Driven Cavity Flow: A Synthesis of Qualitative and Quantitative Observations