### Fluid Physics - (Greg Chini, Joe Klewicki, John McHugh, Chris White and Martin Wosnik)

The University of New Hampshire's Center for Fluid Physics (CFP) is a collaborative cross-disciplinary group of fluid dynamics researchers at UNH. The research represented by CFP researchers includes: analytical, modeling and experimental studies of atmospheric and oceanic waves and circulation processes, magnetohydrodynamic flows and plasma physics, turbulent mixing and combustion processes, the physics, measurement and scaling of turbulent wall-flows, vorticity dynamics, the behaviors and properties of non-Newtonian, biological and/or opaque fluids, and the development and application of the analytical experimental and numerical techniques required to explore complex fluid flows.

The overarching philosophy of the CFP is that the best approach to applications associated with complex fluid dynamical problems is through fundamental understanding of the underlying processes. Over the long term, this engineering science/physics based approach is believed to provide the optimal basis from which practical engineering design and prediction methodologies may devised and reliably implemented.

### Fluid Dynamics

#### Group Members

Prof. Gregory Chini, Mechanical Engineering

Prof. John McHugh, Mechanical Engineering

#### Affiliated Members

Prof. Russell Carr, Chemical Engineering

Prof. Kelly Black, Applied Mathematics

Prof. John Geddes, Applied Mathematics

Prof. Jamie Pringle, Physical Oceanography

#### Overview

Fluid dynamics is a subject that impacts nearly every aspect of life. Humans work and play in a fluid environment - the atmosphere, the oceans, lakes and rivers. The performance of countless devices and natural systems depends sensitively upon fluid phenomena. Consider just a few examples:

Transportation systems (cars, ships, aircraft and space vehicles)

Weather and climate (atmospheric and oceanic flows)

Pollutant dispersion, porous-media flow, oil-spill recovery, and other environmental technologies

Energy conversion devices (internal combustion engines, wind turbines)

Physiological systems (respiratory, cardiovascular, and renal flows)

Acoustic systems (noise generation/diminution, hearing)

Waves (surface, internal, capillary) and fluid-structure interactions

Casual observation of cloud patterns, surface waves, and raindrops indicates that fluids can exhibit very complex behavior. Physically, this is related to the fact that fluids (unlike solids) are capable of continuous deformation; mathematically, the complex dynamics result from nonlinearities in the equations governing fluid flow. Thus, sophisticated approaches are required to analyze the majority of flow problems. Generally, the approaches are categorized as theoretical, computational, or experimental. The fluid dynamics group at UNH conducts research, provides graduate-level training, and performs consulting in all three areas.

### Funding Available for M.S./Ph.D. Students and Post-Doctoral Researchers

Funding is available for well-qualified students seeking an M.S. or Ph.D. degree with a specialty in Fluid Dynamics. The funding usually takes the form of a teaching assistantship, research assistantship, or tuition scholarship. Teaching and research assistants receive a tuition waiver and a stipend. (A tuition scholarship covers only the cost of tuition. Non-standard arrangements are sometimes made for special cases.) Frequently, funding is also available for post-doctoral researchers. Note that financial assistance is not awarded to prospective graduate students until all application materials for graduate admission have been received by the Department. Ideal candidates will possess an aptitude for applied mathematics and a background in mechanics. Students will be expected to complete graduate coursework in Fluid Dynamics, Applied Mathematics, Physics, and Numerical Analysis. Knowledge in these areas provides a firm foundation for investigation of a wide range of research problems, many of which are interdisciplinary in character (e.g. bio-fluids modeling), extending beyond the traditional boundaries defining Mechanical Engineering. All interested students are strongly encouraged to contact Professors G. Chini, J. McHugh, or D. Watt directly.

#### Requirements for the Master's Degree

The coursework required for a Master's Degree in Mechanical Engineering, with specialization in Theoretical or Computational Fluid Dynamics, is shown in the table below:

- Applied Mathematics PHYSICS 931 and 932
- Intermediate Fluid Dynamics ME 807
- Numerical Methods MATH 853 or equivalent (not ME 886 or ME 809)
- Lagrangian Dynamics PHYSICS 939

After completion of these required courses, three electives should be chosen from the following list:

- Gas Dynamics ME 808
- Computational Fluid Dynamics ME 809
- Waves in Fluids ME 895
- Viscous Flow ME 909
- Turbulence ME 910
- Hydrodynamic Stability ME 911
- Convection ME 906
- Asymptotic Methods ME 995
- Continuum Mechanics ME 922
- Elasticity ME 926
- Numerical Methods MATH 854

In addition to the above courseware, a Master's thesis must be completed, in accord with the rules and regulations of the Graduate School.

#### Requirements for the Ph.D. Degree

In addition to satisfying the M.S. courseware requirements, Ph.D. candidates specializing in Theoretical or Computational Fluid Dynamics normally complete approximately 24 credits of additional coursework. Each doctoral candidate also completes a dissertation describing original research (in accord with the rules and regulations of the Graduate School).

#### Fluid Dynamics Research Projects

**I. PHYSICAL OCEANOGRAPHY (G. Chini)**

The fluid dynamics of the upper ocean involves a complex mosaic of surface and internal waves, coherent vortex motions, and turbulence, and encompasses spatial scales from centimeters to kilometers and time scales from seconds to weeks. Mechanical (i.e. wind and wave) and thermal forcing at the sea surface generates turbulent motions which homogenize the properties of the upper 50--100 meters of the ocean. The atmosphere and deep ocean communicate via heat, mass, and momentum exchanges across this well-mixed layer; thus, the dynamics of this region play a pivotal role in weather and climate. For example, the response of the upper ocean to a small number of storms appears to determine much of the annual air--sea exchange of heat. The fluid dynamics of the upper ocean also controls the dispersion of pollutants (e.g. crude oil) introduced at the sea surface and the distribution and proliferation of biota. Langmuir circulation and internal wave propagation are two oceanographic processes which are of particular interest to fluid dynamicists at UNH. Both are studied using a combination of applied mathematical techniques, including analytical (e.g. asymptotic) and computational (e.g. spectral) methods.

Langmuir circulation is a wind and surface-wave driven vortex motion which commonly occurs in the upper layers of lakes and oceans. The counter-rotating Langmuir vortices (or 'cells') have their axes roughly aligned in the wind direction and range in scale from a few meters to several hundred meters. Observational and theoretical evidence indicates that the largest in the hierarchy of Langmuir cells (LC's) fill the near-surface mixed layer in which they reside and have an aspect ratio slightly greater than one (i.e. they are slightly flattened). These large-scale LC's may be viewed as the most energetic `coherent structures' amidst the background of incoherent smaller-scale turbulence in the upper ocean. As such, LC's dominate the transport of heat, mass, and momentum throughout the mixed layer and, thus, are a fundamental feature of mixed-layer dynamics.

Just as surface waves travel along the air--sea interface, internal waves (IW's) propagate within the interior of fluids (including the oceans and atmosphere) whose density increases with depth. Unlike surface waves, however, internal waves are not constrained to propagate along a horizontal interface. IW dynamics are important for a variety of reasons connected with mixing and energy (and momentum) transport. While upper-ocean mixing is achieved directly by surface-driven turbulence in that region, mixing within the interior of the ocean is largely the result of IW degradation. The mixed layer communicates with the abyss across a region of rapid density variation known as the pycno- or thermocline. Since mixed-layer forcing (by LC's, for example) of the pycnocline constitutes an important source of downward propagating IW's, enhanced understanding of the occurrence of interior mixing requires improved prediction of the dynamics of the upper ocean.

Current efforts involve a combination of theoretical analysis and numerical simulation to explore the prospect for LC--IW interactions. Such coupling would be significant for several reasons. For example, energy transfer from LC's to IW's may limit the growth of the mixed layer (since IW's radiate energy away from the upper ocean), but provide a means for enhanced interior mixing (accomplished by breaking IW's). Conversely, energy transfer from IW's to LC's may provide a novel mechanism for maintenance of the mixed-layer, since the presence of LC's counters the natural tendency of a sharp density interface to `smooth out' due to diffusion. Results of these investigations will be compared with open-ocean data obtained by observational oceanographer D. Farmer (University of Rhode Island).

**II. ATMOSPHERIC FLOWS (J. McHugh)**

The atmosphere of Earth (and other planets) is stratified, which means that the density changes with elevation. This aspect of the atmosphere has a predominant effect on the motion of the air. The stratification allows waves to form in the atmosphere, analogous to waves on the surface of the ocean. The waves propagate and even `break,' often resulting in severe patches of turbulence. Larger scale phenomena, such as fronts and thunderstorms, generate the waves, and also lead to turbulence directly. Turbulence is important to many activities, for example air traffic, astronomy, and weather prediction.

Much of the research in this area is currently aimed at elucidating the mechanisms which cause atmospheric waves. Simple models of mesoscale atmospheric flows, such as thunderstorms, are being studied mathematically to attempt to understand the source of the waves. Part of this work is computational; the computational requirements are so severe that the work must generally be performed on a variety of supercomputers around the country. Current theoretical efforts are focusing on the wavy flow generated by a vortex pair in a Boussinesq fluid, and the stability of bound internal waves in flow through a wavy walled channel, as well as other problems.

**III. PHYSIOLOGICAL FLUID DYNAMICS (G. Chini)**

The peripheral airways of the lung are small, wet, and highly deformable. The liquid lining protects the lung from inhaled toxins or pathogens and, because the air-liquid interface is both extensive and highly curved, surface tension forces play an important role in the mechanics of respiration. For these reasons, it is of interest to understand the fundamental mechanisms by which substrate geometry, substrate elasticity, and (surfactant-regulated) surface tension control the distribution of the lung's liquid lining.

Current research is aimed at developing a hierarchy of mathematical models capable of addressing this fundamental question. The fact that the liquid lining is thin (except in `puddle' regions) permits the fluid-mechanical model to be greatly simplified. However, the problem is complicated by the fact that the dynamics of the thin liquid lining are coupled to those of the elastic substrate. The stability of the combined fluid--elastic system is also of great interest (to pulmonary physicians, for example). We investigate the behavior of the models using both analytical and computational techniques. Collaborations with clinicians and experimentalists (who employ, e.g., Magnetic Resonance Imaging and lasers to probe flows in the lung) are being planned.

**IV. SYMMETRY BREAKING MOTION (J. McHugh)**

Fluid flows that are being forced in a symmetric manner often respond with an asymmetric motion, e.g., a horizontal cylinder filled with a liquid and subjected to a linear temperature gradient at infinity (Quarterly of Applied Math, v LVII, pp 425-436). The buoyancy forcing is symmetric about the vertical centerline of the cylinder. The symmetry of the forcing and the geometry implies that the motion of the fluid could be symmetric, at least for small values of the Rayleigh number. Linear stability studies show that indeed the most unstable modes are symmetric, implying that a symmetric disturbance would grow faster than an asymmetric disturbance, finally dominating the motion. However, all experiments of the problem have shown only asymmetric motion (actually antisymmetric for this case), in conflict with the linear stability result.

Another example is the symmetric driven cavity problem. The traditional driven cavity is an often used model for verifying computer programs. The driving force for the traditional problem has a uniform sense across the top of the cavity. The symmetric driven cavity has a sinusoidal variation in the force, such that the force is antisymmetric, and would appear to drive two symmetric vortices. Recent results show however that there is a second asymmetric steady solution. The system may choose either the symmetric or asymmetric solution. The numerical results indicate that the choice depends on the initial conditions, and the system exhibits a symmetry breaking subcritical bifurcation.

**V. STABILITY OF FLOWS OVER COMPLIANT COATINGS (J. McHugh)**

A variety of industrial problems involve flow near a compliant coating. For example, printing presses employ a number of rollers to transport fluids. Some of the rollers are coated with neoprene, such that contact between any pair of rollers only occurs with one steel roller and one neoprene coated steel roller. The flow between these two rollers can exhibit a variety of complicated behaviors at high speed. This problem is being studied with a hierarchy of models of increasing complexity. The initial model is a two-fluid layer flow between a rigid wall and an elastic layer. A more sophisticated model, one which includes the curvature of the boundary, is flow between concentric rotating cylinders with an elastic layer on the outside cylinder. The results assuming axisymmetric disturbances show that the compliant layer has no significant effect.

Current work is focusing on relaxing the assumption of axisymmetric disturbances and demonstrating that the surface modes present in other compliant models are present in concentric cylinders.

**VI. THERMOACOUSTICS (J. McHugh)
VII. FREE SURFACE FLOWS (J. McHugh and G. Chini)**