Radiation Stress Theory Research Articles

Study on Numerical Modeling for Pollutants Movement Based on the Wave Parabolic Mild Slope Equation in Curvilinear Coordinates

Nearshore waves and currents induced by breaking of obliquely incident waves are important dynamic factors that significantly affect pollutants movement at offshore zones. A combined numerical model in orthogonal curvilinear coordinates is developed to simulate pollutants movement in surf zones, including a wave transformation model based on the parabolic mild slope equation, a wave-induced current model, and a pollutant transport model driven by waves and currents. This combined model has been applied to pollutants movement laboratory cases, and comparison of the simulations with experimental measurements shows good agreement. The model has also been applied to simulation of the Gourlay experiment and it shows consistent results with the distribution of waves and offshore currents. This coupled numerical model has preliminarily improved the situation of rare numerical research on the nearshore pollutant transport in coastal wave and wave-induced current based on wave radiation stress theory in orthogonal curvilinear coordinates.

Mechanics of biconcave red blood cells deformed by acoustic tweezers

The deformation of biconcave red blood cells (RBCs) in a fluid environment driven by ultrasonic standing waves is studied theoretically and numerically. The cell contains homogeneous cytosol enclosed by a thin biological membrane. The cell membrane is modeled as a hyperelastic thin shell whose enclosed volume is assumed to be preserved to ensure osmotic equilibrium. Regarding acoustic deformation, the acoustic induced force acting on the cell membrane is calculated based on the acoustic radiation stress theory. The equations governing the interaction of the cell deformation and acoustic wave propagation are then numerically implemented in an axisymmetric finite element framework. The simulation results show that when the biconcave red blood cells are trapped at the pressure node of the acoustic standing wave, they gradually transform into an oblate disc shape with the increase of the acoustic input. Parametric studies are performed to systematically investigate the effects of cell mechanical properties and acoustic wavelength on cell deformation. Given that the mechanical properties of RBCs play an important role in disease development and mechanotransduction, this work is helpful to diagnose RBC-related diseases and study mechanotransduction using acoustic deformation technique.

Cavitation-induced damage model of soft materials in exposure to high-intensity focused ultrasound

High-intensity focused ultrasound can drive cavitation bubbles that damage soft materials. A cavitation-induced damage model is developed to study the mechanical damage of soft materials by high-intensity focused ultrasound. Based on the thermodynamics framework with the acoustic radiation stress theory and the nonlinear elasticity theory, an internal variable which reflects the mechanical damage caused by cavitation bubbles is incorporated into the Helmholtz free energy. Thus, the evolution of material damages for tissue-mimicking gel is established, which is related to the cavitation process and the mechanical dissipation from a macroscopic viewpoint. The theoretical model is then applied to analyze the material damaged area observed in the experiment and the theoretical prediction is found in agreement with the existing experimental results, which shows that the damage induced by cavitation bubbles develops rapidly, then slow down and finally reaches a plateau.

Implementation and comparison of the recent three-dimensional radiation stress theory and vortex-force formalism in an unstructured-grid coastal circulation model

Given the importance of wave–current interaction in estuarine and coastal dynamics, it is crucial to revisit impacts of surface gravity waves on three-dimensional (3D) nearshore circulation. This work investigates wave-induced circulation in three typical coastal systems including an idealized inlet and planar and natural barred beaches, by implementing the recent 3D radiation stress (RS) theory and vortex-force (VF) formalism to an unstructured-grid Finite-Volume Community Ocean Model (FVCOM). In the idealized inlet case, 3D RS generated appreciable currents near barriers and lateral boundaries while VF forced strong flows via breaking and roller-induced accelerations in front of the inlet. Both simulations indicate vertically varying wave-induced circulation that decreases markedly. In the planar beach with obliquely incident waves, both methods successfully produced surface onshore and bottom undertow, as well as the wave breaking and roller-induced longshore currents. Nevertheless, 3D RS generated unrealistic offshore currents close to the shoreline. The coupled models were validated against observations in the natural barred beach, and results indicate that the 3D RS model agrees slightly better with the observed longshore currents while 3D VF captures the vertical shear of the onshore–offshore flows reasonably. Further investigations suggest that both methods produce the wave breaking-induced surface onshore and bottom undertow successfully, yet they are located further offshore resulting from the 3D RS-induced unrealistic offshore currents. Successful implementations of the paired wave–current theories to the unstructured model would be fundamental and beneficial to the coastal ocean modeling community.

An Acoustomechanical Constitutive Model of Gel Considering Cavitation Effect in Exposure to Ultrasound

In this paper, an acoustomechanical constitutive model is developed to describe the heating effect of a tissue-mimicking gel by cavitation in exposure to high-intensity focused ultrasound (HIFU). An internal variable, representing the evolution of cavitation process, is introduced into the Helmholtz free energy under the framework of thermodynamics that combines the acoustic radiation stress theory and the nonlinear elasticity theory together. Thus, the internal variable is related to the cavitation process and the mechanical energy dissipation of a tissue-mimicking gel from a macroscopic viewpoint. Since the temperature rise of cavitation phenomenon is more remarkable than that of heating waves, the temperature inside the tissue-mimicking gel rises rapidly mainly due to large amounts of cavitation bubbles. This phenomenon can be quantitatively described by the present model, which fits the existing experimental data well.

Optomechanical soft metamaterials

We present a new type of optomechanical soft metamaterials, which is different from conventional mechanical metamaterials, in that they are simple isotropic and homogenous materials without resorting to any complex nano/microstructures. This metamaterial is unique in the sense that its responses to uniaxial forcing can be tailored by programmed laser inputs to manifest different nonlinear constitutive behaviors, such as monotonic, S-shape, plateau, and non-monotonic snapping performance. To demonstrate the novel metamaterial, a thin sheet of soft material impinged by two counterpropagating lasers along its thickness direction and stretched by an in-plane tensile mechanical force is considered. A theoretical model is formulated to characterize the resulting optomechanical behavior of the thin sheet by combining the nonlinear elasticity theory of soft materials and the optical radiation stress theory. The optical radiation stresses predicted by the proposed model are validated by simulations based on the method of finite elements. Programmed optomechanical behaviors are subsequently explored using the validated model under different initial sheet thicknesses and different optical inputs, and the first- and second-order tangential stiffness of the metamaterial are used to plot the phase diagram of its nonlinear constitutive behaviors. The proposed optomechanical soft metamaterial shows great potential in biological medicine, microfluidic manipulation, and other fields.

A nonlinear acoustomechanical field theory of polymeric gels

A nonlinear acoustomechanical field theory is presented for polymeric gels undergoing large deformation coupled with diffusion mass transport of solvent molecules in and out of the gel. The theory is developed by combining the acoustic radiation stress theory with the nonlinear elasticity theory of polymeric gels. Explicit velocity and acoustic fields are determined by solving the elastodynamical equations of wave propagation in Eulerian coordinates, which are then employed to determine the distribution of acoustic radiation stresses inside the gel. The nonlinear elasticity of gels is modeled by adopting the Flory–Rehner free energy functions for network stretching and molecules-polymer mixing. For illustration, the developed theory is applied to a layer of polymeric gel immersed in external solvent subjected to two counterpropagating acoustic waves. The acoustically actuated large deformation of the gel is analyzed under three different constraint conditions. Unique acoustomechanical behaviors of polymeric gels are revealed, such as periodical response and nonlinear chaos. This work is expected to enable novel design of ultrasound-triggered sensors and actuators made of polymeric gels, and can also enlighten the application of ultrasonic waves in biomedical engineering.

Acoustomechanical constitutive theory for soft materials

Acoustic wave propagation from surrounding medium into a soft material can generate acoustic radiation stress due to acoustic momentum transfer inside the medium and material, as well as at the interface between the two. To analyze acoustic-induced deformation of soft materials, we establish an acoustomechanical constitutive theory by combining the acoustic radiation stress theory and the nonlinear elasticity theory for soft materials. The acoustic radiation stress tensor is formulated by time averaging the momentum equation of particle motion, which is then introduced into the nonlinear elasticity constitutive relation to construct the acoustomechanical constitutive theory for soft materials. Considering a specified case of soft material sheet subjected to two counter-propagating acoustic waves, we demonstrate the nonlinear large deformation of the soft material and analyze the interaction between acoustic waves and material deformation under the conditions of total reflection, acoustic transparency, and acoustic mismatch.

On theories dealing with the interaction of surface waves and ocean circulation

ABSTRACTThe classic theory for the interaction of surface gravity waves and the general ocean circulation entails the so‐called wave radiation stress terms in the phase‐averaged momentum equation. The equations of motion are for the combined Eulerian current and Stokes drift. On the other hand, a more recent approach includes the so‐called vortex force term in the momentum equation wherein the only wave property is Stokes drift. The equations of motion are for the Eulerian current. The idea has gained traction in the ocean science community, a fact that motivates this paper. A question is: can both theories be correct? This paper answers the question in the negative and presents arguments in favor of the wave radiation theory. The vortex force approach stems from an interesting mathematical construct, but it does stand up to physical or mathematical scrutiny as described in this paper. Although not the primary focus of the paper, some discussion of Langmuir circulation is included since the vortex force was first introduced as the basis of this oceanic cellular phenomenon. Finaly the paper explains the difference in the derivation of the radiation stress theory and the vortex force theory: the later theory entails errors related to its use of curl and reverse‐curl [or uncurl] processes.

Wave Transformation and Wave-Driven Flow across a Steep Coral Reef

Abstract Observations of waves, setup, and wave-driven mean flows were made on a steep coral forereef and its associated lagoonal system on the north shore of Moorea, French Polynesia. Despite the steep and complex geometry of the forereef, and wave amplitudes that are nearly equal to the mean water depth, linear wave theory showed very good agreement with data. Measurements across the reef illustrate the importance of including both wave transport (owing to Stokes drift), as well as the Eulerian mean transport when computing the fluxes over the reef. Finally, the observed setup closely follows the theoretical relationship derived from classic radiation stress theory, although the two parameters that appear in the model—one reflecting wave breaking, the other the effective depth over the reef crest—must be chosen to match theory to data.

Coupling of surge and waves for an Ivan‐like hurricane impacting the Tampa Bay, Florida region

The interactions between waves and storm surge are investigated using an unstructured grid, coupled wave‐surge model forced by a hypothetical Ivan‐like hurricane impacting the Tampa Bay, Florida region. The waves derived from the unstructured version of the third‐generation wave model simulating waves nearshore. The surge derives from the unstructured Finite‐Volume Coastal Ocean Model, to which wave‐induced forces (based on radiation stress theory) are added to the traditional forces by winds and atmospheric pressure. Dependent upon complex bathymetry and geometry, the wave‐induced forces result in an additional 0.3∼0.5 m of surge relative to an uncoupled, surge‐only simulation, and the increase in coastal sea level by the storm surge adds some 1.0∼1.5 m to the significant wave heights nearshore. Such strong interactions through coupling suggest that waves should not be omitted in hurricane storm surge simulations, especially because the forces by waves on coastal structures are perhaps the most damaging of the hurricane related forces.

Long wave generation by the shoaling and breaking of transient wave groups on a beach

This paper presents new laboratory data on the generation of long waves by the shoaling and breaking of transient-focused short-wave groups. Direct offshore radiation of long waves from the breakpoint is shown experimentally for the first time. High spatial resolution enables identification of the relationship between the spatial gradients of the short-wave envelope and the long-wave surface. This relationship is consistent with radiation stress theory even well inside the surf zone and appears as a result of the strong nonlinear forcing associated with the transient group. In shallow water, the change in depth across the group leads to asymmetry in the forcing which generates significant dynamic setup in front of the group during shoaling. Strong amplification of the incident dynamic setup occurs after short-wave breaking. The data show the radiation of a transient long wave dominated by a pulse of positive elevation, preceded and followed by weaker trailing waves with negative elevation. The instantaneous cross-shore structure of the long wave shows the mechanics of the reflection process and the formation of a transient node in the inner surf zone. The wave run-up and relative amplitude of the radiated and incident long waves suggests significant modification of the incident bound wave in the inner surf zone and the dominance of long waves generated by the breaking process. It is proposed that these conditions occur when the primary short waves and bound wave are not shallow water waves at the breakpoint. A simple criterion is given to determine these conditions, which generally occur for the important case of storm waves.

Wave set-up on coral reefs. 1. Set-up and wave-generated flow on an idealised two dimensional horizontal reef

Wave set-up may be significant in determining water levels on coral reefs particularly in microtidal environments and hence is an important factor for the design of reef-top structures and for the stability of reef-top islands. Laboratory experiments have been made on a two dimensional model of an idealised horizontal reef under two different conditions corresponding to a fringing reef (or closed lagoon) situation and a platform reef (or open lagoon) situation. Both wave set-up on the reef-top and the wave-generated flow across the reef were measured and related to wave and tide level conditions. All other factors being the same, wave set-up is greatest at low tide levels whereas wave-generated flow is greater at higher tide levels. The magnitude of the set-up on a platform reef with a wave-generated flow is less than on a fringing reef without any net flow by an amount equal to the velocity head of the flow across the reef. Dimensionless parameters \\ ̄ gh r T√ η o and q √gH o 3 are found to be functions of relative submergence parameters h r H o or ( η r + h r) H o . For values of ( \\ ̄ gh r + h r ) H o > 1 waves break on the reef-top and radiation stress theory can be used to calculate set-up. For ( \\ ̄ gh r + h r ) H o < 0.7 waves break on the reef-face and set-up is determined by broadcrested weir control at the reef-edge. (The symbols are defined as follows: g is gravitational acceleration; h r is still water depth over horizontal reef-top; H o is offreef wave height (equivalent deep water value); q is discharge per unit length of reef edge; T is wave period and \\ ̄ gh r is maximum wave set-up on reef-top.)

Longshore Currents in Two Laboratory Studies: Relevance to Theory

Most post‐1970 theoretical studies of longshore current velocity extend the radiation stress theory of Longuet‐Higgins. Of the two larger sets of laboratory data (1949, 1963) available to test theories, Longuet‐Higgins used the 1963 data and considered but did not use the 1949 data. Most post‐1970 theories reverse these judgments and rely on the 1949 data. Such theories must be reevaluated. The 1949 data are 37 experiments, of which 22 were run on slopes steeper than all but the steepest natural foreshores; 12 of 37 published breaker angles exceed the generator angle; breaker depth‐to‐height ratios for the steep laboratory slopes were computed (not measured) using empirical curves from flat field slopes; and dimensionless velocities have a unique distribution. Breaker angle is the most sensitive variable determining longshore current velocity. Properly defined breaker angles require duplicate measurements along the test beach. The test velocity selected to compare with theory must account for the nonunifo...

The continuity equation for longshore current velocity with breaker angle adjusted for a wave-current interaction

The continuity equation for mean longshore current velocity, V = gmT sin 2 θ b, agrees with selected field and laboratory data covering a wide range of conditions. Agreement between continuity equation and data is improved by eliminating those laboratory data which imply deep-water wave crests at angles near or greater than 90 degrees to the shoreline. Agreement between continuity equation and data is further improved by adjusting breaker angles to account for convection of the breaker point by the longshore current. Breaker point convection increases breaker angle by an amount predictable from the analysis developed here. This increase in angle is significant in those laboratory experiments with breaking wave crests at high angles to the shoreline. In the continuity equation, m is bottom slope, T is wave period, and θ b is breaker angle, but breaker height does not appear. According to radiation stress theory, mean velocity does depend on breaker height, but only weakly. Consistency between the two approaches would require a dimensionless velocity, C b/ gT, to be relatively constant, which it is. (The same dimensionless velocity appears in the analyses of breaker point convection.) The continuity equation is functionally independent of friction and mixing, in keeping with its derivation from simple conservation of mass considerations. The equation has no adjustable coefficients. The degress of agreement with data and the internal consistency of the analysis suggests that it is a good predictor of mean velocity in ordinary longshore currents.

A NUMERICAL INVESTIGATION OF THE LONGSHORE CURRENT PROFILE FOR MULTIPLE BAR/TROUGH BEACHES

A numerical model is developed which calculates the longshore current profile for an arbitrary bottom profile. The basis of the model is the use of radiation stress theory in a longshore momentum balance equation which includes a driving stress, a bottom stress, and a lateral mixing stress. Each of the stresses is derived from previously developed formulations, rederiving them to take into account separate cross shore variations in the wave height and the water depth, as well as the wave approach angle. This is done to dispense with the constant wave breaking index assumption used to model wave decay in the surf zone, which is rejected as unrealistic for natural beaches. A numerical model is used to calculate distributions of the wave height and water depth across the surf zone for arbitrary, yet realistic, bottom profiles. A numerical model of the theoretically derived longshore momentum balance equation is developed and solved using the distributions obtained from the wave decay model. The profiles calculated are compared to previous theoretical models and to laboratory and field measurements.