Modeling the ship white water wake in the midwave infrared.

We have modeled the white water wake of a ship as a single layer of bubbles packed on the sea surface within the perimeter of the trailing turbulent wake. The size of the bubbles is considered greater than the midwave infrared wavelengths such that the optical geometrical approximation remains valid. The upper half bubble hemisphere is meshed into facets, and we calculate the probability density function of their slopes and constrain that distribution by the geometrical limits imposed by the position of the receiver through the shadowing of facets by other bubbles and of facets that are facing away from the receiver. For the facets that are visible, we compute the midwave infrared emitted and reflected radiance for the white water wake for atmospheric, solar, and sea conditions that prevailed during a ship wake measurement trial using a homegrown simulation code, the Sea Surface Radiance Simulator. The range of slopes that are visible to the receiver for the white water wake greatly exceeds those that are present in the turbulent wake and in the sea background. Consequently, the variability in the white water wake radiance is substantial. As a function of the downstream distance astern of the ship, we have ad hoc assumed that the white water wake fraction decays linearly or proportionally to the turbulent intensity in the wake. Comparing to measurements, we find an agreement in trend behavior of the midwave radiance contrast of the white water wake with downstream distance for a white water wake fraction that decays proportionally to the square of the turbulence intensity.

Modeling the turbulent trailing ship wake in the infrared.

The sea surface turbulent trailing wake of a ship, which can be rather easily observed in the infrared by airborne surveillance systems, is a consequence of the difference in roughness and temperature between the wake and the sea background. We have developed a phenomenological model for the infrared radiance of the turbulent wake by assuming that the sea surface roughness is dependent upon the turbulent intensity near the sea surface. Describing the sea surface roughness with a Cox and Munk probability distribution function of slopes, we distinguish on the sea surface between the sea background and the turbulent wake by the variance of sea surface slopes, σCM2=constant and σTW2(x,y)≠constant. The latter dependence is assumed to be inversely proportional to the turbulent intensity of the wake, Urms(x,y). Given the incident solar, atmospheric, and sky infrared radiances, we calculate the reflected and emitted sea surface radiance from both the wake and the background. We compare the infrared contrast of the wake with infrared image data obtained in an airborne trial. Our predictions and the measurements agree very well in trend over a significant range of observer zenith angles. Our calculations reveal the strong dependence of the wake radiance on the observer zenith angle, allowing for positive and negative contrasts with the background.

Direct numerical simulation of supercritical annular electroconvection.

We use direct numerical simulation to study electrically driven convection in an annular thin film. The simulation models a laboratory experiment that consists of a weakly conducting, submicron thick liquid crystal film suspended between two concentric electrodes. The film is driven to convect by imposing a sufficiently large voltage across it. The flow is driven by a surface charge density inversion which is unstable to the imposed electrical force. This mechanism is closely analogous to the mass density inversion which is unstable to the buoyancy force in conventional, thermally driven Rayleigh-Bénard convection. The simulation uses a pseudospectral method with Chebyshev polynomials in the radial direction and Fourier modes in the azimuthal direction. The numerical results, which are in good agreement with previous experimental data and theoretical predictions, reveal several insights. The mode competition near a codimension-two point exhibits hysteresis. The primary bifurcation is supercritical for a broad range of fluid and geometrical parameters.

Charge transport scaling in turbulent electroconvection.

We describe a local-power-law scaling theory for the mean dimensionless electric current Nu in turbulent electroconvection. The experimental system consists of a weakly conducting, submicron-thick liquid-crystal film supported in the annulus between concentric circular electrodes. It is driven into electroconvection by an applied voltage between its inner and outer edges. At sufficiently large voltage differences, the flow is unsteady and electric charge is turbulently transported between the electrodes. Our theoretical development, which closely parallels the Grossmann-Lohse model for turbulent thermal convection, predicts the local-power law Nu approximately F(gamma)R(gamma)P(delta). R and P are dimensionless numbers that are similar to the Rayleigh and Prandtl numbers of thermal convection, respectively. The dimensionless function F(gamma), which is specified by the model, describes the dependence of Nu on the aspect ratio gamma. We find that measurements of Nu are consistent with the theoretical model.

Codimension-two points in annular electroconvection as a function of aspect ratio.

We rigorously derive from first principles the generic Landau amplitude equation that describes the primary bifurcation in electrically driven convection. Our model accurately represents the experimental system: a weakly conducting, submicron thick liquid crystal film suspended between concentric circular electrodes and driven by an applied voltage between its inner and outer edges. We explicitly calculate the coefficient g of the leading cubic nonlinearity and systematically study its dependence on the system's geometrical and material parameters. The radius ratio alpha quantifies the film's geometry while a dimensionless number P , similar to the Prandtl number, fixes the ratio of the fluid's electrical and viscous relaxation times. Our calculations show that for fixed alpha, g is a decreasing function of P , as P becomes smaller, and is nearly constant for P> or =1 . As P-->0, g-->infinity. We find that g is a nontrivial and discontinuous function of alpha. We show that the discontinuities occur at codimension-two points that are accessed by varying alpha.

Aspect-ratio dependence of charge transport in turbulent electroconvection.

We present measurements of the normalized charge transport or Nusselt number Nu as a function of the aspect ratio Gamma for turbulent convection in an electrically driven film. In analogy with turbulent Rayleigh-Bénard convection, we develop the relevant theoretical framework in which we discuss the local power-law scaling of Nu with a dimensionless electrical forcing parameter R. For these experiments where 10(4) less, similar R less, similar 2 x 10(5) we find that Nu approximately F(Gamma)Rgamma with either gamma=0.26 (+/-0.02) or gamma=0.20 (+/-0.03), in excellent agreement with the theoretical predictions of gamma=1/4 and 1/5. Our measurements of the aspect-ratio dependence of Nu for 0.3

Sequential bifurcations in sheared annular electroconvection.

A sequence of bifurcations is studied in a one-dimensional pattern forming system subject to the variation of two experimental control parameters: a dimensionless electrical forcing number R and a shear Reynolds number Re. The pattern is an azimuthally periodic array of traveling vortices with integer mode number m. Varying R and Re permits the passage through several codimension-two (CoD2) points. We find that the coefficients of the nonlinear terms in a generic Landau equation for the primary bifurcation are discontinuous at the CoD2 points. Further, we map the stability boundaries in the space of the two parameters by studying the subcritical secondary bifurcations in which m-->m+1 when R is increased at constant Re.