Abstract

Using an idealized channel representative of a coastal plain estuary, we conducted numerical simulations to investigate the generation of internal lee waves by lateral circulation. It is shown that the lee waves can be generated across all salinity regimes in an estuary. Since the lateral currents are usually subcritical with respect to the lowest mode, mode-2 lee waves are most prevalent but a hydraulic jump may develop during the transition to subcritical flows in the deep channel, producing high energy dissipation and strong mixing. Unlike flows over a sill, stratified water in the deep channel may become stagnant such that a mode-1 depression wave can form higher up in the water column. With the lee wave Froude number above 1 and the intrinsic wave frequency between the inertial and buoyancy frequency, the lee waves generated in coastal plain estuaries are nonlinear waves with the wave amplitude Δh scaling approximately with $V/\overline{N}$ , where V is the maximum lateral flow velocity and $\overline{N}$ is the buoyancy frequency. The model results are summarized using the estuarine classification diagram based on the freshwater Froude number Fr _f and the mixing parameter M. The Δh decreases with increasing Fr _f as stronger stratification suppresses waves, and no internal waves are generated at large Fr _f . The Δh initially increases with increasing M as the lateral flows become stronger with stronger tidal currents, but decreases or saturates to a certain amplitude as M further increases. This modeling study suggests that lee waves can be generated over a wide range of estuarine conditions.

Abstract

The ratio of the buoyancy force driving thermal convection to the surface wave vortex-force driving Langmuir circulation in the Craik–Leibovich mechanism involves the Hoenikker number Ho. The critical value Ho _c , at which wave forcing and thermal convection contribute equally to the circulation, is found to increase with decreasing Langmuir number La and approaches 3 in the small La limit. For a typical wind speed and surface cooling, Ho is of order O(10⁻²) to O(10⁻¹). Thus, wave forcing dominates over thermal convection in driving Langmuir circulation.

Stratification induced by strong surface heating suppresses the circulation generated by wave forcing and could completely inhibit the CL instability. In the physically plausible range of −0.1 < Ho < 0, however, this does not happen for small La and the dynamical effect of heating is very small.

For a given heat flux, the temperature difference between the regions of surface divergence and convergence in Langmuir circulation depends on Ho, Pr, and La and on the depth distribution of the heating, but is typically 0(10⁻²) K.

Abstract

A commonly observed property of near-surface bubble distributions is their collective organization into long rows aligned with the wind under the influence of Langmuir circulation. Time series observations with sonars having fixed orientation reveal the temporal evolution of bubble distributions as they drift through the sonar measurement path, Here this concept is extended to provide a time sequence, at 37-s intervals, of two-dimensional images generated by horizontally rotating sonars. Observations obtained during a storm in the Strait of Georgia show individual Langmuir convergence zones as they evolve above the freely drifting sonar. The resulting images are processed to generate a binary representation of the convergence zone patterns from which their orientation, length, spacing, and other properties can be extracted. Although there is some angular spreading, most convergence lines are aligned within 20° of the wind. The spacing between convergence lines reveals a wide range of scales, but the mean spacing increases slightly with wind speed. Measurement of downwind length reveals the presence of numerous short bubble clouds, possibly associated directly with wave breaking; however, there is a general trend toward a length that increases with wind speed.

A dominant characteristic at higher wind speeds is the formation of Y junctions in which three linear bubble clouds are joined together. Each branch of a Y junction was observed to be approximately 50 m. The junctions preferentially point downwind with the angle between the two side branches being approximately 30°. Although the junctions deform with time, they can be readily tracked through successive images The existence of convergence zone junctions suggests the reconnection of counterrotating longitudinal vortices and the formation of U-shaped vortex tubes.

Abstract

The interaction between wind-driven Langmuir circulation and preexisting stratification is examined in order to elucidate its role in the deepening of the ocean surface mixed layer. For linear stratification, a numerical model suggests that Langmuir cells initially engulf water and create a homogeneous surface layer. The depth h̃ of this layer can be understood in terms of a Froude number Fr = w̃ _dn /( Nh̃), where w̃ _dn is the maximum downwelling velocity generated by Langmuir circulation in homogeneous water and N is the buoyancy frequency. Numerical results show that Fr is a constant ≈ 0.6. Using computed values of w̃ _dn , this implies that the rapid mixed layer deepening stops at h̃ = cu _*/N in which u _* is the water friction velocity and the coefficient c is about 10 for fully developed seas. Alternatively, the deepening is arrested when the buoyancy jump Δb at the mixed layer base reaches about 50u ² _*/h̃ . The above formula, compared with the Price, Weller, and Pinkel value of 0.65 for the bulk Richardson number R _b associated with shear mixing, suggests that engulfment by Langmuir circulation dominates mixed layer deepening if the velocity difference |Δũ| across the base of the mixed layer is less than about 0.01U _w , where U _w is the wind speed. The buoyancy jump criterion is tested for two-layer stratification profiles and found to be a robust formula suitable for incorporation into one-dimensional mixed layer models.

The possibility of further mixed layer deepening through shear instability is studied by examining the distribution of the gradient Richardson number Ri _g , particularly in a transition region beneath the mixed layer. It has great variability across wind, reaching minimum values beneath downwelling jets, but can fall below 0.25, indicating the onset of shear instability. Thus, Langmuir cells may facilitate shear instability in a horizontally confined region beneath downwelling jets, although further study will require allowance for a different background shear.

Abstract

Recent mooring observations at a cross-channel section in Chesapeake Bay showed that internal solitary waves regularly appeared during certain phases of a tidal cycle and propagated from the deep channel to the shallow shoal. It was hypothesized that these waves resulted from the nonlinear steepening of internal lee waves generated by lateral currents over channel-shoal topography. In this study numerical modeling is conducted to investigate the interaction between lateral circulation and cross-channel topography and discern the generation mechanism of the internal lee waves. During ebb tides, lateral bottom Ekman forcing drives a counterclockwise (looking into estuary) lateral circulation, with strong currents advecting stratified water over the western flank of the deep channel and producing large isopycnal displacements. When the lateral flow becomes supercritical with respect to mode-2 internal waves, a mode-2 internal lee wave is generated on the flank of the deep channel and subsequently propagates onto the western shoal. When the bottom lateral flow becomes near-critical or supercritical with respect to mode-1 internal waves, the lee wave evolves into an internal hydraulic jump. On the shallow shoal, the lee waves or jumps evolve into internal bores of elevation.

Abstract

A parameterization of the absorption in the 15 μm CO₂ spectral region has been developed based upon the wing scaling approximation of Chou and Arking (1980, 1981). The spectrum is divided into a band-wing region and a band-center region, and the CO₂ amount in an inhomogeneous atmosphere is scaled separately for the two regions. The spectrally averaged transmittance over each region is then expressed as a simple function of the scaled amount of CO₂. Compared to fine-by-line calculations, the error of the parameterization is <0.025 in the transmittance and <0.04°C day⁻¹ in the tropospheric and lower stratospheric cooling rates. The cooling rate error in the upper stratosphere is generally ten than a few tenths of a degree per day except for the region above the 3 mb level where the error is too large to be acceptable for some studies on the phenomena in that region.

The effect of the parameterization of absorption due to CO₂ on climate studies has been investigated with the Multi-Layer Energy Balance Model (MLEBM) developed at GLAS (Peng et al, 1982). It is found that, compared to the accurate perturbation method, the parameterization introduces very small differences in the model temperatures and radiation budgets for both the normal and doubled CO₂ concentrations. In addition, we have investigated the effect of including the CO₂ absorption in the margins of the 15 μm spectral band on the CO₂ climate sensitivity. It is found that the surface temperature sensitivity is enhanced by 20% for a doubled CO₂ concentration and by 30% for a quadrupled CO₂ concentration when the spectral range of CO₂ absorption is extended from 580–760 to 540–800 cm⁻¹.

Abstract

Since the 1950s, a countergradient flux term has been added to some K-profile-based first-order PBL schemes, allowing them to simulate the slightly statically stable upper part of the convective boundary layer (CBL) observed in a limited number of aircraft soundings. There is, however, substantial uncertainty in inferring detailed CBL structure, particularly the level of neutral stability (z _n ), from such a limited number of soundings. In this study, composite profiles of potential temperature are derived from multiyear early afternoon radiosonde data over Beijing, China. The CBLs become slightly stable above z _n ~ 0.31–0.33z _i , where z _i is the CBL depth. These composite profiles are used to evaluate two K-profile PBL schemes, the Yonsei University (YSU) and Shin–Hong (SH) schemes, and to optimize the latter through parameter calibration. In one-dimensional simulations using the WRF Model, YSU simulates a stable CBL above z _n ~ 0.24z _i , while default SH simulates a thick superadiabatic lower CBL with z _n ~ 0.45z _i . Experiments with the analytic solution of a K-profile PBL model show that adjusting the countergradient flux profile leads to significant changes in the thermal structure of CBL, informing the calibration of SH. The SH scheme replaces the countergradient heat flux term in its predecessor YSU scheme with a three-layer nonlocal heating profile, with f _nl specifying the peak value and $z_{*\mathrm{SL}}$ specifying the height of this peak value. Increasing f _nl to 1.1 lowers z _n , but to too low a value, while simultaneously increasing $z_{*\mathrm{SL}}$ to 0.4 leads to a more appropriate z _n ~ 0.36z _i . The calibrated SH scheme performs better than YSU and default SH for real CBLs.

Abstract

An enhanced version of the hybrid ensemble–three-dimensional variational data assimilation (3DVAR) system for the Weather Research and Forecasting Model (WRF) is applied to the assimilation of radial velocity (Vr) data from two coastal Weather Surveillance Radar-1988 Doppler (WSR-88D) radars for the prediction of Hurricane Ike (2008) before and during its landfall. In this hybrid system, flow-dependent ensemble covariance is incorporated into the variational cost function using the extended control variable method. The analysis ensemble is generated by updating each forecast ensemble member with perturbed radar observations using the hybrid scheme itself. The Vr data are assimilated every 30 min for 3 h immediately after Ike entered the coverage of the two coastal radars.

The hybrid method produces positive temperature increments indicating a warming of the inner core throughout the depth of the hurricane. In contrast, the 3DVAR produces much weaker and smoother increments with negative values at the vortex center at lower levels. Wind forecasts from the hybrid analyses fit the observed radial velocity better than that from 3DVAR, and the 3-h accumulated precipitation forecasts from the hybrid are also more skillful. The track forecast is slightly improved by the hybrid method and slightly degraded by the 3DVAR compared to the forecast from the Global Forecast System (GFS) analysis. All experiments assimilating the radar data show much improved intensity analyses and forecasts compared to the experiment without assimilating radar data. The better forecast of the hybrid indicates that the hybrid method produces dynamically more consistent state estimations. Little benefit of including the tuned static component of background error covariance in the hybrid is found.

Abstract

A formula for the maximum size of a bubble for which surface tension forces can prevent bubble breakup by inertial forces, combined with the observed sizes of air bubbles in breaking waves, implies an energy dissipation rate. One dataset from the surf zone gives a dissipation rate of the order of 0.1 W kg⁻¹, but the large number of small bubbles, and the bubble size spectrum generally, are puzzling. A simple dimensional cascade argument suggests that injected air beneath a breaking wave is rapidly broken up by turbulence, producing an initial size spectrum proportional to (radius)^−10/3 before modification by dissolution and rising under buoyancy. This spectral slope is comparable with data from the surf zone. The cascade argument does, however, predict that for a constant dissipation rate there is a rapid accumulation of a large number of bubbles at the scale at which surface tension prevents further breakup; it is possible that the observed size spectrum reflects the range of turbulent energy dissipation rates rather than the result of a cascade. If so, an estimate of about 40 W kg⁻¹ is obtained for the dissipation rate implied by the surf zone dataset. Once an initial size spectrum is formed by the rapid action of differential pressure forces, it will evolve subject to dissolution and buoyancy. It is shown that the former will tend to flatten the size spectrum at small scales, whereas the latter will tend to steepen the time-averaged spectrum observed at large scales. The slope change and transition radius predicted by a very simple model are in reasonable agreement with observations.

Abstract

Stratification and turbulent mixing exhibit a flood–ebb tidal asymmetry in estuaries and continental shelf regions affected by horizontal density gradients. The authors use a large-eddy simulation (LES) model to investigate the penetration of a tidally driven bottom boundary layer into stratified water in the presence of a horizontal density gradient. Turbulence in the bottom boundary layer is driven by bottom stress during flood tides, with low-gradient (Ri) and flux (R_f ) Richardson numbers, but by localized shear during ebb tides, with Ri = ¼ and R_f = 0.2 in the upper half of the boundary layer. If the water column is unstratified initially, the LES model reproduces periodic stratification associated with tidal straining. The model results show that the energetics criterion based on the competition between tidal straining and tidal stirring provides a good prediction for the onset of periodic stratification, but the tidally averaged horizontal Richardson number Ri _x has a threshold value of about 0.2, which is lower than the 3 suggested in a recent study. Although the tidal straining leads to negative buoyancy flux on flood tides, the authors find that for typical values of the horizontal density gradient and tidal currents in estuaries and shelf regions, buoyancy production is much smaller than shear production in generating turbulent kinetic energy.