Drag produced by trapped lee waves and propagating mountain waves in a two-layer atmosphere

The surface drag force produced by trapped lee waves and upward propagating waves in non-hydrostatic stratified flow over a mountain ridge is explicitly calculated using linear theory for a two-layer atmosphere with piecewise-constant static stability and wind speed profiles. The behaviour of the drag normalized by its hydrostatic single-layer reference value is investigated as a function of the ratio of the Scorer parameters in the two layers l_2/l_1 and of the corresponding dimensionless interface height l_1 H, for selected values of the dimensionless ridge width l_1 a and ratio of wind speeds in the two layers. When l_2/l_1 → 1, the propagating wave drag approaches 1 in approximately hydrostatic conditions, and the trapped lee wave drag vanishes. As l_2/l_1 decreases, the propagating wave drag progressively displays an oscillatory behaviour with l_1 H, with maxima of increasing magnitude due to constructive interference of reflected waves in the lower layer. The trapped lee wave drag shows localized maxima associated with each resonant trapped lee wave mode, occurring for small l_2/l_1 and slightly higher values of l_1 H than the propagating wave drag maxima. As l1a decreases, i.e. the flow becomes more non-hydrostatic, the propagating wave drag decreases and the regions of non-zero trapped lee wave drag extend to higher l_2/l_1. These results are confirmed by numerical simulations for l_2/l_1 = 0.2. In parameter ranges of meteorological relevance, the trapped lee wave drag may have a magnitude comparable to that of propagating wave drag, and be larger than the reference single-layer drag. This may have implications for drag parametrization in global climate and weather-prediction models.

The credit relationship between Henry III and merchants of Douai and Ypres, 1247-70

This article looks at an important but neglected aspect of medieval sovereign debt, namely ‘accounts payable’ owed by the Crown to merchants and employees. It focuses on the unusually well-documented relationship between Henry III, King of England between 1216 and 1272, and Flemish merchants from the towns of Douai and Ypres, who provided cloth on credit to the royal wardrobe. From the surviving royal documents, we reconstruct the credit advanced to the royal wardrobe by the merchants of Ypres and Douai for each year between 1247 and 1270, together with the king's repayment history. The interactions between the king and the merchants are then analysed. The insights from this analysis are applied to the historical data to explain the trading decisions made by the merchants during this period, as well as why the strategies of the Yprois sometimes differed from those of the Douaissiens.

Orographic drag associated with lee waves trapped at an inversion

The drag produced by 2D orographic gravity waves trapped at a temperature inversion and waves propagating in the stably stratified layer existing above are explicitly calculated using linear theory, for a two-layer atmosphere with neutral static stability near the surface, mimicking a well-mixed boundary layer. For realistic values of the flow parameters, trapped lee wave drag, which is given by a closed analytical expression, is comparable to propagating wave drag, especially in moderately to strongly non-hydrostatic conditions. In resonant flow, both drag components substantially exceed the single-layer hydrostatic drag estimate used in most parametrization schemes. Both drag components are optimally amplified for a relatively low-level inversion and Froude numbers Fr ≈ 1. While propagating wave drag is maximized for approximately hydrostatic flow, trapped lee wave drag is maximized for l_2 a = O(1) (where l_2 is the Scorer parameter in the stable layer and a is the mountain width). This roughly happens when the horizontal scale of trapped lee waves matches that of the mountain slope. The drag behavior as a function of Fr for l_2 H = 0.5 (where H is the inversion height) and different values of l2a shows good agreement with numerical simulations. Regions of parameter space with high trapped lee wave drag correlate reasonably well with those where lee wave rotors were found to occur in previous nonlinear numerical simulations including frictional effects. This suggests that trapped lee wave drag, besides giving a relevant contribution to low-level drag exerted on the atmosphere, may also be useful to diagnose lee rotor formation.

Impact of non-hydrostatic effects and trapped lee waves on mountain wave drag in directionally sheared flow

The orographic gravity wave drag produced in flow over an axisymmetric mountain when both vertical wind shear and non-hydrostatic effects are important was calculated using a semi-analytical two-layer linear model, including unidirectional or directional constant wind shear in a layer near the surface, above which the wind is constant. The drag behaviour is determined by partial wave reflection at the shear discontinuity, wave absorption at critical levels (both of which exist in hydrostatic flow), and total wave reflection at levels where the waves become evanescent (an intrinsically non-hydrostatic effect), which produces resonant trapped lee wave modes. As a result of constructive or destructive wave interference, the drag oscillates with the thickness of the constant-shear layer and the Richardson number within it (Ri), generally decreasing at low Ri and when the flow is strongly non-hydrostatic. Critical level absorption, which increases with the angle spanned by the wind velocity in the constant-shear layer, shields the surface from reflected waves, keeping the drag closer to its hydrostatic limit. While, for the parameter range considered here, the drag seldom exceeds this limit, a substantial drag fraction may be produced by trapped lee waves, particularly when the flow is strongly non-hydrostatic, the lower layer is thick and Ri is relatively high. In directionally sheared flows with Ri = O(1), the drag may be misaligned with the surface wind in a direction opposite to the shear, a behaviour which is totally due to non-trapped waves. The trapped lee wave drag, whose reaction force on the atmosphere is felt at low levels, may therefore have a distinctly different direction from the drag associated with vertically propagating waves, which acts on the atmosphere at higher levels.

Reticent autobiography: Henry Green and Christopher Isherwood at the Hogarth Press

Christopher Isherwood’s Lions and Shadows (1938) and Henry Green’s Pack My Bag (1940) are accounts of the authors’ educations in the 1920s. Published by Leonard and Virginia Woolf’s Hogarth Press, these works use reticent narrators to test the limits of autobiography. In each case, authorial self-presentation complicates the work’s classification in the literary marketplace: Green paradoxically extends his use of a pseudonym to autobiography and Isherwood assigns his own name to his purportedly fictional protagonist, and yet Hogarth published both as novels. The two texts and their publication histories exemplify modernist autobiography’s blurring of the lines between fiction and personal history.

Delivery of crop pollination services is an insufficient argument for wild pollinator conservation

There is compelling evidence that more diverse ecosystems deliver greater benefits to people, and these ecosystem services have become a key argument for biodiversity conservation. However, it is unclear how much biodiversity is needed to deliver ecosystem services in a cost-effective way. Here we show that, while the contribution of wild bees to crop production is significant, service delivery is restricted to a limited subset of all known bee species. Across crops, years and biogeographical regions, crop-visiting wild bee communities are dominated by a small number of common species, and threatened species are rarely observed on crops. Dominant crop pollinators persist under agricultural expansion and many are easily enhanced by simple conservation measures, suggesting that cost-effective management strategies to promote crop pollination should target a different set of species than management strategies to promote threatened bees. Conserving the biological diversity of bees therefore requires more than just ecosystem-service-based arguments.

Parliamentary sovereignty, popular sovereignty, and Henry Parker's adjudicative standpoint

Discussions of popular sovereignty in early modern England have usually been premised upon a sharp distinction between ‘legal/constitutional’ forms of discourse (which merely interpret the law) and ‘political’ ones (which focus upon the right to make it). In such readings of the period, Henry Parker has a pivotal position as a writer who abandoned merely legalistic thinking. This chapter takes a different view. It argues that Parker’s major intellectual achievement was not so much to abandon legal/constitutional discourse as to offer a theorisation of its most distinctive features: he offered an account of a new kind of politics in which concern for ‘interests’ in property and in self-preservation replaced humanist concern with promotion of virtue. Parker drew upon ideas about representation best expressed by Sir Thomas Smith and ideas about law best expressed by Oliver St John. The theory he developed was not intended as a justification of legislative sovereignty, but of adjudicative supremacy. His picture of the two Houses as supreme adjudicators was meant to block the path to direct democracy. But the adjudicative standpoint they came to occupy presupposed that freeborn adults had ‘interests’ in life, liberty, and possessions. This had democratising implications.